CONTROL STRATEGIES FOR A MINIMALLY ACTUATED MEDICAL EXOSKELETON FOR INDIVIDUALS WITH PARALYSIS JASON IRA REID

Transcription

1 CONTROL STRATEGIES FOR A MINIMALLY ACTUATED MEDICAL EXOSKELETON FOR INDIVIDUALS WITH PARALYSIS BY JASON IRA REID A DISSERTATION SUBMITTED IN PARTIAL SATISFACTION OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN ENGINEERING MECHANICAL ENGINEERING IN THE GRADUATE DIVISION OF THE UNIVERSITY OF CALIFORNIA, BERKELEY COMMITTEE IN CHARGE: PROFESSOR HOMAYOON KAZEROONI, CHAIR PROFESSOR KAMESHWAR POOLLA PROFESSOR NANCY VAN HOUSE FALL 01

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3 ABSTRACT Control Strategies for a Minimally Actuated Medical Exoskeleton for Individuals with Paralysis By Jason Ira Reid Doctor of Philosophy in Engineering Mechanical Engineering University of California, Berkeley Professor Homayoon Kazerooni, Chair Over 65,000 individuals in the United States have a spinal cord injury [1]. The wheelchair is currently the most prescribed mobility option for this population. Robotic exoskeleton devices are a promising alternative means of mobility that enable a paraplegic user to regain the physical and emotional health benefits of standing and walking. This dissertation will discuss novel gait strategies that were designed for a minimally actuated medical exoskeleton device. Two novel stance control strategies will be presented that are designed to propel the exoskeleton and pilot forward out of double stance. The first stance strategy relies on the movement of the pilot's torso as a means to dynamically propel the system forward through a step. Second, a more advanced strategy that propels the user forward while stabilizing their torso will also be proposed. Through the manipulation of lower extremity kinematics, the user can be propelled forward out of double stance with an exoskeleton that only has actuation at the hips. Sequential methods of trajectory generation will be described for both strategies. Experimental results will be presented that support the efficacy for these stance strategies. In addition, this dissertation proposes an original sequential swing phase model. This model is used to produce a gait trajectory for the swing leg that dynamically controls an unactuated swing knee. A method for swing phase hip trajectory generation will be presented. Experimental results will be shown that validate the efficacy of the swing phase trajectory at producing a natural human like swing phase from a swing leg that has no actuation at the knee. 1

4 Extensive pilot testing of the medical exoskeleton in both structured and unstructured environments was completed. The results from these tests support the efficacy of the control algorithms and show great promise in the minimally actuated exoskeleton paradigm. This work enables a reduction in exoskeleton hardware complexity, reduced weight, and anticipated lower costs for end users so that more spinal cord injury patients may have greater access to this technology.

5 TABLE OF CONTENTS Abstract... 1 List of Figures... vi Acknowledgements... ix 1 Introduction Motivation Major Contributions Outline of this Dissertation... Background Introduction to Spinal Cord Injury Introduction to Walking Biomechanics Standards The Walking Cycle Clinical Gait Analysis (CGA) Prior Art Exoskeleton Assistive Devices for Able Bodied People Rehabilitative Exoskeleton Devices Mobile Medical Exoskeleton Devices Berkeley Medical Exoskeletons: Primer Austin Exoskeleton Passive Knee Exoskeleton Contributions to Exoskeleton Development Microcontroller Architecture Control Software Architecture Human Machine Interface (HMI) HMI Hardware Human Centered Control Design Motor Dynamics Human Pilot Considerations Parallel Bars... 1 i

6 4.. Walker Crutches The Control Problem Exoskeleton Stance Control Three Solutions that Enable a Minimally Actuated Double Stance to Double Stance Transition Exoskeleton Swing Leg Control Torso Controlled Propulsion Sequential Development of the Torso Controlled Propulsive (TCP) Gait Propulsive Phase The Propulsive Human Exoskeleton System Model Inertial Coupling PFL Propulsive Controller Design Propulsive Phase Simulation Results Generating and Simulating the Complete TCP Gait Ballistic Single Stance Full Walker Results with TCP Gait Pilot Testing of TCP Gait User Feedback on the TCP Gait Evolution of the TCP Gait Passive Knee Exoskeleton Testing Results Stance Control Conclusions Swing Phase Control with Passive Knees The Sequence of the Swing Phase The Swing Leg Model Pendular Phase Knee Re extension and Locked Knee Dynamics Motion of the Pelvis Through Space Sequential Swing Phase Trajectory Design Double Stance Phase Gait Generation... 5 ii

7 6.3. Pendular Phase Gait Generation Knee Impact Conditions Calculation Locked Leg Phase Gait Generation Swing Hip Trajectory Generation Results Actuator Considerations User Testing of the Swing Trajectory Pilot Testing of the Passive Knee Exoskeleton Meter Walk Test (10MWT) MWT Methods MWT Results Quarter Mile Time Trials Quarter Mile Time Trial Methods Quarter Mile Time Trial Results Endurance Testing in Unstructured Environments Other Real World Scenarios Minimally Actuated Double Stance (MADS) Propulsive Gait Introduction to the MADS Propulsive Gait Controllability of Double Stance Ballistic Single Stance Model Ballistic Single Stance Input Control Policies Knee Re extension Initial Conditions for Ballistic Single Stance Simulation Results and Discussion MADS Propulsive Gait Generation Double Stance Gait Generation Ballistic Single Stance Gait Generation User Testing of the MADS Propulsive Gait Conclusions References Appendices iii

8 11.1 Introduction to Point Tracking Qualitative Torso Dynamics Introduction to Partial Feedback Linearization Partial Feedback Linearization Internal Dynamics Passive Knee Initial Viability Test Initial Passive Knee Results Swing Model Tuning and Validation Knee Pendular Dynamics Isolation: Experimental Protocol Swing Knee Model Identification of Knee Parameters Knee Parameter Identification Results Borg Perceived Exertion Handout Development of Lower Extremity Double Stance Kinematics Exoskeleton Software Documentation Control Code: Exobed The Main File (main.cpp) Exoskeleton I/O Setup Routines (initexovars.cpp) Encoder Maintenance (encoders.cpp) Finite State Machine (FSM.cpp) Gait Generation (gaitgenerator.cpp) HipMotorControl.cpp linearactuatorcontrol.cpp databedcomm.cpp hapticfeedback.h Datalogging Code: Databed The Main File (main.cpp) Initialization of Databed (initdatabed.cpp) Datalogging (datalogger.cpp) HMI Routines (UI_routines.cpp) Troubleshooting iv

9 1.3.1 Exobed LED Error Patterns Databed LED Error Patterns v

10 LIST OF FIGURES Figure 1: Spinal Cord Injury Level and Remaining Extremity Function... 3 Figure : Reference Planes of the Body... 4 Figure 3: Flexion and Extension Standards for the Human Hip, Knee, and Torso... 5 Figure 4: Illustration of the Complete Walking Cycle, Adapted from [45] and [13]... 5 Figure 5: Variation in Swing and Stance Periods as Walking Speed Increases [9]... 6 Figure 6: CGA Data for the hip, knee, and ankle angles in the sagittal plane. Data from [51] Figure 7: Three Exoskeleton Assistive Devices for Able Bodied People... 8 Figure 8: Two Rehabilitative Exoskeleton Devices... 9 Figure 9: Current mobile ambulation devices on the market Figure 3 1: Austin Exoskeleton Hardware Overview... 1 Figure 3 : State Machine of the Austin Exoskeleton Figure 3 4: High Level Overview of Exoskeleton Subsystems Figure 3 3: Passive Knee Exoskeleton Hardware Overview Figure 3 5: Flow of Information Figure 3 6: Control Software Sequence Figure 3 7: Finite State Machine for Medical Exoskeleton Figure 4 1: Human Exoskeleton Control Block Diagram with a Simplified Trajectory Generator Figure 4 : Exoskeleton Pilot Testing New Gait Using Parallel Bars... 1 Figure 4 3: Trajectory of Pelvis with a Locked Stance Knee... 3 Figure 4 4: Concept of Physically Constraining the Torso to Assist with Propulsion... 4 Figure 4 5: Movement of the Torso with Respect to Displacement of the Two Hips... 5 Figure 4 6: Displacement of the Pelvis Through a Normal Walking Gait... 6 Figure 4 7: Lower Extremity Four Bar Model with Flexed Stance Knee... 6 Figure 5 1: The Sequence of the TCP Gait... 9 Figure 5 : Sample Timing Diagram for TCP Gait... 9 Figure 5 3: The Simplified Propulsive Stance Model Figure 5 4: a) Off Diagonal Inertia Matrix Elements Over Range of q, b) Operating Range of q in Single Stance Model Where Inertial Coupling Holds... 3 Figure 5 5: Propulsive Phase Results Figure 5 6: TCP Gait Trajectories for Two Hip Actuators Figure 5 7: Frames Showing Progression of 7 Link Walker Through the TCP Gait Figure 5 8: Frames Showing Test Pilot Executing a TCP step Figure 5 9: Hip and Knee angles through Several Steps Using the TCP Gait on the Austin Exoskeleton Figure 5 10: Global Torso and Stance Leg Angles During a Step Using the TCP Gait vi

11 Figure 5 11: Gait Trajectory Used with Passive Knee Exoskeleton Figure 5 1: Frames Showing Test Pilot Executing a Step With the Passive Knee Exoskeleton... 4 Figure 5 13: Hip and Knee Angles Through Several Steps Using the Passive Knee Exoskeleton... 4 Figure 5 14: Global Torso and Stance Leg Angles During a Step with the Passive Knee Exoskeleton Figure 6 1: Swing Generation Sequence Figure 6 : Swing Leg Model Figure 6 3: The Lower Extremity Progression Through a Step to Define Translational Dynamics of the Pelvis Figure 6 5: Knee Flexion Profile Based on Human Clinical Gait Analysis Data Figure 6 4: Stance Leg Dynamics and Translational Accelerations of the Hip Joint Through Space During a 1. Second Step Figure 6 6: Swing Phase Generation Results Figure 6 7: Frames Showing the Lower Extremities Throughout the Swing Phase Figure 6 8: Torque as a Function of Angular Velocity During the Swing Phase Figure 6 9: Motor Performance Plot with Swing Requirements Figure 6 10: Experimental Swing Phase data Figure 6 11: Swing Phase Knee Flexion Profile Comparison to Scaled Human Data [51] (dotted) and the Simplified Profile (dashed) Figure 7 1: Heart Rate Throughout the Quarter Mile Tests... 6 Figure 7 : Route of Two Walks Through the University of California, Berkeley Campus Figure 7 3: An Exoskeleton Pilot Boarding a Non Accessible Bus Figure 7 4: An Exoskeleton Pilot Getting into a Standard Car Figure 8 : Propulsive Double Stance Gait Generation Sequence Figure 8 3: Sample Propulsive MADS Gait Timing Sequence Figure 8 1: Discrete Walking States of the MADS Propulsive Gait Figure 8 4: Double Stance Model Figure 8 5: Ballistic Single Stance Model Figure 8 6: Two Ankle Foot Orthotic (AFO) Designs... 7 Figure 8 7: Surface Plots of Initial Conditions for Ballistic Single Stance model Figure 8 8: Set of Valid Initial Conditions for a Successful Ballistic Single Stance Phase Figure 8 9: Frames Through Ballistic Single Stance Figure 8 10: Hip and Estimated Knee Angles During Double Stance Period Figure 8 11: Various Trajectories for the MADS Propulsive Gait Figure 8 1: Frames Showing Biped Throughout the Duration of a Step with the MADS Propulsive Gait vii

12 Figure 8 13: Ground Reaction Forces on the Stance and Swing Feet as a Percentage of Total Weight Figure 8 14: Frames Showing Test Pilot Executing a Step with the MADS Propulsive Gait. 8 Figure 8 15: Hip and Knee Angles Through Several Steps Using the MADS Propulsive Gait8 Figure 8 16: The Global Torso Angle Throughout the MADS Propulsive Gait Figure 11 1: The Extraction of Sagittal Plane Angular Data from a Frame of Testing Video 94 Figure 11 : Torso and Stance Leg Simplified Model Figure 11 3: Free Body Diagrams of a) stance leg and b) torso Figure 11 4: a) Sample Single Stance Data, b) Single Stance Still Frames Figure 11 5: Generalized Underactuated System of Links Connected by Revolute Joints Figure 11 6: Modified Knee Assembly for Passive Knee Viability Tests Figure 11 7: Initial Swing Trajectory and Knee Locking Profile for Passive Knee Viability Tests Figure 11 8: Two Swing Phase Point Tracking Results Figure 11 9: Knee Pendular Dynamic Isolation Experimental Setup Figure 11 10: Hip and Knee Angles During a Sample Swing Phase While Suspended The pendular period has been noted between times 0.5 and 0.9 seconds Figure 11 11: Comparison of Knee Flexion Profiles Obtained from Trained Model and Experimental Data Figure 11 1: Simplified Lower Extremity Double Stance Four Bar Model Figure 11 13: Sample Input Output Curves for the Double Stance Four Bar Linkage Model Figure 1 1: Exoskeleton Computer Architecture and Flow of Information Figure 1 : Exoskeleton Control Code Hierarchy Figure 1 3: The Exoskeleton Finite State Machine (FSM) That Governs the Exoskeleton State Evolution Figure 1 4: Databed Software Hierarchy viii

13 ACKNOWLEDGEMENTS I owe a debt of gratitude to Professor Homayoon Kazerooni, my research advisor. He gave me the opportunity to work on satisfying and interesting projects. I gained a wealth of implementation experience in his lab, which has strengthened my engineering skills and intuition. I greatly admire his dedication to innovation and his commitment to using engineering for the purpose of helping others. Thank you to Professors Kameshwar Poolla and Nancy Van House for taking time from their busy schedules to participate on my thesis committee. I would like to thank all of my teammates in the Robotics and Human Engineering Laboratory (HEL). They have made my time at Berkeley enriching, fun, and memorable. I will always remember debugging hardware with Michael McKinley while rocking out to Supertramp, Wayne Tung's infectious laugh, Minerva Pillai's amazing cooking and grilling skills, Lee Huang Chen's photography talents, and Stephen McKinley's great homebrewed beer. I am also grateful for the camaraderie of Yoon Jung Jeong, Dongjin Hyun, Kyunam Kim, Patrick Barnes, and Nick Um. I have great expectations for Bradley Perry and Christina Yee, the newest generation in HEL. I would also like to thank the previous generation of HEL Ph.D.'s, namely Katie Strausser, Tim Swift, Kurt Amundson, Bram Lambrecht, and Adam Zoss for their invaluable insight and guidance. I am incredibly grateful for the hard work that Josh Cherian, our previous staff engineer, has provided to HEL and to me personally. He is so dedicated that he continued to design and machine great hardware on a voluntary basis after his term was completed. In addition to being a teammate, Josh is a good friend. I am confident that great things are in store for him as he embarks on his own journey toward the Ph.D. Thank you to all of the current and previous HEL undergrads. They have been a tremendous help in machining, maintaining hardware, and performing countless other tasks. Specifically, I owe gratitude to Daniel Driver, Mimi Lan, Matt Fisher, Alex Wen, Nate Poon, Chris Guichet, Leonard Carrier, Jonathan McKinley, and Leo Qu. I also want to express a sincere thanks to all of the test pilots who patiently worked with us and provided invaluable feedback along the way. I would like to thank my huge family back in Maryland I could not have finished my Ph.D. without their support. Despite the large geographical separation, they have always made me feel connected. I want to thank my mother, Elaine, for her unwavering love and support. I am also grateful for all of the support, help, and advice that my brothers, Jarrett ix

14 and Stephen, have given me throughout graduate school and the process of searching for my first "real" job. I want to thank my sister, Ilyse, for all of the entertaining phone calls and always planning a complete fun filled agenda for whenever we would get to see each other. I also want to thank my Aunt Di, my sisters in law, Jodie and Lisa, all of my nieces and nephews (Alan, Alanna, Michal, Jacob, Alex, Sam, Shannon, and Mira), and my cousins Mark, Beth, Alethea, Chandler, Danny, Aden, Alana, and Aryeh for providing me with fun webcam chats on Sundays and always welcoming me home on my visits to Maryland that were never long enough. I would also like to thank my Aunt Janet and my cousins Felice, Doug, Sofie and Izzie for all of their support. They always made me feel welcomed and right at home throughout my graduate school experience. I greatly appreciate all of the Shabbat dinners and other family events that I had the opportunity to join. I am also thankful for the access to their laundry facilities and for the copious amounts of great food they always gave me to take home. I will definitely pay it forward to Sofie and Izzie in the future. Last but not least, I want to thank Ilana for all of her help, constant support, and friendship. She was always able to keep me grounded and bring the best out of me. x

15 1 INTRODUCTION 1.1 MOTIVATION More than 65,000 individuals in the United States have a Spinal Cord Injury (SCI). Of those, more than 100,000 of them are paralyzed and use a wheelchair as their primary means of mobility [1]. Depending on the injury level, SCI can cost between $300,000 and $950,000 in the first year after injury, and between $40,000 and $165,000 every year after that []. These recurring costs are largely due to pain management and the secondary injuries that can arise due to continually being seated in a wheelchair. Common health issues that arise among wheelchair users are urinary tract infections, blood clots, reduction in cardiovascular functioning, decreased bone mineral density, and osteoporosis [3]. It has been shown that being upright and standing has numerous benefits such as increased circulation, improved bladder and bowel functioning, and an overall feeling of well being [4]. 1. MAJOR CONTRIBUTIONS Robotic exoskeleton devices have the potential to make standing and walking possible for many wheelchair users. This dissertation presents multiple novel gaits that enable paraplegic individuals to walk with the use of a minimally actuated exoskeleton. The core control challenge of the minimally actuated exoskeleton is to create forward propulsion to aid in locomotion without having power input (actuation) at the knees and ankles. It will be shown that simply making a reciprocal walking gait is not sufficient to cause the exoskeleton user to progress forward through a step. To address this problem, two original stance based propulsion strategies were designed. The first stance strategy relies on the movement of the pilot's torso as a means to dynamically propel the system forward through a step. A second, more advanced strategy that propels the user forward while stabilizing their torso will also be proposed. Through the manipulation of lower extremity kinematics, the user can be propelled forward out of double stance with an exoskeleton that only has actuation at the hips. Another control challenge that was addressed was the control of swing foot ground clearance for an exoskeleton without powered knees. During a normal step, the swing knee flexes rearward so that the swing foot will clear the ground. This dissertation will present an original method for generating a swing phase trajectory to control a passive swing knee so that positive swing foot ground clearance is achieved. The efficacy of all gait strategies are validated with experimental results. The novel strategies presented in this dissertation enable paraplegic individuals to achieve natural 1

16 human like walking with a new mobility exoskeleton that has fewer actuated degrees of freedom than current systems. This reduction in hardware complexity results in reduced weight and an anticipated lower cost for end users, so that more spinal cord injury patients may access this technology. 1.3 OUTLINE OF THIS DISSERTATION This dissertation is organized as follows: Chapter will provide background on the topic of spinal cord injury and walking. The chapter will conclude with a brief overview of prior work in the areas of human performance augmentation with exoskeleton devices. Chapter 3 will present the medical exoskeleton devices developed in the Berkeley Robotics and Human Engineering Laboratory. The software and human machine interface that was developed to experiment with these devices will be discussed. Chapter 4 will discuss the human centered control design practices and philosophies used. Human considerations will be outlined. The central control problem that this dissertation addresses will be presented. Chapter 5 develops the first original stance strategy implemented in this work. This strategy relies on the motions of the pilot's torso as a means to dynamically propel the system forward through a step. A sequential method of trajectory generation will be presented and the efficacy of this strategy will be experimentally verified. Chapter 6 presents a sequential swing phase model. This model is used to produce a gait trajectory for the swing leg that dynamically controls an unactuated swing knee. A method for swing phase hip trajectory generation will be presented. Experimental results will be shown that validate the efficacy of the swing phase trajectory at producing a natural human like swing phase from a swing leg that has no actuation at the knee. Chapter 7 details results and findings from extensive pilot use of a medical exoskeleton. Results will be presented from both structured tests and unstructured real world use of the system. Chapter 8 discusses the second original stance strategy. This method generates propulsion through the manipulation of lower extremity kinematics. In doublestance, if the rear knee is locked against flexion, and the front knee is unlocked and free to rotate, the lower extremities resemble a four bar mechanism. This insight is used to create a gait that propels the system forward and out of double stance. A method for generating a gait trajectory for this strategy will be described. Experimental results from implementation of this stance strategy will be presented. Chapter 9 summarizes the contributions of this dissertation.

17 BACKGROUND.1 INTRODUCTION TO SPINAL CORD INJURY Spinal cord injury (SCI) is a general term for damage that is local to the spinal cord. The damage can be the result of trauma, such as a car accident, or a disease, such as cancer or arthritis. The spinal cord consists of a bundle of nervous tissues that travel from the brain down the spine. The nervous tissues can be thought of as cables that transmit and receive electrical impulses or signals from all parts of the body. Depending on where the spinal cord is injured, varied amounts of extremity functioning may be lost. Figure 1 shows how remaining extremity function of the body varies depending on where the spinal cord is injured. Figure 1: Spinal Cord Injury Level and Remaining Extremity Function Image from [5] The work in this dissertation is applicable to individuals with paraplegia, which is a loss of functioning in the lower extremities. While nearly half of all SCI due to trauma results in a complete loss of functioning below the injury level [6], in some cases there are varied degrees of extremity functionality remaining. The American Spinal Injury Association (ASIA) created an impairment scale (AIS) which is used to describe the level of impairment. On a scale of A E, a classification of A is a complete impairment, B through D are decreasing levels of impairment, and an E classification is considered normal motor and sensory functioning [7].. INTRODUCTION TO WALKING..1 BIOMECHANICS STANDARDS Several biomechanical standards will be defined so that various dynamic behaviors during walking can be clearly and consistently described. 3

18 ..1.1 Body Planes There are three planes fixed about the body that are used to describe motion of various joints (as shown in Figure ). The coronal (or frontal) plane vertically slices through the body width wise, passing through both arms and both legs (side to side). The transverse plane slices horizontally through the body parallel with the ground. The sagittal plane is a vertical plane that slices orthogonally to the coronal plane, passing through from the front to the rear of the body. For this thesis, the human exoskeleton dynamics are generally considered in the sagittal plane. This treatment is often referred to as "planar walking." Figure : Reference Planes of the Body Edited Image from [45]..1. Lower Extremity Joint Angles When describing the motion of various joints, the terms flexion and extension are commonly used to describe whether a particular relative joint angle is growing or shrinking in the sagittal plane. These standards are depicted in Figure 3 for the knee and hip. Joint angles are relative angles, which means that they are defined with respect to another body, not globally. The ankle angle (not pictured) is measured with respect to an orthogonal foot shank and knee shank. Plantarflexion of the ankle increases the angle between the foot and knee shanks while dorsiflexion decreases that angle. 4

19 Figure 3: Flexion and Extension Standards for the Human Hip, Knee, and Torso Image from [8].. THE WALKING CYCLE Walking is considered to be a hybrid and cyclical process. At the most fundamental level, each leg is in one of two states, stance or swing. When a leg is in stance, its foot is planted on the ground. During the swing phase, the leg swings forward with the foot off of the ground. The first part of swing is characterized by the positive acceleration of the hip forward and the flexing of the knee rearward so that the swing foot clears the ground. The latter segment of swing involves the negative acceleration of the hip as the knee re extends to prepare for heel strike, when the leg enters stance. The walking cycle is illustrated in Figure 4. Phase Stance Phase Swing Phase Periods Initial Double Stance Single Stance Second Double Stance Initial Swing Mid Swing Terminal Swing Event % of Cycle Foot Strike Opposite Toe Off Reversal of Fore Aft Shear Opposite Foot Strike 5 Toe Off Foot Clearance Tibia Vertical Foot Strike 0% 1% 50% 6% 100% Figure 4: Illustration of the Complete Walking Cycle, Adapted from [45] and [13]

20 Throughout the process, the two legs alternate roles between stance and swing. When walking at slower speeds, there are periods when both legs are in stance. These periods are referred to as double stance or double support. There are two double stance periods of about 10 percent of the gait cycle when walking at 1 meter per second. This leaves a pure swing period of about 40% of the walking cycle. As walking speed increases, time in double stance decreases until there is no time spent in double stance. An individual running has periods of flight where both legs are in swing. The relationship between swing and stance periods at different speeds of ambulation is shown in Figure 5. Figure 5: Variation in Swing and Stance Periods as Walking Speed Increases [9]..3 CLINICAL GAIT ANALYSIS (CGA) When studying human walking, the motion of the joints throughout the walking process can be described using the biomechanical standards discussed in Section..1. Biomechanics laboratories will typically capture video as a subject walks. The motion of the various joints is then extracted from the video using a motion capture system. The joint angles throughout the walking cycle for several steps is typically averaged to produce gait plots, which will be referred to as Clinical Gait Analysis data. Figure 6 shows CGA data for the motion of the hip, knee, and ankle in the sagittal plane collected by three biomechanics labs. 6

21 [deg] Winter CGA Kirtley CGA Linskell CGA Stance Swing [deg] Winter CGA Kirtley CGA Linskell CGA Stance Swing Stance Swing % % % Figure 6: CGA Data for the hip, knee, and ankle angles in the sagittal plane. Data from [51]. Note: The vertical dashed line at 60% denotes toe off. Experimental results throughout this dissertation will be presented using joint angle plots similar to those shown above. [deg] Winter CGA Kirtley CGA Linskell CGA.3 PRIOR ART The first exoskeleton concepts can be traced back as far as 1890, when passive devices were designed to enhance human capability. The successful implementation of powered exoskeleton systems was largely enabled by the increasing maturity of supporting technologies such as batteries, actuation, sensors, and computers..3.1 EXOSKELETON ASSISTIVE DEVICES FOR ABLE BODIED PEOPLE The first practical exoskeletons were designed to enhance the physical abilities of the ablebodied. By providing actuation in parallel with several of the user's biomechanical joints, the user's physical capabilities could be amplified. This section describes three of the first untethered exoskeleton devices that augment the physical abilities of able bodied people Berkeley Lower Extremity Exoskeleton (BLEEX) The Berkeley Lower Extremity Exoskeleton (BLEEX) is an assistive device for carrying loads. It is considered to be the first energetically autonomous lower extremity exoskeleton [10]. The BLEEX consists of an exoskeletal structure, power units at the ankles, knees, and hips, a computer and power supply, and a payload that is attached to the structure. The mass of the payload gets transferred through the exoskeleton structure to the ground, so that the pilot is not carrying the load. A model based control algorithm was developed that uses the inverse dynamics of the system to create a positive feedback controller with a loop gain close to one [11]. The exoskeleton control algorithm is designed to mimic the pilot's motions and account for his or her own dynamics. One of the core tenants to the control and design of BLEEX is that the human is the central control system for the exoskeleton. While the system augments the wearer's strength by providing power 7

22 at various joints, it is the wearer's responsibility to balance and walk the system. This system was able to carry up to 75 kilograms of payload while walking at speeds up to 1.3 meters per second [1]. The BLEEX is shown in Figure 7a Human Universal Load Carrier (HULC) HULC evolved from the BLEEX system in the Berkeley Robotics and Human Engineering Laboratory. The system has hydraulically powered hips and knees (extension only). Instead of powering the ankle, a passively sprung ankle was designed to simplify the system and minimize the mass of the legs [13]. HULC is capable of carrying up to 00 pounds (~91 kilograms) and has demonstrated its ability to decrease metabolic costs of the pilot walking at a speed of two miles per hour. HULC is shown in Figure 7b Hybrid Assistive Limb (HAL) HAL is a powered exoskeleton system that is designed to amplify the wearer s strength. HAL comes in multiple forms which include powered modules for the lower and upper extremities. HAL reads the wearer's intent through myoelectric signals with electromyographic (EMG) sensors that are placed on the user s skin. The controller interprets the myolectic signals, which correspond to muscle activity, and controls the actuation units to amplify the user s power ([14], [15]). Unfortunately, the control method does not work for patients with paralysis due to the requirement to read myolectric signals. The engineers that designed HAL are working on a method of interpreting the ground reaction forces to determine user intent for a paralyzed individual [16]. HAL is shown in Figure 7c. a) b) c) Figure 7: Three Exoskeleton Assistive Devices for Able Bodied People a) BLEEX [86], b) HULC [87], c) HAL [88].3. REHABILITATIVE EXOSKELETON DEVICES Some of the first implementations of exoskeleton technology in the medical domain were gait training rehabilitation devices. These devices were designed to assist with moving a 8

23 patient's lower extremities as they learn to walk again after a neurological disease or injury. After an individual suffers from a brain injury such as a stroke, the functions handled by damaged regions of the brain may be impacted. The brain has the ability to "reorganize" using healthy areas of the brain to compensate for the damaged regions [17]. There are numerous rehabilitation avenues that a mobility impaired individual can access to "relearn" tasks such as walking. Aggressive bracing assisted walking and partial body weight supported treadmill training are two methods that involve multiple physical therapists assisting the patient in relearning how to walk [18 0]. These methods have been shown to be effective, but are not very accessible because they require training by skilled therapists. Several rehabilitative exoskeleton devices have been developed that seek to address this issue by somewhat automating the process of gait training. Lokomat, developed by Hocoma, and the Active Leg EXoskeleton (ALEX), developed at the University of Delaware, are two robotic orthotic devices that automate the process of treadmill training ([1], []). Both devices consist of a motorized structure that drives the patients legs as they walk on a treadmill. ALEX employs a "force field" controller that seeks to actively alter the gait of the patient using the system. Lokomat uses a gait pattern adaptation algorithm that is designed to both help patients walk and encourage them to remain active in the process [3]. Both systems are shown in Figure 8. a) b) Figure 8: Two Rehabilitative Exoskeleton Devices a) Lokomat [89], b) ALEX [90].3.3 MOBILE MEDICAL EXOSKELETON DEVICES While the rehabilitative exoskeleton devices have shown promise in helping individuals with gait impairments re learn how to walk, a mobile system would enable gait training to continue outside of a clinic. Additionally, a mobile medical exoskeleton device could be used as an alternative means of mobility for individuals with SCI. Three powered mobile exoskeleton devices that enable a user to stand and walk are currently on the market. The 9

24 Rex, ReWalk and Ekso systems are shown in Figure 9a, b, and c, respectively. The Rex exoskeleton was developed by Rex Bionics in New Zealand. Rex is a self balancing structure that has powered ankles, hips, and knees. The device enables a user to take slow controlled steps as commanded by a user interface located on the arm rest [4]. The ReWalk exoskeleton was developed by Argo Medical Technologies in Israel. ReWalk has powered knees and hips and relies on the pilot to use crutches or a walker to balance. The system executes steps by sensing the tilt of the user's torso [5]. Ekso, developed by Ekso Bionics, is similar to the ReWalk system in that the hips and knees are powered in the sagittal plane. However, Ekso determines user intent using sensors on the pilot's arms and crutches to estimate the user's pose [6]. Depending on the pose, a step will be executed. These three powered exoskeleton systems currently vary in cost between $100,000 and $150,000. A lower cost (~$10,000) alternative is the unpowered Reciprocating Gait Orthosis (RGO), shown in Figure 9d. The RGO is considered to be the most practical and prescribed orthotic brace for assisting individuals with paralysis in ambulation [7]. The device consists of a pair of leg braces that are connected to a torso constraint. A connecting bar spans the back of the torso that connects one hip to the other hip. This bar acts as a transmission that transfers torque from the stance leg to the swing leg to power the swing leg forward as the user ambulates. This method of ambulating is highly inefficient. Bernardi et al. claims that walking at 1 meter per second using the RGO requires 14 times more work than the average person [8]. Factors such as low efficiency and unrealistic patient expectations contribute to a low long term adoption rate of the RGO. In one longitudinal study, only 9 percent of RGO users continually used the device [9]. a) b) c) d) Figure 9: Current mobile ambulation devices on the market. a) Rex [91], b) ReWalk [9], c) Ekso [93], d) RGO [94] 10

25 Functional Electronic Stimulation (FES) can be used to help some individuals with paralysis ambulate. FES involves the application of electrical pulses to muscles to control their contractions [30]. Coordinating these contractions enables the actuation of a user's paralyzed joints with their own muscles. FES can be used in conjunction with standard orthotics, such as the RGO or leg braces, to help a paralyzed individual gain limited mobility [31 34]. Muscle fatigue during FES limits its use as the muscle force decreases with time. Additionally, a patient must have preserved excitability of the lower motor neuron for FES to be effective [35]. 11

26 3 BERKELEY MEDICAL EXOSKELETONS: PRIMER Two medical exoskeleton prototype platforms serve as the hardware foundation for all work discussed within this dissertation. These systems were developed in the University of California, Berkeley Robotics and Human Engineering Laboratory. 3.1 AUSTIN EXOSKELETON The Austin exoskeleton is the initial result of a design investigation to minimize exoskeleton hardware complexity through the reduction of actuation units. While the previously discussed powered exoskeletons have between four and ten actuated degrees of freedom, the Austin exoskeleton has one actuation unit per leg at the hip that is connected to a "mechanical gait generator." This gait generator mechanically programs a healthy human walking gait into the exoskeleton hardware. While the exoskeleton hip is directly controlled by the actuator, the knee is controlled through a series of mechanisms that transfer power to the knee during the first phase of swing when the knee is flexed. As the knee is flexed, a spring at the knee is charged that is discharged during the second part of swing to assist with knee re extension. The Austin exoskeleton is shown in Figure 3 1. Computer and Batteries Actuation Output Gait Generator Spring Knee Pullies Locking Knee Joint Knee Figure 3 1: Austin Exoskeleton Hardware Overview A locking mechanism is located at the knee joint that is unlocked during swing to allow flexion, but is locked during stance to allow weight bearing on the stance leg. The knee 1

27 coupling and locking behaviors are dictated by the mechanisms in the mechanical gait generator. Figure 3 depicts the state machine that defines how the discrete states of the Austin exoskeleton transition. Figure 3 : State Machine of the Austin Exoskeleton The transitions of the hardware state machine were designed to match the natural behavior of the hip and knee throughout the walking cycle. The only sensors on the Austin exoskeleton are rotary absolute encoders at the output of each actuation unit. 3. PASSIVE KNEE EXOSKELETON The Passive Knee Exoskeleton was designed to enable maximum flexibility for different users while further reducing hardware complexity. The hip is directly powered by an actuation unit that is axially aligned with the pilot's biological hip. In lieu of the mechanical gait generator developed for the Austin system, the knee is entirely passive. A computer controlled locking mechanism is located at each knee. This allows the unlocking of the knee for swing, and the locking of the knee during stance. Flexion of the knee will be dynamically controlled by the motions of the swing hip. The torso, leg links, and knee joints are all individual components that can be changed to create the optimal configuration for the user. This is important because each user has different functional requirements that need to be accommodated with the suit. The configuration of the Passive Knee Exoskeleton as used in this dissertation is shown in Figure 3 3. Similar to the Austin exoskeleton, the only sensor on the Passive Knee Exoskeleton is a rotary absolute encoder at each hip actuator. 13

28 Torso Constraint Computer and Batteries Hip Actuation Unit Computer Controlled Knee Joint Orthotic Leg Brace Figure 3 3: Passive Knee Exoskeleton Hardware Overview 3.3 CONTRIBUTIONS TO EXOSKELETON DEVELOPMENT The exoskeleton systems developed for this work are composed of several interconnected subsystems. The author has primarily contributed to the embedded system development, computer software and communications, and the human machine interface (HMI). A highlevel exoskeleton system overview is shown in Figure 3 4. Figure 3 4: High Level Overview of Exoskeleton Subsystems Author's primary contributions are highlighted with dashed outlines 3.4 MICROCONTROLLER ARCHITECTURE The exoskeleton computer is composed of two microcontrollers networked together. The mbed microcontroller was used because it is a low cost microcontroller designed for rapid prototyping that has a 3 bit ARM Cortex M3 processor running at 96MHz. The mbeds also 14

29 provide access to a variety of inputs, outputs, and communication standards including serial peripheral interface (SPI), controller area network bus (CAN), and others. Two mbed computers were networked together using both the SPI and UART protocols to simultaneously handle control computation, gait generation, datalogging, and human machine interface (HMI) computation. The main exoskeleton microcontroller handles control of the motors, gait generation, and transitions of the exoskeleton finite statemachine. The second microcontroller handles datalogging and communications with the HMI system. The primary reason for using two networked microcontrollers on the exoskeleton was to maximize data frequency during datalogging. Data is sent wirelessly using an XBee or bluetooth wireless radio to a receiver connected to a computer to receive the data. 115,00 bits per second is the fastest that the current wireless hardware can reliably transmit data. During datalogging, there are twenty seven 8 bit packets of data to send per wireless transmission, therefore, data transmission takes a minimum of milliseconds per frame of data. To minimize interruption to the control loop, data is transmitted through SPI at 1MBit per second from the control computer to the data handling computer. The data handling computer stores this data in a buffer as it transmits the data out continuously over a comparatively slower wireless connection. A high level overview of the flow of information is shown in Figure 3 5. Figure 3 5: Flow of Information 3.5 CONTROL SOFTWARE ARCHITECTURE The control software consists of a sequence of operations that is executed at 1kHz. The control software sequence is shown in Figure

30 Figure 3 6: Control Software Sequence This sequence of commands is triggered every 1ms using a timer based interrupt at 1 khz. The first operation is the reading of the exoskeleton sensors. The encoders at the hip are read so that the angular position of the hips with respect to the torso can be estimated. The next operation is checking the communication line from the datalogging controller to see if a new command from the HMI has arrived. Following this, the state machine is referenced to see if a state transition was triggered. State transitions are both timer based and event based. An example of a timer based transition is the completion of a step which occurs in a specified amount of time. After the step is completed, the state automatically transitions to double stance. An example of an event based transition is the progression of the exoskeleton state from double stance to another step if the user issues the step command with the HMI. The state transitions according to the rules shown in Figure 3 7. After the exoskeleton state is referenced, the trajectory that the hip actuation units track is generated. This reference trajectory is used to control the hips in the next operation in the sequence. Following this, a small motor attached to the knee locking mechanism on both knees is controlled to either lock or unlock each knee. The control sequence is completed by sending current control data through an SPI communication bus if data is requested from the datalogging computer. Data is not requested every control loop because it takes the datalogging computer more time than the control period to wirelessly transmit data. A more in depth description of all software processes is available in the Appendices in Chapter 1 of this dissertation. 3.6 HUMAN MACHINE INTERFACE (HMI) The Human Machine Interface (HMI) is a device that the pilot uses to communicate his or her intent to the system. At the highest level, the exoskeleton can be in one of three states, sitting, standing, or walking. There are also several transition and sub states associated with the three main states. Depending on the user's signaled intent, the current state of the exoskeleton transitions according to the rules dictated by the state machine shown in Figure

31 Figure 3 7: Finite State Machine for Medical Exoskeleton As discussed previously, the state transitions are either timer based or event based. Referring to the state machine, the pilot has a maximum of two options at any given moment. If the user is sitting, he or she can either continue to sit, or stand up. If the user is standing, he or she can either begin walking, or sit back down. While the state is doublestance, the pilot can either take another step, bring his or her feet back together, or do nothing and remain in double stance. The pilot can trigger the next step while in a step. The state will still transition to double stance, but it will immediately transition from double stance to the next step HMI HARDWARE The HMI can take a variety of physical forms. Only two unique signals need to be generated that correspond to the maximum two options the pilot may have. One form of the HMI is a hand controller fabricated on a crutch or walker grip that has two buttons ergonomically embedded into the grip. Another form of the hand controller uses a rocker switch, which can be toggled either up or down, instead of individual buttons. Haptic feedback is given to the pilot to communicate various messages and mediate various confirmation processes. This feedback can be applied by using a vibration motor embedded in the HMI hand controller. Another method of haptic feedback utilizes the hip actuation units to communicate with the user. By varying the pulse width modulation 17

32 frequency of the motor controllers within the auditory frequency range, the motors can produce different pitches. The motors also produce a slight vibration on the pilot's body as the frequency is changed. This enables the use of the motors to provide vibration and auditory feedback to communicate with the user. A confirmation process was incorporated to transition the exoskeleton state from sit to stand or from stand to sit. This was done to minimize unintentional standing or sitting transitions. The confirmation process requires the user to hold the sit or stand button until a haptic pattern signals to the user that the intent was received. After this, the user must release the button and then reapply and hold the button to confirm. If confirmed, the exoskeleton will transition from sit to stand (or vice versa). If the user idles, another haptic pattern communicates to the user that the command was canceled. 18

33 4 HUMAN CENTERED CONTROL DESIGN For the human exoskeleton system, consistent and predictable performance is of the utmost importance because the human pilot is the central controller and intelligence for the system. For this reason, the control strategy for the system is to use a closed loop control scheme for the hip actuators to follow a set of fixed trajectories that will depend on the state of the system, such as walking or sitting. If predictable trajectories are used, the pilot will learn the system behavior and be able to react and modify system performance as desired to attain a higher level of functionality. Figure 4 1 shows a block diagram for the control of the hip actuators with a simplified trajectory generator. Swing t ref, l l e l il Tl 1 Is Bs l Stance t ref, r r e r ir Tr 1 Is Bs r Figure 4 1: Human Exoskeleton Control Block Diagram with a Simplified Trajectory Generator 4.1 MOTOR DYNAMICS A brushless DC motor is located at each hip of the Berkeley medical exoskeleton devices. The dynamics of a DC motor are typically characterized by the first order differential equation: di V L Ri Kb (4.1) dt V is the voltage across a motor winding, L is the motor inductance, R is the resistance, K b is the back electromotive force constant ("back EMF"), and is the rotational velocity of the motor shaft. Each DC brushless motor is powered by a current control amplifier. These amplifiers have an internal feedback loop to track a commanded current within an acceptable range. Therefore it will be assumed that the motor current can be directly controlled. The motor torque output is directly proportional to motor current: T K i (4.) T 19

34 The K T is the torque constant, which is a motor specific parameter. The torque output of the actuator causes a rotational acceleration of some inertia: T I B (4.3) I is the inertia connected to the output (the pilot's leg), and B is damping due to the actuator and the pilot's biological hip. The motor control policy in the exoskeleton control software is a proportional controller that minimizes the error between the actuator output,, and the desired angle, ref. i K e, e (4.4) P In equation (4.4) K P is the proportional gain of the controller. Combining with equation (4.3): T P ref ref K K I B (4.5) Transforming the dynamics to the frequency domain with a Laplace transform assuming zero initial conditions: K K s s s Is Bs (4.6) T P ref The actual output frequency dynamics can be isolated using equation (4.6). s ref s I K K s 1 B K K T P T P s1 (4.7) Because all constants in equation (4.7) are greater than zero, the final value theorem can be used to solve for the steady state output of the actuator. The reference input is assumed to be a set position (static value) that is modeled as a step input of magnitude ref : ref 1 lim t lim sss t s0 s I B s s1 KK KK T P T P ref (4.8) Equation (4.8) proves that the actuator output eventually settles to the desired reference position using a proportional controller with a current controlled amplifier. While this study neglects dynamic contributions due to gravity and limitations on actuator performance, it demonstrates the relative efficacy of the simple control policy. 0

35 4. HUMAN PILOT CONSIDERATIONS For the work presented in this dissertation, it is assumed that the pilot has functioning upper extremities that can exert reasonably high forces (~50 lbs, N). All gaits developed primarily consider the dynamics in the sagittal plane. It is assumed that the pilot will be capable of balancing their body in the frontal (coronal) plane. To assist the pilot with balancing, an ambulation aid will be used at all times when the pilot is not sitting. Three ambulation aids were used throughout this work: parallel bars, a walker, and forearm (loftstrand) crutches PARALLEL BARS Parallel bars are the preferred ambulation aid when a pilot is beginning to train with the exoskeleton or is learning a new gait. The Berkeley Robotics and Human Engineering Laboratory facilities have a 10 foot long (3.05m) set of parallel bars that a pilot can use during gait training and testing (shown in Figure 4 ). The parallel bars provide a stable means of support and balance without having to consider placement of a mobile ambulation aid. Figure 4 : Exoskeleton Pilot Testing New Gait Using Parallel Bars 4.. WALKER The walker is the first mobile ambulation aid that a new exoskeleton pilot will use after he or she becomes confident enough to leave the parallel bars. This aid still provides stability for the pilot while providing more freedom to ambulate. The walker that is used in the laboratory was widened so that it fits around the user's lower extremities while sitting in a bariatric wheelchair. This places the handles more comfortably at the pilot's sides to provide him or her with better leverage to assist with the sit to stand process CRUTCHES 1

36 Crutches are the next choice of ambulation aid if the pilot gains enough experience and confidence using a walker. More experience is needed to use crutches because they provide less stability compared to the walker which has a fixed base of support. Crutches have been shown to have a lower energy expenditure associated with their use than the walker [36]. Additionally, certain gaits are not practical with the walker because the horizontal bars that connect the two sides prevent the lower extremities from passing in front of the user s base of support. Therefore, crutches may be the preferred ambulation aid if the pilot has the ability to use them. 4.3 THE CONTROL PROBLEM The core focus of this thesis is the design of gaits for a minimally actuated medical exoskeleton. Medical exoskeleton control strategies have been developed that effectively enable individuals with paralysis to walk ([6], [37]). However, all current medical exoskeleton devices have at least four independently actuated degrees of freedom which power flexion and extension of each hip and knee. The Berkeley medical exoskeletons have only two actuation units, one at each hip to power flexion and extension. The knees of the Austin machine are controlled by the mechanical gait generator at the hip, while the knees of the Passive Knee Exoskeleton are entirely unpowered. This poses an interesting challenge to create effective walking gaits because the knees cannot be directly controlled. This control problem is broken into two smaller problems, stance and swing, that are dealt with throughout this dissertation. The first problem is generating a stance phase trajectory. The main stance phase challenge is how to create forward propulsion to assist the pilot in ambulating forward while minimizing his effort. The second problem is the generation of a swing phase trajectory that will effectively control an unpowered knee. It is important that the swing foot clears the ground during the swing phase. The swing phase will be generated by using the natural dynamics of the unpowered knee to control flexion and extension. 4.4 EXOSKELETON STANCE CONTROL When an exoskeleton system is at rest in between steps, both feet are planted on the ground (double stance) and the knees are locked. The lower extremities of the humanexoskeleton system are essentially a structure. From this configuration, if one tries to take a step in the manner shown in Figure 4 3, the pelvis follows an arc like trajectory from one double stance to the next double stance. The states of a biped are shown at times t 0, t 1, t, and t 3 where t 0 <t 1 < t <t 3. The angle from the vertical axis to the starting position of the stance leg is defined as S 0.

37 Torso t 0 t 1 t V t 3 Pelvis h Swing Leg S 0 Stance Leg Figure 4 3: Trajectory of Pelvis with a Locked Stance Knee The potential energy of the body increases due to the positive vertical displacement, h, of the torso through the first half of the step. This is shown by the biped as it transitions from double stance at time t 0 to the state at time t 1 where the stance leg is vertical (at the peak of the arc). The change in potential energy from the initial state t 0 to t 1 can be approximated with the head arms and trunk (HAT). This approximation is acceptable because the HAT is roughly /3 of the overall mass of the typical human body. Labeling the length of the walker's leg, l L, and the mass of the HAT, m HAT, and assuming the global torso angle remains constant and the ground is level: HAT HAT L S 0 3 PE m gl 1 cos (4.9) Intuitively, as the size of a step increases, the change in potential energy increases due to the increase in S 0. Considering this increase in potential energy, the bipedal system starting at rest cannot successfully complete a step without some sort of energy input or external constraint THREE SOLUTIONS THAT ENABLE A MINIMALLY ACTUATED DOUBLE STANCE TO DOUBLE STANCE TRANSITION A large body of literature supports that the ankle extensor muscles (plantar flexors) are a major contributor to the propulsion of an able bodied human ([38], [39], [40], [41]). The following sections discuss some original concepts that are designed to propel a pilot in a minimally powered exoskeleton that has unpowered ankles and knees. This is a challenge as it has been shown that when a user no longer has normal functioning ankles, such as a

38 trans femoral (above knee) or trans tibial (below knee) amputee, their walking speed and efficiency drops considerably ([4],[43],[44]). These strategies are designed to propel a user wearing a minimally actuated exoskeleton while requiring minimal effort from the user Physically Constrain the Torso This method requires an external apparatus that constrains the torso. Consider the simplified system shown in Figure 4 4a that shows the bipedal walker without a swing leg. Assume that the torso constraint consists of a set of rollers attached to a rolling support in a similar manner as depicted in Figure 4 4b. The torso "link" in this constraint can translate forward and backward (support rolls) and up and down (rollers and support move) while maintaining a constant global torso angle,. a) b) c) Torso T act V Constraining Rollers Rolling Support t 0 t 1 t Stance Leg Figure 4 4: Concept of Physically Constraining the Torso to Assist with Propulsion a) Simplified stance model, b) possible torso constraint concept, c) constrained simplified model through the the knees can be controllable enabling a double stance phase so that conditions are nonzero before single stance progression of a single step The constraining rollers exert an external force on the torso to keep constant. When the actuator at the hip is controlled to increase the angle between the stance leg and the torso,, then the angle between the stance leg and the ground,, decreases. The progression through a step is shown in Figure 4 4c. As increases from t t0 to t ( t 0 t 1 t ), t decreases, thus the walker is propelled forward. t Using the Torso to Generate Propulsion Chapter 5 of this dissertation presents a stance strategy that uses dynamic motions of the torso to propel the walker forward. While the lower extremities resemble a structure, if the hips of the system are controlled to both flex or extend at the same rate, the global 4

39 torso angle of the system can be controlled. Figure 4 5 demonstrates that the pure movement of the torso results in an equal displacement for both hip actuators. Torso at time t 1 Torso at time t 0 swing t 0 Swing Leg stance t 0 Stance Leg Figure 4 5: Movement of the Torso with Respect to Displacement of the Two Hips The angles between the stance and swing hip shanks at time t 1 are the following: stance swing t1 stance t0 t t 1 swing 0 (4.10) Extending equation (4.10), if both actuators have equal relative angular velocities of the hip shank with respect to the torso, the torso will move globally with that angular velocity. This provides the control designer with a degree of freedom through the control of the torso. This is significant because the torso has a large inertia that can be manipulated to influence the dynamic behavior of the overall system. The average human HAT is approximately two thirds of one's body weight, and the exoskeleton battery and electronics are also concentrated at the torso. Chapter 5 discusses this method in more detail Create a Double Stance "Phase" Chapter 8 of this dissertation proposes a novel method for creating a double stance propulsive phase with a bipedal system that has unactuated knees. This gait strategy will employ stance knee flexion (the front leg) to enhance double stance kinematics. If the knees are allowed to flex during double stance while both feet are planted, the system is not a static structure as shown in Figure 4 3. This enables a small degree of lower extremity maneuverability. Knee flexion of the stance leg in natural walking serves several purposes, such as the minimizing and smoothing of the vertical displacement of the trunk ([45], [46]) as shown below in Figure 4 6. Conversely, knee flexion of the stance leg from double stance into stance has been thought to be a mechanism for energy absorption after heel strike ([47], [48], [49], [50]). 5

40 Figure 4 6: Displacement of the Pelvis Through a Normal Walking Gait Image from ([45]) If the stance knee is allowed to flex, while the swing knee (rear leg) remains locked, the lower extremities in double stance resemble a four bar mechanism. Using this knowledge, the four bar mechanism kinematics can be manipulated to translate the HAT forward and propel the pilot out of double stance. This concept is depicted in Figure 4 7. Swing Leg Stance Hip V Stance Knee 3 1 Figure 4 7: Lower Extremity Four Bar Model with Flexed Stance Knee Intuitively, if the angle between the two hips,, is increased, then the angle between the swing leg and the ground, 3, and the angle between the stance knee and the ground, 1, both decrease. Therefore, increasing the angle between the hips essentially pushes the system forward. This kinematic property can be manipulated so that the velocity conditions upon toe off of the swing leg are non zero. This method is discussed in more detail in Chapter EXOSKELETON SWING LEG CONTROL 6

41 Chapter 6 in this dissertation discusses control of an exoskeleton swing leg with an unpowered knee. Current lower extremity medical exoskeletons on the market all have an actuation unit at the knee for directly controlling knee behavior. During natural walking, power is delivered to the knee to control knee flexion and extension behavior during swing and to keep the knee from buckling during stance. CGA biomechanical data for able bodied individuals shows that power during swing is largely dissipative (negative) [51]. Additionally, if a locking or braking mechanism is located at each knee, the knee can be locked during stance without an actuator. This supports the argument that an actuation unit at the knee may be superfluous for regular level ground walking. Previous studies have investigated the viability of removing power delivery to the knee for bipedal walking robots. Several passive dynamic walkers have been created that are able to achieve natural gaits walking down shallow inclines with no actuation power input ([5], [53],[54],[55]). Additionally, it has been shown that with minimal power input, a semi passive walker can walk on level surfaces ([56],[57],[58]). These passive walkers show that extremely energy efficient and natural locomotion can be attained by preserving the natural dynamics with a carefully designed walking device. Endo et al. [59] developed a quasi passive robotic leg model with a hip, knee, and ankle that only has actuation power input at the hip and passive mechanisms at the knee and ankle. They demonstrated that the dominant behaviors of the leg can be produced without actuation at the knee and ankle. The case for a passive exoskeleton knee is further supported by the ability to better preserve the natural pendular dynamics of the swing leg. Ferris et al. [60] stresses that disrupting those natural dynamics could increase metabolic costs. An additional benefit to omitting actuation at each knee or a mechanical gait generator at each hip, is the further simplification of the overall exoskeleton hardware design in comparison to current systems. This enables a lighter, more reliable, and lower cost exoskeleton system. Design of hip trajectories for a swing leg with an unpowered knee will be discussed in detail in Chapter 6 of this dissertation. 7

42 5 TORSO CONTROLLED PROPULSION This chapter discusses a method of generating torques for the hip actuation units during double stance and single stance phases. A sequential gait strategy will be developed that uses dynamic motions of the torso to propel the exoskeleton and pilot forward. The torso of the system can be maneuvered in double stance despite the static nature of the lower extremities. It can be shown that if the torso is accelerated in a particular manner, the overall bipedal system can be propelled forward. One can experience a similar phenomenon if they oscillate their arms back and forth at their sides while standing. When the arms are accelerated forward, the torso is "pushed" backward, and when the arms are accelerated backward, the torso is pushed forward. A qualitative discussion of the inertial dynamics of the torso is located in the Appendices in Section 11.. The central concept of the propulsive gait is that the positive angular acceleration of the torso propels the bipedal system forward. Propulsion can be controlled through an "inertial coupling" between the torso and the lower extremities. 5.1 SEQUENTIAL DEVELOPMENT OF THE TORSO CONTROLLED PROPULSIVE (TCP) GAIT The Torso Controlled Propulsive (TCP) gait will be broken into three main segments; the pre propulsive phase, the propulsive phase, and the ballistic single stance phase. These gait segments will be developed in the following sections of this chapter. The sequence of the TCP gait is shown in Figure 5 1. During the pre propulsive phase the torso is tilted downward to an acceptable starting position for the propulsive phase. This is done by slowly flexing both hips at an equal rate to lean the pilot's torso forward. After the torso is lowered, it will be accelerated back up by rapidly extending both hips during the propulsive phase. This will propel the biped forward out of double stance. A controller based on Partial Feedback Linearization (PFL) will be designed to generate the gait segment for this phase. The final phase of the gait is the ballistic single stance phase. In this phase, the biped completes the step by swinging the swing leg and falling forward into the next double stance. 8

43 Figure 5 1: The Sequence of the TCP Gait Figure 5 shows sample timing for the two legs of the bipedal system during the propulsive gait. Leg 1: Leg : Pre-propulsive Phase Pre-propulsive Phase Double-Stance Propulsive Phase Propulsive Phase Ballistic Single- Stance Phase Swing Phase Pre-propulsive Phase Pre-propulsive Phase Double-Stance t0 t t t Propulsive Phase Propulsive Phase t, t Swing Phase Ballistic Single- Stance Phase time t, t t 3 0 Figure 5 : Sample Timing Diagram for TCP Gait The trajectory for the propulsive phase is generated first. This is because the prepropulsive and single stance segments are generated based on the propulsive phase initial and final conditions. As such, the trajectory generation for the propulsive phase is discussed first in Section 5.. The trajectory generation for the pre propulsive and ballistic single stance phases is discussed in Section PROPULSIVE PHASE This section discusses the generation of the trajectory for the propulsive phase. A simplified model of a biped is controlled with a Partial Feedback Linearized controller (PFL) to propel the biped forward. PFL uses the inertial coupling between the actuated torso and the unactuated stance leg (about the ankle). First, the propulsive model of the human exoskeleton system will be described. Next, the viability of using the inertial coupling between the torso and stance leg to generate propulsion will be investigated. The section closes with the development and simulation of the PFL propulsion controller THE PROPULSIVE HUMAN EXOSKELETON SYSTEM MODEL A bipedal walker can be modeled as a kinematic chain for the legs with a torso attached at the pelvis. This model is identical to the acrobot underactuated system. 9

44 To simplify analysis, a double pendulum is used to model the biped in the sagittal plane for the propulsive phase. The top link represents the torso, and the lower link represents the stance leg, in which the knee is fully extended and locked. Assuming that the dynamic contributions of the swing leg to the bipedal system are negligible, the swing leg has been removed from this model. Actuation is provided at the hip joint between the two links while the ankle (bottom revolute, q 1 ) is unactuated. The simplified model is shown in Figure 5 3. l d m, I T q m1, I1 Torso v l 1 d 1 Stance Leg q 1 Figure 5 3: The Simplified Propulsive Stance Model CCW Angle is positive Dynamic equations for the propulsive stance model derived with Lagrangian analysis are shown below: hq, q M q q M q h q, q 0 T cos cos md m l d ld q I I md d l q I md d l1cos qi md I sin cos cos mld 1 qqq 1 q md 1 1ml 1 q1 md q1q g mldq 1 1sin qmd gcosq1q (5.1) The system has two degrees of freedom, q 1 and q, at the ankle and hip respectively. The matrix M is a positive definite inertia matrix. The parameters for the human exoskeleton system are shown in Table

45 Table 5 1: Parameters for the Human Exoskeleton Single Stance Model m 1 (kg) m (kg) l 1 (m) l (m) d 1 (m) d (m) I 1 (kg m ) I (kg m ) INERTIAL COUPLING A PFL controller will be used to compute the gait segment for the propulsive phase. PFL linearizes control of a nonlinear system through a nonlinear feedback policy. An introduction to Partial Feedback Linearization is given in the Appendix of this dissertation in Section For PFL to be viable, the dynamics need to be inertially coupled in the operating space. If inertial coupling holds, the torso can be used to generate propulsion to assist with transferring the human exoskeleton system out of double stance. Spong discussed various PFL controllers for the flip up problem of the Acrobot system ([61], [6]). The flip up maneuver is the process of bringing the Acrobot from a stable o equilibrium at q 90 0 T o, to an unstable equilibrium vertically up at q 90 0 T. The concept of using the actuated torso in the single stance model to propel the system forward is similar to the flip up problem. For strong inertial coupling to hold for this system, the off diagonal elements of the inertia matrix in equation (5.1), M1 M1, should be nonzero everywhere in the state space. The condition for this to hold is: min md d lcos q I 0 md ld I (5.) 1 1 In this system, strong intertial coupling does not hold due to singularities, but inertial coupling nevertheless holds in the range between the singularities. Using the parameters listed in Table 5 1, the off diagonal elements pass through 0 at approximately q 15 degrees. The control input of the torso in the passive space is nullified in these singular configurations. The off diagonal elements, M1 M1, as a function of q is displayed in Figure 5 4a. 31

46 a) 35 b) Operating Space 30 [kg m ] q S q S Torso Singularities Singularities Swing Leg [deg] Figure 5 4: a) Off Diagonal Inertia Matrix Elements Over Range of q, b) Operating Range of q in Single Stance Model Where Inertial Coupling Holds o o Inertial coupling holds in the range between the singularities for q 15,15. This result is beneficial because this encompasses more than the entire torso operating range that would be reasonable for a pilot to use. A depiction of the torso operating space is shown in Figure 5 4b PFL PROPULSIVE CONTROLLER DESIGN Using the general controller design algorithm laid out in Section 11.3 in the Appendix, the actuated degree of freedom is q at the hip, and the unactuated degree of freedom is q 1 at the stance ankle. Setting the active control input, v A, to be the angular acceleration of the torso, q, and solving for the control input yields the result: M q M v h 0 v M M q h (5.3) A 1 A The active control input, v A, exists as long as the torso is in the operating range where inertial coupling holds. The hip actuator has control authority over the angular acceleration of q. Setting the angular acceleration of the stance leg, q 1, to be a synthetic control input, v, and substituting the active control input from equation (5.3) into the dynamic equation for the actuated space, the nonlinear policy for hip torque based on equation (11.13) is: q 1 Stance Leg Stance Ankle 3

47 cos md I md 1 1 m l1 d ld 1 q I1I T mdd l1cos qi v md d l1cos qi md I mld 1 q qq 1sin qmd 1 1ml 1gcosq1mdg cosq1q mldq sin q mdgcosq q md d lcos q I 1 Defining a stable differential operator that will attract tracking error of the stance leg to zero yields: (5.4) e q q 1 1, d d dt e 0 e e e vq e e0 1, d (5.5) Using equation (5.5) to solve for the synthetic control, which is based on the desired dynamics of the passive link, results in the following: vq e eq q q q q (5.6) 1, d 1, d 1, d 1 1, d 1 The synthetic control shown in (5.6) will force tracking error of the passive link to zero as long as inertial coupling holds. This will be modified for use with a set point that will be used to describe the desired angle of the stance leg at the end of the propulsive phase. This set point, q 1,d, has a zero velocity and acceleration associated with it. Accounting for this, the set point based synthetic control is now the following: 1 1, d 1 v q q q (5.7) This is simply a proportional derivative controller, with the proportional part acting on the q 1 error and the derivative component acting to dampen the response Error Dynamics Defining z, as a state vector based on the tracking error of the stance leg: z1 e z z z z z Az 33 (5.8)

48 If is greater than zero, the matrix A is Hurwitz with eigenvalues at. Therefore, the stance leg tracking error will be attracted to zero. As long as the torso is in the operating range where inertial coupling holds, the nonlinear feedback hip torque policy results in stable linear control of the stance leg. The error dynamics can be described by the following homogeneous second order Ordinary Differential Equation (ODE): e e e0 (5.9) The variable x will replace e for error of q 1, and e now denotes the mathematical constant that is the base of the natural logarithm. It is assumed that the system starts from rest, x 0 0, and from an initial error state of x0 x0 yields the following error response: 34. Solving the ODE in equation (5.9) x t x t e (5.10) 1 t 0 The eigenvalues of A in the linear dynamic system above are the negative reciprocal of the time constant for the response of the error dynamics. As is increased, the response of the error dynamics becomes faster. It can be shown that the "rise time," which will be used to denote the approximate time duration of the propulsive phase, is approximately 4. Considering pilot comfort and limitations on actuator bandwidth, it is desirable to have a propulsive phase between 0.5 and 0.7 seconds. This time range was determined experimentally. Thus, values for should vary between 5.7 and PROPULSIVE PHASE SIMULATION RESULTS Simulation results for the PFL based controller were obtained using the properties listed in Table 5 1 and setting 16 to have a propulsive phase time of approximately 0.5 seconds. It was desired to have a step length of approximately 1 foot (0.30 meter), therefore the initial condition for q 1 was 100 degrees. The desired q 1 set point, q 1d, was set to 89 degrees. This value was chosen to propel the stance leg past the vertical at the end of the propulsive phase. Having q 1d set past the vertical does not guarantee a successful ballistic single stance, particularly if the hips over extend leaving the torso center of mass behind the stance ankle revolute joint. The initial condition for q was chosen through an iterative process considering the tradeoffs of pilot discomfort from tipping the torso, and the benefits of having a larger operating space to accelerate the torso (the internal 0 45 dynamics). A value of q degrees was used. The global torso angle, q1 q, at the beginning of the propulsive phase was 55 degrees from the horizontal.

49 Results for the PFL torso controller during the propulsion segment of the gait strategy are shown in Figure 5 5. a) 100 b) q 1,d [deg] [deg] time [deg] V t=0 t=0.5s Figure 5 5: Propulsive Phase Results a) Data showing stance leg and torso angles, b) Frames showing single stance system during propulsion phase The results show that the system model is propelled forward and would fall forward into the next double stance. This supports the concept of using the torso to propel the exoskeleton pilot forward to a higher potential energy state. 5.3 GENERATING AND SIMULATING THE COMPLETE TCP GAIT Results from the propulsive phase are used to generate both the pre propulsive gait and the ballistic single stance gait. The initial conditions for the propulsive phase dictate the final state for the pre propulsive phase. During this phase, the hips are slowly flexed at the same rate to tip the torso forward to the initial global torso angle at the beginning of the propulsive phase. The initial conditions for the ballistic single stance phase are defined by the terminating state of the propulsive phase BALLISTIC SINGLE STANCE After the system center of mass (CoM) passes the ankle revolute joint, the gait phase advances from the propulsive phase to the ballistic single stance phase. When this happens the controller switches to a torso stabilizer controller. This controller takes the form of a Proportional Derivative (PD) controller that is designed to keep the global torso angle, q1 q, constant. The torso stabilizer controller is the following: 35

50 1,, 1 1 T K p q switch q switch q q Kd q q (5.11) where q1, switch q, switch is the global torso angle at the time instant that the gait phase advances to the ballistic single stance phase FULL WALKER RESULTS WITH TCP GAIT The TCP gait strategy was tested using a seven link sagittal plane walker model developed with SimMechanics in the Matlab Simulink environment. To simulate the actual control strategy and trajectories that would be employed on the Austin exoskeleton, no dynamic controllers were used during the simulation. Instead, the trajectory was pre computed according to the three phases of the TCP gait shown in Figure 5 1. The first phase, the pre propulsive phase, was characterized by the torso being slowly leaned forward. The pre propulsive phase trajectory was based on a ramp that takes the torso from the initial pose in double stance to the initial conditions dictated by the propulsive phase. The trajectory for this phase can be somewhat arbitrary, as long as both hips comfortably flex at the same rate. The second phase, the propulsive phase, was based on the result of the PFL controller using the simplified propulsive model to propel the system out of double stance. Both hip actuators for the seven link model were controlled with equal rates of extension so there was pure torso movement based on the PFL results. The last phase, ballistic single stance, was based on the trajectory that resulted from stabilizing the torso as the simplified model fell forward to complete the step. The swing leg trajectory was based on CGA swing data during this period. The seven link biped model was based on the Austin exoskeleton with the coupled knee mechanism for controlling knee flexion and extension. The Propulsive Gait trajectories are shown in Figure

51 , [deg] DS Stance DS Swing, [deg] DS time [s] t 0 t 1 t Swing Using this trajectory on the seven link bipedal model produced favorable results. Frames showing the progression through the step are shown in Figure 5 7. DS Stance Figure 5 6: TCP Gait Trajectories for Two Hip Actuators Note: Time markers t0 t correspond to time markers shown on sequential gait strategy in Figure 5 1 a) b) c) t=0 t=1s t=1.3s t=1s t=1.5s t=.1s Show plots... Figure 5 7: Frames Showing Progression of 7 Link Walker Through the TCP Gait a) Pre propulsive phase b) Propulsive phase c) Ballistic single stance phase The trajectory required modest modification to work effectively. Most notably, the torso acceleration during the propulsion phase was made less aggressive. This was done because the swing leg contributed to forward progression during the single stance phase. The swing leg propulsion contribution diminished the reliance on the torso acceleration which allowed a less jarring propulsion phase. 37

52 5.4 PILOT TESTING OF TCP GAIT The TCP Gait was tested by a user with a T1 complete Spinal Cord Injury. Tests were performed in the exoskeleton testing and training center in the Berkeley Robotics and Human Engineering Laboratory. The pilot used the Austin Exoskeleton system and a modified (widened) walker ambulation aid to assist with balance and stability. The user was safety tethered at all times to an overhead rolling gantry to prevent falls, but was otherwise unencumbered. The pilot was free to walk around the training space as desired. The only instruction given to the pilot was to use the walker to only balance in the coronal plane and try to avoid pushing or lifting forward in the sagittal plane. This was instructed because the user had already trained in the Austin device for approximately 10 hours and was accustomed to having to propel himself forward throughout the gait. Another reason for the instruction to only balance in the coronal plane was to make the efficacy of the propulsion in the sagittal plane as clear as possible. If the pilot successfully progressed forward to the next step, the strategy would appear to be effective. Frames showing the test pilot during various phases of the propulsive gait are shown in Figure 5 8. a) b) c) d) Figure 5 8: Frames Showing Test Pilot Executing a TCP step a) time t0 b) time t1 c) time t d) between time t and t3 The joint angles during the step period were calculated by post processing video in the sagittal plane of the pilot taking steps using the method detailed in Section 11.1 of the Appendices. Angular data for the right and left hip and knee is shown in Figure

53 a) b) [deg] [deg] [s] The global torso angle, q1 q, and the global stance angle, q 1, both with respect to the horizontal plane, were extracted from the testing results. Figure 5 10 shows these angles through the duration of a step for both sides. It is apparent that the stance angle decreases as the torso is accelerated upward during the propulsive phase which begins at one second. This supports the propulsive concept that the acceleration of the torso causes the forward progression of the pilot Figure 5 9: Hip and Knee angles through Several Steps Using the TCP Gait on the Austin Exoskeleton a) Left side, b) Right side. Note: The dotted line denotes the separation of the stance and swing phases. [deg] [deg] [s] [deg] [deg] [s] Figure 5 10: Global Torso and Stance Leg Angles During a Step Using the TCP Gait The global torso angle is q1 q and the stance angle is q 1. Both are with respect to the horizontal plane USER FEEDBACK ON THE TCP GAIT The pilot acknowledged that he sensed the efficacy of the propulsion when interviewed about the TCP Gait. However, he felt that he was expending significant effort trying to keep the system balanced and brace his body through each step. He found the movements to be 39

54 unnatural and uncomfortable, particularly with the manner his torso was aggressively maneuvered. Additionally, user testing of this gait revealed that users with SCI may be very sensitive to aggressive torso movements. In one particular case, testing of the propulsive gait had to be terminated when the pilot became nauseous. This raises a concern for gait generation in patients with spinal cord injury who are actively managing pain with medication. As reported by Siddall et al, approximately 64 percent of SCI patients have lasting pain after their injury and take various medications such as opioids to try to manage pain [63]. Opioids commonly have many adverse side effects such as nausea stemming from motion sickness [64]. Therefore, a patient taking a prescription such as morphine may be more sensitive to having their torso involuntarily moved and the control engineer should take this into consideration when evaluating a potential gait. 5.5 EVOLUTION OF THE TCP GAIT This section will discuss early testing results of the Passive Knee Exoskeleton with minimal torso support. The torso component of the Passive Knee Exoskeleton was designed to be modular to provide flexibility in the level of trunk support that the user receives. Additional torso constraints can be added higher up the trunk as needed, depending on a variety of factors such as injury level and user preference. The torso in this minimally constraining configuration provides significantly less trunk support than the Austin hardware. In this configuration, the user's trunk is constrained by a belt that is secured across the navel region. Since the rest of the trunk is unconstrained, there is a lower level of control authority over the torso dynamics compared to the heavily constrained Austin hardware. This is largely due to the significant amount of compliance in the pilot's trunk that is free to move independent of the system. Therefore, it was determined that the TCP Gait would not be as effective as the original implementation with the Austin hardware. The initial trajectory for the Passive Knee Exoskeleton was designed without a propulsive element. The stance phase was based on CGA data while the swing phase was designed to provide knee flexion with the unpowered passive knee. Swing phase trajectory generation is discussed in Chapter 6 of this dissertation. The hip trajectories for the Passive Knee system are shown in Figure

55 , [deg] Stance Swing , [deg] Stance Swing [s] Figure 5 11: Gait Trajectory Used with Passive Knee Exoskeleton PASSIVE KNEE EXOSKELETON TESTING RESULTS The Passive Knee Exoskeleton was extensively tested by a user with a T1 incomplete spinal cord injury. The test pilot had approximately 1 hours of experience using the suit by the time data was collected. The objective of this experiment was to investigate how the user was controlling their torso. The user had a large amount of control over his trunk dynamics through his ambulation aid, a set of crutches in this case. The user was instructed to walk down a path approximately 0 feet long (~6.1 meters) as video was recorded in the sagittal plane. When the pilot reached the end of the path, he turned around and walked back the other way. The user was given no other instructions as it was desired to examine how the user learned to ambulate with the basic gait trajectory shown in Figure Tracking markers were placed on the pilot at the shoulder, hip, knee, and ankle on each side. Video was collected at 10 frames per second in the sagittal plane. The video was post processed to extract position data of tracking markers. Angular data was extracted using the protocol discussed in Section 11.1 of the Appendices. Data revealed that the pilot learned to implement his own double stance phase. Shortly before triggering each step, the pilot readied himself by placing both crutches in front of him and lowering his torso down. Then, upon triggering the step, he gradually raised his torso back up through the duration of the step. This process is shown in Figure

56 a) b) c) d) Figure 5 1: Frames Showing Test Pilot Executing a Step With the Passive Knee Exoskeleton a) time t0 b) time t1 c) time t d) between time t and t3 In essence, a gait evolved that is similar to the propulsive gait previously developed. However, instead of having the propulsive phase before the single stance phase, the torso is raised throughout the step. Angular data is presented in Figure a) b) [deg] [deg] [deg] [s] [deg] Gait data is shown that includes the time period before the step is commanded. This time period of 0.6 seconds is approximately the time period that the pilot is initiating the step and lowering his torso. As shown in Figure 5 13, the stance period is between times 0.6 and 1.8 seconds, and the swing period is between times.4 and 3.6 seconds for the left leg. The stance and swing periods are reversed for the right leg. The double stance periods are approximately between 0 and 0.6 seconds and 1.8 and.4 seconds [s] Figure 5 13: Hip and Knee Angles Through Several Steps Using the Passive Knee Exoskeleton a) Left side, b) Right side. Note: The dotted lines denote the separation of various gait phases 4

57 Figure 5 14 shows the torso and stance leg angles with respect to the horizontal plane. Using the standards defined in Figure 5 3, the global stance leg angle is q 1 and the global torso angle is q1 q (generalized coordinates). [deg] [deg] [s] Figure 5 14: Global Torso and Stance Leg Angles During a Step with the Passive Knee Exoskeleton The global torso angle is q1 q and the stance angle is q 1. Both are with respect to the horizontal plane STANCE CONTROL CONCLUSIONS The user developed his own method of initiating gait that he found the most comfortable and required the least amount of effort by him to propel himself forward out of doublestance. A central tenet for control design in the Berkeley Robotics and Human Engineering Laboratory is that the human is the central control element. Giving the user greater control of their own torso dynamics may be a possible solution to the shortcomings of the first implemented propulsive gait. Individuals that are more motion sensitive may benefit from controlling their own torso dynamics rather than controlling it for them. In short, the user is in the best position to determine which gait is most comfortable for him, so user feedback is essential to developing gait control strategy. 43

58 6 SWING PHASE CONTROL WITH PASSIVE KNEES This chapter discusses the control of a swing leg with an unactuated knee. A hybrid model of the swing leg will be developed and used to generate the trajectory of the swing hip that will control flexion of the unpowered knee. The concept of controlling the unpowered knee with the swing hip was initially tested with the Austin Exoskeleton prior to developing the Passive Knee Exoskeleton. The initial passive knee test with the Austin Exoskeleton is described in Section 11.4 in the Appendices. This chapter concludes with experimental results that support the efficacy of the generated hip trajectory. 6.1 THE SEQUENCE OF THE SWING PHASE The unpowered swing knee will be dynamically controlled by the motions of the swing hip. A model will be designed and used as a tool to generate the swing hip trajectory that will yield a desired knee flexion profile throughout the swing cycle. The swing cycle is assumed to be a sequential process. The process begins in double stance with the swing foot on the ground and the knee fully extended. As the leg starts to swing, the swing toe rises off the surface. After toe off, the swing leg is assumed to behave in a pendular manner. During the pendular period, the swing knee will be dynamically controlled to flex so that the swing toe will clear the ground. The swing knee will then re extend in late swing to prepare for heelstrike. The moment of full re extension is assumed to be an inelastic collision. After full extension, the knee is locked in line with the swing thigh shank. The swing sequence is shown in Figure 6 1. t t 0 hip F hip Figure 6 1: Swing Generation Sequence 44

59 Throughout the sequence, the swing leg is modeled as a double pendulum moving through space. When the process begins in double stance, the foot is kinematically constrained to move on the surface of the ground until it dynamically rises from the surface. The dynamics for the pendular phase will be developed in Section The post knee impact conditions and the dynamics for the locked leg are described in Section 6... The sequential swing model will be used in Section 6.3 to design a swing hip trajectory. Desired knee dynamics throughout the swing phase will be defined. These knee dynamics will be used to solve for the necessary hip dynamics through the gait sequence. Section 6.4 discusses results from implementing a resultant swing trajectory with the Passive Knee Exoskeleton. 6. THE SWING LEG MODEL 6..1 PENDULAR PHASE Many different swing leg models of varied complexities have been designed for a variety of purposes ([65]) such as to aid in the design of prosthetics, the study of various gait abnormalities and conditions, and the investigation of various issues in walking energetics [66]. For this investigation, a double pendulum model for the thigh and knee shanks are used and the hip joint is assumed to be moving through space. This model is similar to other models developed for the design and control of prosthetic knees [[65], [67], [68]], however the foot is assumed to be rigidly attached at the ankle. This is an acceptable simplification because the orthotic knee joint on the exoskeleton system is very stiff to minimize flexion of the ankle. The swing leg model is shown in Figure 6. 45

60 a 0 y T hip 1 m I d 1 1, 1 hip a 0 x l 1 T knee d l m, I d 3 knee l 3 foot a m3, I3 Figure 6 : Swing Leg Model The foot is considered to be rigidly attached at the distal end of the knee shank. The quantity of knee flexion is, assuming the knee rotates about Ez and hip flexion is 1. The dynamics for the two degree of freedom swing model are as follows: M 1 a0 x H A T g a 0 y 1, (6.1) M is defined as a square positive definite inertia matrix: a M md m m l m d m l d ld cos l d cos a 3 a md ml lcos I I I M md md ml lcos m l d ld cos ld cos I I M M M m d m l d l d cos I I The H matrix is defined as: a a (6.) 46

61 H H H H ml 3md sinmd 3 3sin + a l 1 l 1 1 md 1 1ml 1ml 3 1sin1ml 3 md sin 1+ md 3 3sin 1+ + a md m3lsin m3d3sin l 1 1 m d m l sin m d sn i a (6.3) The A matrix is defined as: cos cos + cos + + a sin sin + sin + + a cos cos a sin sin A md m m l m l m d m d A md m m l m l m d m d A m d m l m d A m d m l m d a (6.4) The torque vector is defined as: T T Thip T knee (6.5) The knee joint is assumed to be a passive joint with linear damping. Therefore, the torque at the knee is assumed to be: Tknee b (6.6) 6.. KNEE RE EXTENSION AND LOCKED KNEE DYNAMICS The impact of the knee joint reaching full extension is considered to be an inelastic collision. The knee is assumed to have a locking mechanism that keeps the knee fully extended in line with the hip link. When this happens, the system becomes a single pendulum (with 0 ) moving through space. The dynamics for the single degree of freedom pendulum after full re extension is described with the following equation: M A a A a h g T (6.7) S 1 S,1 0 x S, 0y S hip The dynamic variables are defined: M S a 1 cos cos a md 1 1 ml1 d m3l1 lsin1 md 3 3sin 1 a sin sin S, S, S md m l d m l l d d l l cos I I I A md m l d m l l m d A 1 1 a h md m l d m l l m d A S, 3 (6.8) 47

62 Immediately after the impact of full re extension of the knee, the integrator initial conditions are calculated by considering that rotational momentum is preserved about the hip joint. It can be assumed that position before and after the impact are the same, but that rotational velocity changes instantaneously after the impulse. The initial conditions are as follows: M M M S (6.9) The superscript and + represent the conditions immediately before and after the impact, respectively. The rotational velocity of the hip after impact can be calculated by solving for : 1 M M M (6.10) 1 1 S The knee is assumed to be stationary with respect to the hip, 0, after full re extension MOTION OF THE PELVIS THROUGH SPACE The swing hip axis of rotation is assumed to be perfectly in line with the stance hip in the sagittal plane. The translational dynamics of the hip will be defined by the stance leg dynamics as the human exoskeleton system makes forward progress through the step. While the stance leg could be in any pose, for this exercise the knee is assumed to be perfectly extended throughout stance ( knee,stance 0 ). Figure 6 3 shows the lower extremities through the duration of a step. The stance angle, S, is defined as the angle between the stance leg and the horizontal plane. In this model, when the stance angle is greater than 180 o a, the stance leg is assumed to rotate about the stance heel. As the system progresses forward, when the stance angle is 180 o S a, the point of rotation instantaneously switches to the stance toe. This assumption is made to approximate the behavior of the rigid ankle foot orthotic that is on the exoskeleton. 48

63 a) a b) 0 y a 0 y a 0 x a 0 x 1 hip,1 hip, S stance leg l l 1 knee v stance foot l 3 a a Figure 6 3: The Lower Extremity Progression Through a Step to Define Translational Dynamics of the Pelvis a) At the initiation of a step b) approximately halfway through a step The progression of the stance angle through the step can be treated as a design degree of freedom. In this work, all swing trajectory generation uses experimental stance angle data to define S through the step. This is determined to be an acceptable simplification because it is assumed that the swing leg behavior will not significantly alter the stance dynamics. With these assumptions, the translational accelerations of the pelvis throughout the step can be defined. As the stance leg rotates about the heel ( 180 o ): S a a a 0 x 0 y l1l S sins S coss l1l S coss S sins (6.11) The translational accelerations of the hip as the stance leg rotates about the stance toe are: S l1 l S l 3 S a S l1 l S l3 S a cos cos l sin l sin S a0 x sin sin cos cos a l l l l 0y S 1 S 3 S a S 1 S 3 a Figure 6 4 shows sample data for the stance angle, S t accelerations of the hip through a step of duration 1.1 seconds., and the translational (6.1) 49

64 [deg] [s] [m/s ] [m/s ] Figure 6 4: Stance Leg Dynamics and Translational Accelerations of the Hip Joint Through Space During a 1. Second Step [s] 6.3 SEQUENTIAL SWING PHASE TRAJECTORY DESIGN This section discusses the sequential swing phase trajectory for the swing leg. The sequence depicted in Figure 6 1 defines the order of the swing phase trajectory generation process. The swing models for the various phases will be used to determine the necessary hip dynamics as a function of the desired knee dynamics. The desired knee dynamics used in this process are based on human CGA data. Figure 6 5 shows the simplified knee flexion profile based on clinical gait analysis data from [51] Human Simplified 50 [deg] % Figure 6 5: Knee Flexion Profile Based on Human Clinical Gait Analysis Data. A simplified profile based on a sinusoid is also shown. 50

65 The desired knee dynamics based on human CGA are described by a piecewise function that transitions halfway through the swing phase. The knee dynamics for the first half of F the swing phase ( t 0, t ) are described by a squared sinusoid: knee knee knee t sin t t sin t t cos t (6.13) tf For the second half of the profile ( t, t knee dynamics: F ) a regular sinusoid is used to describe the knee knee knee t sin t t cos t t sin t (6.14) Where is the maximum flexion magnitude, t goes from 0 to t, and F t. The squared F sine was chosen for the first half of the flexion profile so that the knee starts with zero velocity, as opposed to a standard sinusoid which starts with maximum velocity at t 0. This piecewise approximation was also chosen because it resembles the human knee flexion profile through swing. These choices further the goal of the control work to enable natural, human like walking. Fundamentally, walking is a periodic process. Therefore, the gait is assumed to be symmetric with the end of the swing phase mirroring the beginning. In other words: t 0 t t t hip hip F 0 0 knee knee F (6.15) In this equation, t F is the time at the end of the swing phase. The initial hip angle is t 0 15 degrees, which would make the hip angle at t F equal to +15 assumed to be hip degrees. Initial hip velocity is zero because the pilot is at rest. Using the knee flexion dynamics defined in equations (6.13) and (6.14), and the hip translational dynamics defined in equations (6.11) and (6.1), the hip angle through the swing phase can be computed using the sequential swing model. 51

66 6.3.1 DOUBLE STANCE PHASE GAIT GENERATION The first phase, which is labeled "Double Stance," is the period before toe off where knee flexion begins. During this period, the hip trajectory is kinematically computed to follow the knee flexion profile considering that the swing toe is still in contact with the ground. Throughout the double stance phase, the pendular dynamics are referenced to identify the moment that the swing foot would dynamically come off the ground. When toe off occurs, the sequence advances to the pendular dynamics phase PENDULAR PHASE GAIT GENERATION The model developed in the previous section is used as a tool to solve for the hip dynamics as a function of desired knee dynamics. It is assumed that the swing model is an accurate representation of the actual swing leg dynamics. The tuning and validation of the pendular phase swing model is described in the Appendices in Section Throughout the pendular period, the hip dynamics can be solved for as a function of the knee flexion and hip translational dynamics using the second dynamic equation from (6.1): 1 1 M 1 Tknee M H1 Hg A1a0 x Aa 0 y (6.16) The hip dynamics are well defined as long as M 1 is never zero. This condition is referred to as strong inertial coupling and is discussed in Section 11.3 in the Appendices KNEE IMPACT CONDITIONS CALCULATION To decrease the likelihood of toe drag in late swing, the knee flexion period is slightly shorter than the total swing period. This is based on the assumption that the trajectory of the pelvis through space during a step resembles an arc. Therefore, the height of the pelvis is at a minimum at the beginning and end of each step. When the knee fully extends, the sequence advances to the knee impact state where the knee is assumed to inelastically collide with a mechanical hardstop. At this state, the post impact hip velocity is recalculated according to equation (6.10) LOCKED LEG PHASE GAIT GENERATION The swing phase is completed after the swing leg is lowered for heel strike. The trajectory is computed for this phase with a cubic spline of the following form: Where hip t tt c tt c tt (6.17) 3 hip hip hip i i 3 i is the angle of the hip at impact of full knee re extension, hip is the post impact angular velocity, t i is the time of impact, and the coefficients c and c 3 are determined by 5

67 the boundary value problem assuming that the hip ends at zero angular velocity and at an angle mirroring the initial hip angle. The final hip angle mirrors the initial hip angle so that the gait is symmetric SWING HIP TRAJECTORY GENERATION RESULTS The swing model was tested over a variety of swing periods with a maximum knee flexion amplitude of 70 o ( 70 o ). The tuned model parameters are listed in the appendices in Table 11 1 and Table 11. Results for a successful swing cycle are presented for a step time of 1.1 seconds. The knee pendular period was set to be approximately 80 percent of the full swing cycle, or 0.9 seconds. The resulting hip trajectory and anticipated knee flexion profile are shown in Figure 6 6. a) b) [deg] [deg] [s] Toe off for the swing leg occurs at approximately 0.15 seconds after which the swing foot has acceptable toe clearance throughout the step. The swing toe does not return to 0 at the end of swing because at heel strike, the heel contacts the ground and leaves the toe slightly elevated. A series of frames showing the lower extremities throughout the swing phase are displayed in Figure 6 7. [cm] [s] Figure 6 6: Swing Phase Generation Results a) Trajectories for the hip and knee b) Toe clearance throughout the swing phase Figure 6 7: Frames Showing the Lower Extremities Throughout the Swing Phase Stance leg and foot are represented by dashed lines 53

68 6.3.6 ACTUATOR CONSIDERATIONS It is important that the motor and transmission are properly paired to fulfill torque and bandwidth requirements in the process of designing the actuation units for a medical exoskeleton system. If the units are overpowered, the actuation units will add unneccesary mass and girth to the system. If the units are underpowered, they will not be able to properly assist the pilot in ambulating with the system. To assist with actuation design, the hip torques throughout the swing cycle can be estimated with the system dynamics obtained from the simulation. To estimate the torques during the pendular period, the first dynamic equation of (6.1) is used. To estimate hip torques after full knee re extension, equation (6.7) is used. The torque and angular velocity data of the hip during swing is shown in Figure 6 8 below [Nm] [RPM] Figure 6 8: Torque as a Function of Angular Velocity During the Swing Phase The start of swing is denoted with a * To ensure a properly designed actuation unit, the torque versus angular velocity curve should safely fit within the limits of the actuation performance. Neglecting motor inductance, the voltage through a winding of a motor can be modeled with the following: V ir KB (6.18) Where R is the winding resistance, i is the current through the winding, K B is the voltage constant or "Back Electromotive Force," and is the rotational speed of the motor. Assuming the torque output of the motor is linearly proportional to the current across the motor winding: T motor K i (6.19) T 54

69 Where K T is the torque constant of the motor. Combining equations (6.18) and (6.19), an expression for the maximum torque a motor can produce is obtained: K (6.0) R T Tmotor V KM K M is defined as a motor constant where K K K R T B M. It is evident that the motor torque versus speed is defined by a line that connects a maximum torque of motor is stalled ( 0 ), and a maximum speed of V K B KT V R where the where there is no load on the output of the motor. This line defines the boundaries of the motor performance. At this performance limit, excessive heat may damage the internal components of the motor. To consider power dissipation, a continuous power performance limit can be calculated. With these limits in place, the continuous power limits can be obtained with this simple relationship [69]: KD TPR K K T T B (6.1) M T Where T is an admissible temperature increase, TPR is the temperature rise per watt, T is the root mean squared (RMS) torque, and D is the damping through the actuation unit. A small actuation unit that consists of a Maxon EC90 flat profile pancake motor connected to a harmonic drive transmission with a 100:1 gear reduction will be considered. The torque output at the hip will be assumed to be amplified by 100 through the transmission, so Thip 100TMotor. The output of the transmission is assumed to be one percent of the motor speed. The data for this actuation unit is shown in Table 6 1. It should be noted that the damping value used is the damping constant from the harmonic drive transmission because it is assumed to be the most significant source of damping at the hip. Table 6 1: Actuation Unit Parameters R (Ω) K T (Nm/A) K B (V/rad/s) K M (Nm/ ) V (V) ( o C) TPR ( o C/W) D (Nm/RPM) e 5 Figure 6 9 shows the motor plot considering the actuation unit discussed. The motor performance line and continuous power curve are shown, in addition to the motor 55

70 performance requirements during swing. All torque and angular velocity data from the simulation have been moved into the first quadrant. 6 5 Swing Motor Line Continuous Power (Nm) (RPM) Figure 6 9: Motor Performance Plot with Swing Requirements The actuation unit under consideration is well designed to handle the swing phase of the walking cycle. The motor speed needed is very close to the limits of the motor performance, but the torque speed curve is well below the continuous power line. Therefore, there is minimal risk of damage to this actuation unit during the swing phase. 6.4 USER TESTING OF THE SWING TRAJECTORY The swing trajectory developed in the previous section was implemented on the Passive Knee Exoskeleton and tested by a pilot with a T 1 incomplete spinal cord injury. Testing was completed in the Berkeley Robotics and Human Engineering Laboratory in accordance with the Berkeley Committee for Protection of Human Subjects. The subject was asked to don the exoskeleton suit and stand up. The pilot was then allowed to practice taking steps using parallel bars for support until he felt confident walking with crutches. Point tracking markers were placed on the shoulder, hip, knee, and ankle of each side of the pilot. As the pilot took steps using crutches for support, a high frame rate camera was used to capture video of both legs in the sagittal plane during several swing phases. The hip and knee angles were extracted from the point tracking data using the geometric relationships shown in Section 11.1 of the Appendices. The hip and knee angular data for the left and right sides is shown in Figure

71 a) b) [deg] [deg] [s] The gait consistently produced between 75 and 80 degrees of knee flexion which provided ample toe clearance during walking. The exoskeleton knee starts and ends hyper extended (at a negative angle) to minimize the locking load needed at the knee during weight bearing periods. A comparison of experimental knee flexion results to simulated results is shown in Figure The human flexion profile from [51] has been scaled to match the maximum amplitude ( ) of the simulated profile for comparison purposes. [deg] [deg] Figure 6 10: Experimental Swing Phase data a) Left Leg (10 swings) b) Right Leg (8 swings) [s] a) b) Human Simplified Human Simplified [deg] [deg] % % Figure 6 11: Swing Phase Knee Flexion Profile Comparison to Scaled Human Data [51] (dotted) and the Simplified Profile (dashed) a) Left Leg (10 swings) b) Right Leg (8 swings) The results show that the general shape of the simulated and experimental knee flexion profiles generally agree. The experimental results yielded a higher maximum amplitude of knee flexion than the simulation predicted. This is a positive result because this produces 57

72 more toe clearance. This discrepancy is due to un modeled dynamics. If the simulated maximum knee flexion amplitude,, is increased to 75 degrees, the resulting hip trajectory requires higher motor speeds than the actuators can provide. Several other factors contribute to the slight differences in the flexion profile from the simulation results. The exoskeleton has significant compliance at the user's thigh which allows abduction of the hip. The interface between the pilot and the exoskeleton is not a rigid connection. Rather, the various pilot constraints are soft pliable interfaces. Additionally, the exoskeleton torso is loosely attached at the user's abdomen, which allows a moderate amount of hip drop to occur throughout the step. This alters the arc like trajectory of the pelvis that was one of the assumptions in the modeling process. The hipdrop may actually extend the "double stance" period prior to toe off, which may account for some of the additional knee flexion. All factors considered, the knee flexion profile consistently yields 75 to 80 degrees of knee flexion and sufficient toe clearance throughout the step. The pilot was able to comfortably and effectively walk with this gait. 58

73 7 PILOT TESTING OF THE PASSIVE KNEE EXOSKELETON This chapter discusses the extensive testing of the Passive Knee Exoskeleton. Results will be presented from a variety of tests, including a 10 Meter Walk Test (10MWT), a quarter mile time trial, and extended walks through unstructured environments. One test pilot was used for all testing. The user had approximately 10 hours of use before any results were collected. At the time the first test began the user had a high level of confidence using the suit. The test pilot is a 30 year old male with a T 1 incomplete SCI. He normally ambulates using leg braces that lock his knee joints in the fully extended position. The pilot uses crutches with a swing through gait. The swing through gait is a method of ambulation where the user lifts his or her body to swing both lower extremities forward like a pendulum. This pilot is unique because rather than using a wheelchair as his primary mode of ambulation, he is familiar with being upright and balancing with crutches METER WALK TEST (10MWT) The 10MWT is commonly used as a means to assess the walking abilities of SCI patients. The test involves timing a participant walking a 10 meter distance at a self selected speed. The 10MWT is quick to administer and results have been shown to have a high correlation with ambulatory functioning [70]. This test will be used to determine the comfortable walking speed of the pilot using different methods of ambulation combined with different walking aids. This implementation of the 10MWT is similar to the testing strategy employed by Farris et al [71] MWT METHODS The 10MWT was completed on a flat and level surface. The testing track was prepared by placing markers at 0,, 8 and 10 meters along the surface. The participant had the first meters to accelerate before timing began at the meter mark. The middle 6 meters were timed between the and 8 meter markers. The participant had the final meters to decelerate. Eighteen runs of the 10MWT were completed with the pilot. This consisted of 6 sets of 3 runs each. Each set tested the pilot walking with the exoskeleton or leg braces, using crutches or a walker. When the pilot used leg braces, he employed either a swing through gait or a reciprocating gait. The pilot can make a reciprocating gait by keeping one foot planted on the ground while manually swinging the other leg forward in a pendular manner by accelerating his hip. 59

74 Before each run began, the pilot's heart rate was measured using a finger pulse oximeter (SantaMedical SM 110). The pilot's pulse was measured again after each run was completed. The pulse was measured within 30 seconds after completion, which gave the pilot time to maneuver to a wall where he could lean and safely provide access to his right index finger. After each set of 3 runs was completed, the pilot was asked to assess his level of exertion using the Borg Rating of Perceived Exertion (RPE). The Borg RPE provides a means for test pilots to subjectively evaluate their level of physical strain and effort [7] during each set of runs. The Borg RPE rating sheet that was handed to the test participant is located in Section 11.6 in the Appendices MWT RESULTS The six sets of three runs were completed in the following order: 1. Exoskeleton with crutches. Exoskeleton with walker 3. Leg Braces with crutches, swing through gait 4. Leg Braces with walker, swing through gait 5. Leg Braces with crutches, reciprocating gait 6. Leg Braces with walker, reciprocating gait Table 7 1 shows the average timing and speed results for the middle six meters along with associated average change in heart rate and RPE rating for the six sets of 10MWT tests. Table 7 1: 10MWT Testing Results Test t (s) Speed (m/s) BPM Borg RPE Exoskeleton with Crutches 7.4 ± ± ± Exoskeleton with Walker 9.5 ± ± ± Braces, crutches, swing through 11.5 ± ± ±.6 11 Braces, walker, swing through 9.7 ± ± ± Braces, crutches, reciprocating 9. ± ± ± Braces, walker, reciprocating 37.1 ± ± ± The pilot wearing leg braces using crutches while doing a swing through gait provided the fastest means of ambulation. This result was somewhat expected as this is the pilot's normal mode of ambulation. Additionally, the swing through gait results in approximately twice the distance covered per step compared to a normal reciprocating gait. The exoskeleton results are more directly comparable with results for leg braces while using a reciprocating gait. This is a more reasonable comparison because the reciprocating gait is more akin to natural human bipedal walking. The pilot ambulates faster wearing the exoskeleton and using a walker than using leg braces and walker with a reciprocating gait. 60

75 The difference in speed between the two sets was found to be significant (p=0.014). However, the speed results for the testing sets using crutches were not found to be significantly different (p=0.356). Heart rate results are also presented in Table 7 1. However, differences in heart rate between testing sets using a walker (p=0.708) and crutches (p=0.190) are not statistically significant. This may be largely due to the short testing duration of the 10MWT and the limited sample sizes. The pilot said that he felt very comfortable ambulating with the exoskeleton using either crutches or a walker. However, he felt the exoskeleton with a walker required slightly less exertion, as shown by an RPE of 11. The RPE for the reciprocating gaits with leg braces and the exoskeleton with crutches were all relatively high at QUARTER MILE TIME TRIALS The exoskeleton was tested at a track facility so that performance over longer distances could be evaluated. The 10MWT produced limited results that were insufficient for drawing conclusions on sustained walking speeds due to the short testing duration. A quarter mile (~400 meters) is a more significant distance that should provide ample testing time to monitor speed and heart rate QUARTER MILE TIME TRIAL METHODS Testing was completed at the track in Edwards Stadium on the University of California, Berkeley campus. Comparative testing was completed using the exoskeleton and leg braces. Testing was broken into four eighth mile runs for a total of 0.5 miles ambulated. Therefore, a quarter mile was walked with both the exoskeleton and the leg braces. Testing was done in an ABAB pattern for eighth mile runs beginning with the exoskeleton. When only leg braces were tested, the torso power unit was removed to leave only the leg bracing structure. Additionally, the legs were connected together with constraints so the pilot could ambulate with a swing through gait. Testing time was monitored by two individuals. The final time was the average of the two results. Heart rate data was collected by a Garmin Forerunner 50 device. A sensor was strapped on the pilot's chest that wirelessly transmitted heart rate data to a receiver approximately every five seconds (0.Hz). 7.. QUARTER MILE TIME TRIAL RESULTS The pilot successfully walked a quarter mile both with and without the exoskeleton device. Timing results are presented in Table 7. 61

76 Table 7 : Timing Results for Quarter Mile Time Trials Segment Distance (m) Time (s) Total Time (s) Average Speed (m/s) Exoskeleton A Exoskeleton B Leg Braces A Leg Braces B The pilot ambulated with a greater average speed for both exoskeleton and leg brace quarter mile runs compared to respective results of the 10MWT. This is interesting because these higher speeds were sustained over a significantly longer distance and the acceleration phase was included in each segment of the test. As expected, the pilot had a considerably higher average speed using leg braces with a swing through gait than walking with a reciprocating gait using the exoskeleton. However, the pilot sustained a similar cadence of one step approximately every two seconds for both methods. This supports the assertion that the swing through gait is faster because of the increased distance covered per stride. Heart rate data throughout both eighth mile runs is shown in Figure 7 1. a) b) [BPM] [BPM] [s] The difference in the pilot's exertion as measured by his heart rate was not found to be statistically significant between the two sets (p=0.691). The average heart rate using the exoskeleton was 86.8 beats per minute while the tests with leg braces yielded an average of 86.9 beats per minute. The pilot commented that he felt very comfortable ambulating with both methods and could have walked considerably longer. He also felt that his exoskeleton [s] Figure 7 1: Heart Rate Throughout the Quarter Mile Tests a) Using exoskeleton, b) Leg braces. Note: Vertical dashed line separates eighth mile runs

77 walking speed was largely limited by the speed the exoskeleton would walk rather than by his own abilities. The results overall are largely positive because they demonstrate that the exoskeleton can be used as a practical means of ambulation for extended distances in a structured environment. 7.3 ENDURANCE TESTING IN UNSTRUCTURED ENVIRONMENTS The exoskeleton was used to walk longer distances in unstructured environments. The exoskeleton pilot walked through the varied terrains of the University of California, Berkeley campus on several different days. Results are presented here for endurance walks on two separate days. The routes through campus are presented in Figure 7. The walks were approximately 0.6 miles (~965 meters) and 0.8miles (~1390 meters) on the first and second days respectively. a) b) Figure 7 : Route of Two Walks Through the University of California, Berkeley Campus a) walk 1, length 0.6mi, b) walk, length 0.8mi (Map data from Google) There was no testing protocol for the walks. The pilot walked at a comfortable, selfselected speed and was free to take breaks as desired. The first walk took approximately hours to complete including breaks, which is an average speed of about 0.13 meters per second. The second walk took 1 hour and 35 minutes including breaks to get to the point that the first walk concluded. Unfortunately testing had an extended delay due to technical 63

78 issues. The average speed had increased to 0.17 meters per second before testing was delayed. The pilot had no significant problems throughout the endurance testing sessions. He generally found walking through the unstructured environments to be relatively intuitive and not too strenuous. There is an elevation drop of approximately 150 feet (~46 meters) in the direction the pilot did the walking routes through campus. Therefore, he was generally walking downhill which is expected to reduce effort needed to ambulate. When the pilot encountered a slight up slope, he was required to bring his feet together so he could do short swing through steps to make it up the slope. This is largely because toeclearance throughout a normal step using the exoskeleton is not high enough to walk up positive inclines. The walking routes required the crossing of two intersections. At these intersections the pilot had to walk using the crosswalk when it was safe to do so. While the pilot was not harmed, the exoskeleton is not currently able to walk fast enough to make it through the intersection without disrupting traffic. Ambulation standards have been set that dictate walking speeds that an individual should be able to attain to be a "community walker." These standards are determined by a variety of speed requirements that an individual should be able to attain to be functionally independent [73]. Walking speeds between 0.5 and 1.4 meters per second are recommended depending on the walking environment ([74],[75]). Referencing results from the 10MWT and quarter mile tests, the exoskeleton is currently not able to attain those speeds OTHER REAL WORLD SCENARIOS This section discusses three scenarios in which the user was able to successfully adapt and operate the system to achieve a desired outcome. An exoskeleton user may be able to climb steps while wearing the system. In one situation, the test pilot was able to maneuver into a bus while wearing the exoskeleton. Many busses have lifts that enable wheelchair users to board the bus. However, the pilot was able to board a non accessible bus by lifting his body up the stairs with his feet together. He supported himself using a handrail in the stairwell and his right crutch as he progressed up the stairs. This process is depicted in Figure 7 3. The minimal and light weight design of the exoskeleton enables the user to adapt and handle physical challenges that may be restrictive to a wheelchair user. 64

79 Figure 7 3: An Exoskeleton Pilot Boarding a Non Accessible Bus The exoskeleton can also be used in tight and narrow spaces that an individual may regularly encounter. A small convenience store may have aisles that are too narrow for a wheelchair. The pilot was able to ambulate through a convenience store and a restaurant while wearing the exoskeleton. An individual wearing the exoskeleton potentially has the ability to get into a vehicle without removing the system. The exoskeleton pilot demonstrated this by getting into a standard vehicle without removing the system. The pilot was even able to drive a retro fit vehicle while wearing the suit. Figure 7 4 shows the pilot in a vehicle while wearing the exoskeleton. In contrast, a typical independent wheelchair user must transfer to the driver's seat, and then collapse and load their wheelchair from within the vehicle. Thus, the exoskeleton may enable users to board cars more efficiently. a) b) c) Figure 7 4: An Exoskeleton Pilot Getting into a Standard Car a) The pilot lowering himself into the driver's seat, b) the pilot in the driver's seat shutting the door, c) the pilot sitting in a passenger seat 65

80 8 MINIMALLY ACTUATED DOUBLE STANCE (MADS) PROPULSIVE GAIT This chapter discusses a second method of generating torques for the hip actuation units during the double stance and single stance phases. The double stance phase will be used to accelerate the exoskeleton and pilot forward so that the system can advance through the step with minimal input from the pilot. For this gait strategy, it is assumed that the exoskeleton knees have computer controllable knee flexion locking mechanisms. If the knee is locked, flexion of the knee is prevented, however the knee may still freely extend. If the knee is unlocked, the knee is free to rotate in either direction. In the double stance phase, the rear leg will be referred to as the swing leg, even though it is planted on the ground in stance. The front leg will be referred to as the stance leg. In double stance with both feet planted, if the swing knee is locked and the stance knee is unlocked and allowed to flex, the lower extremities resemble a four bar mechanism. The four bar kinematics enable the translation of the torso in the forward direction. Mochon et al. proposed that a bipedal walker can "ballistically" follow through the single stance segment of a step with no energy added to the system if conditions are properly set during double stance before toe off of the swing leg [76]. The Minimally Actuated Double Stance (MADS) gait is based on this principle. If the system is accelerated forward to a high enough speed during the double stance phase, the system will continue to travel forward to complete the step. 8.1 INTRODUCTION TO THE MADS PROPULSIVE GAIT To design a gait that will bring the human exoskeleton system from one double stance to the next, the MADS gait process is broken into two discrete states. The first state is the double stance phase. This state is depicted in Figure 8 1a. The walker has both feet planted on the ground and the stance knee is unlocked while the swing knee is locked against flexion. The human exoskeleton system is assumed to start from rest in doublestance and the lower extremities resemble a four bar mechanism. During this state, the human exoskeleton system is accelerated forward by flexing the stance hip and extending the swing hip. At the end of double stance, the stance knee is locked against flexion and the swing knee is unlocked. If the system is traveling forward as the stance knee is locked, the swing foot will naturally come off of the ground. 66

81 The state after double stance begins on toe off of the swing leg. This state will be referred to as the ballistic single stance phase. This phase is shown in Figure 8 1b, omitting the swing leg for simplicity. a) b) Torso Torso t 0 v t 1 t 1 t Swing Leg Stance Thigh Stance Thigh Stance Knee Stance Knee Figure 8 1: Discrete Walking States of the MADS Propulsive Gait a) Double stance Propulsive Phase b) Ballistic single stance with no swing leg The MADS gait sequence is shown in Figure 8. Figure 8 : Propulsive Double Stance Gait Generation Sequence A sample timing schedule for the Propulsive Double Stance gait is shown in Figure 8 3. t t t, t 1 t, t t 0 Figure 8 3: Sample Propulsive MADS Gait Timing Sequence This chapter will begin by showing that the exoskeleton system in double stance is fully controllable assuming that the lower extremities are constrained as a four bar mechanism. 67

82 Following this, the ballistic single stance model will be presented in Section 8.. The ballistic single stance model will be used to determine how fast the system should be traveling at the end of double stance (toe off) to successfully complete the step. In Section 8.3, a conservative set of toe off conditions will be calculated. These conditions result in the successful forward propulsion of the ballistic single stance model. Gait generation for the double stance and single stance phases will be discussed in Sections and 8.4. respectively. This chapter will conclude with experimental testing and results in Section CONTROLLABILITY OF DOUBLE STANCE The exoskeleton in double stance is a fully controllable system. Considering biological limitations, Figure in the Appendices shows that if any single angle of a four bar mechanism is defined, all other angles are defined. If a torso link is added to the pelvis of the lower extremity model, the system would then have two degrees of freedom. The model under consideration is shown in Figure 8 4. Torso stance Swing Leg swing Stance Thigh Stance Knee v 3 1 Figure 8 4: Double Stance Model The actuator unit located at each hip provides a torque which works to open or close the angle between the torso and each respective thigh shank. This provides direct control over the angles swing and stance. With the lower extremities in any pose, the torso can be controlled to any global angle. Rotating the torso at the hips about stationary lower extremities yields an equal displacement in stance and swing. Consider that the torso is rotated by some angle,. The new angles of the torso with respect to the hips are: swing, new stance, new swing stance (8.1) 68

83 However, the angle between the hips is swing stance. This angle is defined by the pose of the lower extremities. If the torso is rotated by, the angle between the hips becomes: swing, new stance, new swing stance swing stance (8.) As expected, the angle between the hips remains unchanged. This shows that considering the four bar linkage constraints, the total lower extremity and torso system can be independently controlled through double stance with only a single actuator at each hip. 8. BALLISTIC SINGLE STANCE MODEL The bipedal walker during the ballistic single stance phase is modeled using the stance leg and torso. While it has been shown that the oscillations of the swing leg can contribute to forward propulsive forces in transfemoral above knee amputees ([77], [78]), this model omits any contributions of the swing leg. Neglecting this propulsive contribution will result in a more conservative set of toe off conditions that will propel the system forward. This will also simplify analysis of the ballistic single stance phase. The ballistic single stance model is shown below in Figure 8 5: Torso q 3 m, I 3 3 Stance Thigh Stance Knee d 3 d l l 1 Torso, global T hip q T knee m, I m, I 1 1 d 1 q 1 T ankle Figure 8 5: Ballistic Single Stance Model The generalized coordinates q 1 and q are the same as the angles 1 and defined previously for the four bar lower extremity model shown in Figure 8 4. Additionally, the angle q is the same as the biomechanical quantity of knee flexion. The angle of the torso with respect to the ground, Torso, global, is defined as: Torso, global q1 q q3 (8.3) 69

84 The dynamics for this system are the same as a triple pendulum (or 3R system) which is shown below: The inertia matrix, C, is defined as the following: c11 c1 c13 C c1 c c 3 c31 c3 c33 c md m l d ld q 11 Cq hwt (8.4) cos ld 1 3cosq q3ll 1 cos q ld 3cos q3i1i I3 cos cos cos cos q3 cos cos m l l d c m d ld q m l d l d q ll q ld q c m d ld q q l d q I c c cos 3 3 c m d l d cos q I c m d m l d l d q I I c31 c13 c c c m d I The vectors h and w are defined as: I sin qq 1 3qq 3sin q 3 ld 1 q1qs in q sin s h m ld q q q q q q q ll q qq sinq ld q m q h m lq d q q l in q l d q q q q sin q m ld q sin q cos cos cos cos cos cos q h m d lq sin q q l q q sin q (8.6) w md m l m l q m d m l q q m d q q q g w m l m d q q m d q q q g w m d g q q The torque input vector, T, is defined as: I 3 (8.5) 70

85 T T Tankle Tknee T hip (8.7) The torque at the hip is provided by the actuator, the torque at the knee is the controllable flexion damping module, and the torque at the ankle is from the passive humanexoskeleton ankle. The control policies for the input vector are defined in the following section BALLISTIC SINGLE STANCE INPUT CONTROL POLICIES The control policies for the hip, knee, and ankle are defined below Hip Control The control policy for the hip actuator is designed to keep the global torso angle, Torso, global, constant. The angle Torso, global was previously defined in equation (8.3). The hip controller is a proportional derivative (PD) controller that regulates the error between the global torso angle and the desired angle: e q q q torso Torso, global, desired 1 3 T K e K e hip P, hip torso D, hip torso (8.8) Knee Control The control policy for the knee is designed to model the controllable knee module. Knee flexion is assumed to be highly damped during the ballistic single stance period and have no damping resistance against extension. The resulting control law for the knee torque during single stance is: T knee cknee, ssq q 0 0 otherwise (8.9) Ankle Torque Model The ankle on the human exoskeleton system is a passive component with no active actuation unit. A simplified ankle model was created that is based on two orthotic ankles shown in Figure

86 a) b) Figure 8 6: Two Ankle Foot Orthotic (AFO) Designs a) Custom molded Ankle foot orthosis with stiff ankle, b) Stiff Modified Ossur ankle brace Figure 8 6a and b show two Ankle Foot Orthotic (AFO) designs which have a stiff ankle and foot shank. This AFO limits the amount of plantar flexion of the ankle. Therefore it is assumed that the foot rotates about the heel during early stance and behaves as a stiff torsional spring when the foot becomes planted on the ground. This is similar to natural human ankle functioning. The human ankle also behaves as a torsional spring that charges through stance and discharges at toe off ([39], [79]). The model for the AFO is: T ankle o o KPankle, 90 q1 KDankle, q 1 q otherwise (8.10) It is assumed that there are no ankle torque contributions before the foot is planted. The AFO has a very stiff ankle which keeps the angle between the foot and knee shanks nearly constant at 90 degrees. Therefore, the ankle does not behave as a torsional spring until the knee shank rotates past the vertical. 8.. KNEE RE EXTENSION If the knee fully re extends, q 0, it is assumed that there is an inelastic collision and the integrator resets with new initial conditions. The knee is modeled to have a locking mechanism that keeps the knee fully extended in line with the thigh shank in a similar manner as the swing leg model. Therefore the system becomes a double pendulum (with q 0) when knee re extension occurs. The stance leg is the lower link and the torso is the upper link. The single stance model after knee re extension is the same stance model used for the TCP Propulsion gait. The dynamics for the two degree of freedom single stance model are the following: 7

87 Cˆ q hˆ wˆ Tˆ A 1 3 T Tˆ Tankle T hip ˆ ˆ ˆ C11 C 1 C Cˆ ˆ 1 C Cˆ md m l d m l l d l l d cosq I I I Cˆ m d d l l cos q I Cˆ Cˆ A q q q C 1 1 m d T I ˆ m3 l1l d3q q q sinq h wˆ m l l d q sin q md 1 1ml1dm3l1lcos q1md 3 3cosq1q3 md cosq q g (8.11) Immediately after the impact of full re extension of the knee, the integrator initial conditions are recalculated considering that rotational momentum is preserved about the ankle joint. It is assumed that position before and after the impact are the same, but that velocity changes instantaneously after the impulse. The new initial conditions are: q q q 1 C11 C1 C13 ˆ q 1 q C C31 C3 C 33 q 3 q 3 (8.1) The superscript and + represent conditions immediately before and after the impact, respectively. The angular velocities immediately after impact can be obtained as follows: q 1 q 1 ˆ C 1 11 C1 C 13 C q q C 3 31 C3 C 33 q 3 q q 0 q (8.13) 73

88 The matrix Ĉ is invertible because it is an inertia matrix. Inertia matrices are positivedefinite ( Cˆ Cˆ, det Cˆ 0 q). * 8.3 INITIAL CONDITIONS FOR BALLISTIC SINGLE STANCE The ballistic single stance model developed in the previous section will be used to compute a conservative space of initial conditions that should propel the ballistic single stance model through a step. A set of valid initial conditions will be estimated by running the ballistic single stance model with many different sets of initial conditions that "flood the space" across a range of realistic initial conditions. The set of initial conditions are defined as the joint angles and rotational velocities at the end of double stance. The four angles that define the pose of the walker at the end of double stance are the stance knee, stance hip, swing leg (which has knee = 0 through double stance), and torso angles. However, it will be assumed that the lower extremities are constrained as a four bar mechanism at toe off. Therefore, only two angles need to be defined, namely the torso angle and any lower extremity angle. The lower extremity initial conditions were somewhat arbitrarily defined by the amount of knee flexion of the stance knee on toe off and the horizontal velocity of the pelvis, x. Using the angular standards defined in Figure 8 4 and length standards defined in Figure 8 5, the horizontal velocity of the pelvis can be defined in two different ways: x l sin l sin l l sin (8.14) The range of horizontal velocities that will be tested are between 0 and 1.6 meters per second. This range of horizontal velocities encompasses the range of most normal human walking speeds [80]. While it is desired to keep the global torso angle, Torso, global, constant, it can be assigned to any value desired. The global torso angle was set to 85 degrees (five degrees forward from vertical) for this investigation. Figure 8 7 shows surface plots of the space of initial conditions that are to be tested. 74

89 Figure 8 7: Surface Plots of Initial Conditions for Ballistic Single Stance model Note: This is using the standards defined for the four bar double stance model shown in Figure and are the same as q1 and q used in the single stance model A state belongs to the valid set of initial conditions if the pelvis is propelled past the vertical. Additionally, the stance knee must fully re extend before the initial swing leg pose is reached. The initial swing leg pose is defined as the swing angle with respect to the horizontal, 3, where the stance knee is fully extended ( 0 ) SIMULATION RESULTS AND DISCUSSION The model was run over a discretized set of initial conditions that cover the space of initial conditions shown in Figure 8 7. Each trial was run for a simulation time period of two seconds. The run was terminated early if the state was classified as valid or a failure. The values of the model parameters shown in Figure 8 5 are listed in Table 8 1. Table 8 1: Ballistic Single Stance Model Parameters m 1 (kg) m (kg) m 3 (kg) d (m) d (m) d (m) l (m) l (m) 3 1 I (kg m ) 1 I (kg m ) I (kg m ) The initial pose of the lower extremities was based on a step size of approximately one foot (0.3 meters). Therefore, if the knee was fully extended then 3 80 degrees and

90 degrees. The stance knee must re extend before hitting 1 80degrees to be considered a valid initial condition. Figure 8 8 shows a set of valid initial conditions that result in a successful ballistic singlestance phase. The lower boundary of a space of valid initial conditions can be approximated with the lower boundary of a set. [m/s] [deg] Figure 8 8: Set of Valid Initial Conditions for a Successful Ballistic Single Stance Phase All black points on the plot represent initial conditions that resulted in successful ballistic single stance phase The set shows that the pelvis should conservatively be traveling between 0.35 and 0.45 meters per second to have a successful ballistic single stance phase over a large range of knee flexions. Figure 8 9 shows a sample response of the single stance system. Initial conditions were 15 degrees of knee flexion and a horizontal velocity of 0.6 meters per second. t =0 t =0.5s Figure 8 9: Frames Through Ballistic Single Stance 76

91 Due to the stiff AFO, full knee re extension is achieved as the pelvis passes over the ankle. More than 15 degrees of stance knee flexion is common during double stance into singlestance during natural human walking at a self selected speed ([51],[81]). Additionally, allowing higher levels of knee flexion during double stance provides a larger space to gracefully accelerate the CoM forward before toe off. 8.4 MADS PROPULSIVE GAIT GENERATION In the previous section, a conservative set of valid initial conditions were computed based on a stance model with no swing leg. If the bipedal system state at toe off lies within the set of valid initial conditions, it should have a "safe" ballistic single stance period. Trajectory generation for a full gait cycle considering a full planar walker model will be discussed. The MADS gait sequence is shown in Figure 8 with a sample timing schedule shown in Figure 8 3. The gait will be generated explicitly for the double stance segment using geometric constraints, while the gait will be generated dynamically for the ballistic singlestance segment using a seven link walker model DOUBLE STANCE GAIT GENERATION The double stance phase will be used to accelerate the system from rest to a state that lies within the valid set of initial conditions for a "safe" ballistic single stance that was computed in the previous section. Using the angles of the lower extremities as defined Figure 8 4, the stance hip and knee, and the swing hip (swing knee is locked until toe off) angles are all defined if any one angle is defined. The gait will initially be generated using. This was chosen to simplify the calculation of horizontal velocity of the pelvis, 3 x. A terminal state for double stance can be defined using any state within a valid set of initial conditions. The terminal state will be defined by a combination of some x and. Using knee the chosen terminal state, and 3 3 at toe off can be calculated based on the following: x l l sin knee x l l sin 1 3 (8.15) With defined, and 1 can be calculated using Freudenstein's equation as discussed in 3 Section 11.6 in the Appendices. Because a step length of approximately one foot (0.3 meters) is desired, the swing and stance hip angles are 10 and +10 degrees (with respect 77

92 to a vertical torso) with both knees fully extended. For this example, the terminal values of x 0.6 meters per second and 15 degrees of knee flexion were chosen. This results in degrees and degrees per second. The trajectory for 3 can be calculated using a cubic spline of the following form: The constants are defined as: 3 t 0 c t c t (8.16) tf t F tf tf c c tf t F 3 3 tf tf (8.17) where t F is the time at the end of double stance. With defined through double stance, 3 1 and can be defined. The stance and swing hip angles are defined as follows: hip, swing 3 Torso, global hip, stance 1 Torso, global (8.18) Torso, global is the angle of the torso with respect to the horizontal. A double stance trajectory and estimated knee flexion profile is shown in Figure 8 10 with Torso, global 90 degrees and t 0.15 seconds. F a) b) [deg] [deg] [deg] [s] [deg] [s] Figure 8 10: Hip and Estimated Knee Angles During Double Stance Period a) stance angles, b) swing angles 78

93 8.4. BALLISTIC SINGLE STANCE GAIT GENERATION A seven link planar bipedal walker is used to generate the remaining gait. The doublestance trajectory is pre computed and tracked by the hip actuators to propel the walker forward. After the double stance phase, dynamic controllers are used. The stance hip uses the state feedback policy of equation (8.8) to stabilize the torso. The swing hip tracks a trajectory designed using the swing phase trajectory generation method laid out in Section 6.3 of this dissertation. The stance knee is assumed to be locked which is modeled by the policy of equation (8.9) to restrict flexion (high damping), but allow the knee to re extend, while the swing knee is assumed to have no torque (lock disengaged). Gait generation using the full walker model becomes an iterative process now that the swing leg is considered. A slower double stance phase is computed because the original double stance trajectory did not keep the stance foot planted on the ground. The doublestance trajectory that is used results in a state at toe off that is slightly outside of the conservative set shown in Figure 8 8. The set is conservative because it does not include the propulsive contributions of the swing leg both before toe off and during the swing phase. These contributions enable the walker to have a successful ballistic single stance phase at lower speeds. This is beneficial because the final gait will be slower and more comfortable for the pilot in the suit. The swing phase generation is also an iterative process because the swing leg dynamics affect the stance dynamics and vice versa. Results converged to a stable walking gait that takes 1.4 seconds per step. The double stance period is 0.45 seconds with a horizontal velocity of the pelvis of 0. meters per second at toe off and the ballistic single stance phase is 0.95 seconds. The hip trajectories and the resultant knee flexion profiles are shown in Figure a) b), [deg] DS Stance DS Swing , [deg] , [deg] DS Swing [s] DS Stance 79, [deg] [s] Figure 8 11: Various Trajectories for the MADS Propulsive Gait a) Trajectories for the two hips, b) Trajectory for hip 1 and the resultant knee flexion profile throughout the gait cycle

94 The swing phase should yield a maximum knee flexion of approximately 70 degrees with an unpowered knee. Figure 8 11b shows simulation results for the seven link walker. The knee during swing has a maximum flexion of 68 degrees. The knee flexion during the double stance phase reaches 0 degrees at the end of the phase and quickly re extends in early single stance. Figure 8 1 displays frames throughout the duration of a step with the MADS propulsive gait. a) b) t=0s t=0.45s t=0.45s t=0.61s c) t=0.76s t=0.93s t=1.08s t=1.4s t=1.4s Figure 8 1: Frames Showing Biped Throughout the Duration of a Step with the MADS Propulsive Gait a) Double stance phase, b) knee re extension, c) ballistic single stance phase to heel strike Figure 8 13 shows the vertical ground reaction forces throughout the step. Stance [%] DS Swing [%] DS Toe Off [s] Heel Strike Figure 8 13: Ground Reaction Forces on the Stance and Swing Feet as a Percentage of Total Weight Both feet remain planted on the ground throughout double stance. However, most of the human and exoskeleton load is transferred to the swing foot during this period. The swing 80

95 foot is firmly planted and the swing hip is opening the angle between the torso and the swing leg (extension). The swing leg is essentially propelling the system forward while the stance leg cooperates with the swing leg to help maintain the torso angle and minimize forward impedance. After double stance, the swing foot remains in contact with the ground for approximately 0.5 seconds until toe off. This may also contribute to propulsion in a manner that the original ballistic single stance model did not predict. As expected, the stance leg supports all system weight throughout the single stance period after toe off. 8.5 USER TESTING OF THE MADS PROPULSIVE GAIT The MADS propulsive gait was tested by a user with a T1 incomplete SCI. Tests were performed in the exoskeleton testing and training center in the Berkeley Robotics and Human Engineering Laboratory. The Austin Exoskeleton system was used for these tests. The knee flexion pulleys from the mechanical gait generators were disconnected to make the knees passive. Modular variable impedance knee joints were installed on the device. The variable impedance knees allowed the modulation of braking force in the flexion direction while always allowing free extension. The user donned the Austin Exoskeleton system and used a set of parallel bars to assist with balance and stability. The user completed the tests between the parallel bars because he did not feel comfortable enough to walk with a walker or crutches while using this gait. The user was safety tethered at all times to an overhead rolling gantry to prevent falls, but was otherwise unencumbered. The pilot was asked to use the parallel bars to balance in the coronal plane and to avoid pushing or lifting in the sagittal plane. Video was captured in the sagittal plane using a high speed camera at 10 frames per second. Tracking dots were placed on the test pilot at the shoulder, hip, knee, and ankle on each side. Angular data was calculated using the method discussed in the Appendices in Section Frames showing the test pilot during various phases of the double stance propulsive gait are shown in Figure

96 a) b) c) d) Figure 8 14: Frames Showing Test Pilot Executing a Step with the MADS Propulsive Gait a) time t0 b) End of Double Stance c) Mid stance d) End of Step Angular data for the left and right hip and knee throughout the gait cycle is presented in Figure a) 60 b) 60 [deg] [deg] [deg] [s] [deg] The angular data results for the hips and knees are very similar to what the model predicted. The right and left knees both attain approximately 0 degrees of flexion at the end of double stance. However, both knees have significantly less knee flexion during the swing phase than was originally predicted. This is a result of mechanical wear on the hubs inside of the knee joints. The wear caused additional resistance at the knee that reduced anticipated knee flexion. After inspection of the knee joint hardware, the hub in the right knee was observed to have significantly more wear than the hub in the left knee joint. This was reflected in the swing knee flexion profiles, which show that the right knee consistently had a lower peak flexion than the left knee [s] Figure 8 15: Hip and Knee Angles Through Several Steps Using the MADS Propulsive Gait a) Left side, b) Right side. Note: The dotted lines denote the separation of various gait phases

97 Figure 8 16 shows the data for the angle of the torso with respect to the horizontal,. Global, torso, [deg] [s] Figure 8 16: The Global Torso Angle Throughout the MADS Propulsive Gait The torso angle is relatively constant throughout the step. This is particularly evident when compared with the torso data for the TCP Propulsive gait shown in Figure The increase in torso angle at the end of a step is the result of the pilot keeping his hands fixed on the parallel bars throughout the step. As the pilot reached the end of a step, his arms naturally made his trunk more erect as his trunk moved closer to where his hands were placed. These results show promise in the MADS Propulsive gait to enable users to effectively and comfortably ambulate. This finding is particularly valuable for individuals who are prone to motion sickness. 83

98 9 CONCLUSIONS This dissertation proposed several viable strategies for controlling a minimally actuated lower extremity mobility exoskeleton. Two novel stance control strategies were presented that propel the exoskeleton and pilot forward from rest. The first stance strategy relied on the use of the pilot's torso as a means to dynamically propel the system forward through a step. Accelerating the torso by extending both hips at the same rate imposes a torque about the stance ankle that pushes the exoskeleton and pilot forward. Although this method was shown to effectively propel the user forward, but it had the potential to adversely affect users with motion sensitivity. A potential solution to this problem was presented that involved giving users control over their torso dynamics. Initial results showed that users can learn how to control their own dynamics to effectively propel themselves forward while keeping torso motions at tolerable levels. The second stance strategy effectively propelled the user forward while stabilizing his torso. In double stance, it was shown that if the rear knee is locked against flexion, and the front knee is unlocked and free to rotate, the lower extremities resemble a four bar mechanism. This insight was used to create a gait that propels the system forward and out of double stance. Experimental results were presented that support the efficacy of this stance strategy. It was shown that the torso stability was significantly improved compared to the previous stance method. In addition, this dissertation proposed an original sequential swing phase model. This model was used to produce a gait trajectory for the swing leg that dynamically controlled an unactuated swing knee. A method for swing phase hip trajectory generation was presented. Experimental results supported the efficacy of the swing phase trajectory at producing a natural, human like swing phase from a swing leg that has no actuation at the knee. Extensive pilot testing of the Passive Knee Exoskeleton in both structured and unstructured environments was completed. Walking was sustained over longer distances with comfortable levels of pilot exertion while ambulating with the Passive Knee Exoskeleton. Although it is important that faster walking be achieved so that community ambulation standards are met, the results and findings from the tests support the efficacy of the control algorithms and show great promise in the minimally actuated exoskeleton paradigm. 84

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108 11 APPENDICES 11.1 INTRODUCTION TO POINT TRACKING Throughout the dissertation, point tracking is used as a means to extract angular data in the sagittal plane from frames of video. Tracking points will typically be placed at the shoulder (torso), hip, knee, and ankle on each side of the test pilot. The angles are defined in Figure a) b c) torso hip, global hip knee Figure 11 1: The Extraction of Sagittal Plane Angular Data from a Frame of Testing Video a) Screenshot from a "Tracker" software session, b) Lines showing the links of the torso, thigh, and knee shank c) Definitions of the biomechanical joint angles A software package such as "Tracker: Video Analysis and Modeling Tool" [8] can be used to extract the locations of the tracking points in each frame of video. The extracted location data consists of vectors of Cartesian coordinates for each tracking point from each frame of video. The biomechanical angles depicted in Figure 11 1 can be computed with the following equations: torso xtorso x hip arctan ytorso y hip (11.1) 94

109 xhip x knee hip, global arctan yhip y knee (11.) (11.3) hip hip, global torso knee xknee x ankle hip, global arctan yknee yankle (11.4) The arctangent function can be computed in Matlab with the four quadrant arctangent function, atan. 95

110 11. QUALITATIVE TORSO DYNAMICS Dynamics of the human exoskeleton system in double stance can be described as a double pendulum with actuation between the two links. The top link represents the torso, and the lower link represents the stance knee. The swing leg is removed from the model as the dynamic contributions of the swing leg to the bipedal system are assumed to be negligible. The simplified system using global coordinates is shown in Figure 11. m, I l Torso d V l 1 m1, I1 Stance Leg d 1 Figure 11 : Torso and Stance Leg Simplified Model The free body diagrams of the torso and stance links are shown in Figure

111 R 1y a) b) T act p 1 R 1x d mg l 1 mg 1 d 1 R 1x R 1y T act p 1 e r E y c) R 0x R 0 y p 0 e E x Figure 11 3: Free Body Diagrams of a) stance leg and b) torso c) coordinate standard Intuitively, if the system were released from the initial position with no input, the angle between the horizontal plane and stance leg,, would grow larger because the center of mass of the system is behind the ankle (pivot point). A sample set of results for the singlestance system is shown in Figure 11 4 where the control input at the hip is only working to keep the torso angle with the horizontal plane,, constant. a) 160 b) [deg] t=1 t=0 [deg] time [s] Figure 11 4: a) Sample Single Stance Data, b) Single Stance Still Frames Considering forward locomotion of the bipedal system, propulsion will be roughly defined as 0. If this condition holds, then the stance leg is rotating clockwise about the ankle in 97

112 the forward direction toward the next double stance. The reaction forces at the joint connecting the torso and stance leg can be calculated with Newtonian analysis: sin cos sin cos cos sin cos sin R1x m l1 d R1y m gl1 d (11.5) The "Coupled Torque," T C, is defined as the torque about the ankle due to the reaction forces at the hip. The coupled torque can be calculated by taking the cross product of the Cartesian displacement vector from the ankle to the hip with the reaction force vector: Ex Ey E z T r R det l cos l sin 0 R l cos R l sin E R1x R1y 0 TcEz mgl1cos m1 l m1 ld cos sin c y 1 1x 1 z (11.6) The dynamic equations of motion derived for the single stance system using Lagrangian mechanics are shown below: md 1 1I1ml 1 mld 1 cos mld 1 cos md I mld 1 sin md 1 1 ml 1 gcos Tact mld 1 sin mdg cos T act (11.7) Substituting the coupled torque, T C, into the dynamics about the degree of freedom (about the ankle): md I T mdg T (11.8) act 1 1 cos Qualitatively analyzing the relationship shown in equation (11.6) reveals that a positive torso angular acceleration, 0, will decrease the coupled torque. If T is decreased, the C angular acceleration of the stance knee,, will effectively be decreased too. The system is propelled forward if is negative, as is the integral of. This is a highly simplified qualitative overview and it should be noted that there are limits to this simplified discussion. c 98

113 11.3 INTRODUCTION TO PARTIAL FEEDBACK LINEARIZATION Feedback Linearization provides a means of generating a linear control policy for a nonlinear system through a nonlinear feedback policy. Spong pioneered a modified Feedback Linearization method called Partial Feedback Linearization to control a large class of under actuated systems such as the Acrobot ([83], [61], [6]). This method of control is utilized at multiple points throughout this dissertation to generate system trajectories. Consider a general open kinematic chain of linkages connected by revolute joints as shown in Figure 11 5: d 4 q 4 T 4 l 4 l 3 d 3 q 3 T 3 l d q l 1 d 1 q 1 Figure 11 5: Generalized Underactuated System of Links Connected by Revolute Joints In this case, there are four rotational degrees of freedom of which two are actuated (joints 3 and 4). The dynamics for the system can be partitioned into passive and active 99

114 components by defining q P and q A for the passive and active states, respectively. For this system, the passive component vector consists of the generalized coordinates q 1 and q, and the active component vector, q A, consists of q 3 and q 4., D11 q D1 q qp h1 q, q 1 q 0 D q D q q h q q q T 1 A (11.9) For the general form it can be assumed there are n degrees of freedom, m are actuated and l are passive ( n m l). Therefore dimensions of the partitioned vectors and matrices are: P T l 1 l T m 1,,, q q q q q q A l n lxl lxm mxl mxm D q D q D q D q For the control strategies that would utilize partial feedback linearization in this dissertation, it is assumed that the active degrees of freedom are being used to control the passive degrees of freedom. A short derivation of a partial feedback linearization controller will be derived for a generic underactuated system with n degrees of freedom similar to that done by Spong in [83]. Taking the dynamic equations for the passive space: D q q D q q h q, q q 0 (11.10) 11 P 1 A 1 1 The angular accelerations of the active degrees of freedom will be used to control the passive degrees of freedom. Setting q to be an input, A v, equation (11.10) can be arranged A as follows:, D q v D q q h q q q 1 A 11 P 1 1 We can see that the control input, v A, is mapped through D 1 into the passive space. For v A to initiate motion anywhere in the passive space, it is necessary for the range of D 1 to be the entire passive space, or more concisely: 100 l D1 q (11.11) In other words, the dimension of the passive space is l, therefore the rank of D 1 must also n be l ( q, for any potential state of the system). Because it is known that the rank of a matrix is less than or equal to its smallest dimension: lxm 1 1 D q, rank D q min l, m

115 Thus, controlling the passive degrees of freedom with partial feedback linearization requires there to be at least as many active degrees of freedom as passive degrees of freedom. These conditions including (11.11) are referred to as "Strong Inertial Coupling." Assuming Strong Inertial Coupling holds, v A can be solved for by taking the pseudo inverse of D 1 (or simply the inverse if m=l) where the pseudo inverse is the least norm projection from dimension m to l: This yields v A : A T 1 D D D D T P 1 1 v D D q h (11.1) Defining the angular accelerations of the passive degrees of freedom as a second control input, which will be referred to as a "synthetic input", v: v q P Taking the dynamics for the active space, a non linear feedback policy can be defined: T D q D q h 1 P A T D D D D vd D h h (11.13) It is a necessary condition for D1 DD1D11 to be rank l so that the synthetic input is well defined in both the passive and active spaces. This condition is proven true with the following identity: Il D11 D1 Il 0lxl D D 1 D 11 D 1 D D 1 D 11 D 1 D D 1 D 11 (11.14) It can be assumed that the inertia matrix, D, is full rank n everywhere and that the lxl identity matrix is rank l everywhere, such that the left side is rank l. Therefore, the right side of the equality is also rank l which means that D1 DD1D11 is rank l everywhere if Strong Inertial Coupling holds. If Strong Inertial Coupling does not hold, then the psudoinverse (least norm projection), D 1, does not exist for some states. The nonlinear feedback policy for the joint torques enables the design of a linear control policy for the passive degrees of freedom. Any linear technique can be used to do this, such 101

116 as PID, Linear Quadratic Regulator, or pole placement techniques ([84]). Defining error, e, and a stable differential operator to base the linear control on: e q q P P, d d I l e e e e dt 0 (11.15) The error, e, is defined as the difference between the actual passive joint states and the desired passive joint states. The matrix,, is a diagonal matrix that contains the eigenvalues of the linear control policy ( diag control input, v, the following is obtained: ). Solving for the synthetic 1 l e e evq e e0 Pd, vq q q q q P, d P, d P P, d P (11.16) This linearizes the control of the passive degrees of freedom. By defining the state z, we can analyze the dynamics of the passive states: z1 eqp qp, d z 1 0lxl Il z1 z Az z z z1 e z (11.17) The matrix A, which is dimension l, will have two sets of eigenvalues at i, where i are the l diagonal elements of the matrix. It is evident that as long as the elements i are greater than zero, A will be Hurwitz and error for the passive states will be forced to zero arbitrarily fast. It is important to note that partial feedback linearization is a model based control method. If the system is not accurately modeled, this method may not yield positive results. This is acceptable for use in this research because this controller will only be used in a simulation environment to generate trajectories using what is assumed to be a perfect model. If one desires to implement a dynamic controller on an actual system that is not accurately modeled, more robust control methods are recommended for use. Potential alternative nonlinear controller methods such as various flavors of sliding mode control (variable structure control), integrator backstepping, and dynamic surface control are better suited, depending on the system and known model inaccuracies PARTIAL FEEDBACK LINEARIZATION INTERNAL DYNAMICS 10

117 Partial Feedback Linearization provides a means to decouple the actuated and passive degrees of freedom of an underactuated nonlinear system, and linearize the control of the passive degrees of freedom through a nonlinear feedback policy on the actuated degrees of freedom. While the dynamics of the passive degrees of freedom can be controlled in any manner desired (PID, LQR, etc), the state dynamics of the actuated degrees of freedom are not as easily characterized. A diffeomorphism exists, which is a one to one invertible mapping from one space to n another; in this case from the original system state space, q, to the transformed space. For this system, the diffeomorphism is the following mapping: qp z1 qp qp, d q q q A 1 A (11.18) It is evident in completing the diffeomorphism that while the l passive degrees of freedom are controllable and observable, there are unobservable dynamics, or internal dynamics, in the system which are the dynamics for the active degrees of freedom. The internal dynamics of the system are the following: 1 qa q 1 A 1 D1 D11q 1 1 P h D1 D11 qpd, z z1 h1 1 (11.19) Because the controllable states, z, can be sent to zero arbitrarily fast, it may be useful to analyze the zero dynamics of the system which are the internal or unobservable dynamics when z goes to zero. For this system the zero dynamics are: z0,0 D1 D11 qpd, h1 1 (11.0) 103

118 11.4 PASSIVE KNEE INITIAL VIABILITY TEST The initial experiments to investigate the passive knee concept were completed with the Austin exoskeleton. This was done to gain an acceptable level of confidence in the concept prior to developing the Passive Knee Exoskeleton. The Austin system had several modifications to its knee components for this test. The pulley connecting the knee to the mechanical gait generator to power flexion was disconnected and the spring that assists with knee extension was removed. A small linear actuator was added at the exoskeleton knee joint to control the locking and unlocking of the ratchet mechanism as shown in Figure Detached knee flexion pulley cables Ratcheting knee Linear actuator Figure 11 6: Modified Knee Assembly for Passive Knee Viability Tests The linear actuator at the knee can be used to disengage the knee joint ratchet mechanism to allow knee flexion during swing. Then, the linear actuator can engage the ratcheting mechanism to prevent flexion while still allowing knee extension during mid to late swing. When the knee is fully extended, the knee joint ratchet mechanism safely locks the knee in line with the hip during stance to enable weight bearing. A simple hip swing trajectory based on modified Clinical Gait Analysis (CGA) data along with the respective knee ratchet engagement trajectory is shown in Figure This gait is designed as an initial test to investigate how much knee flexion can be attained at the performance limits of the actuation systems at the hips of the Austin exoskeleton. 104

119 40 30 [deg] Locked Knee Unlocked time [s] Figure 11 7: Initial Swing Trajectory and Knee Locking Profile for Passive Knee Viability Tests INITIAL PASSIVE KNEE RESULTS A test pilot with a T1 complete spinal cord injury donned the modified Austin exoskeleton. The user was asked to take individual steps with a large pause in between each step. This was done so that testing staff could confirm the re extension of the knee before the leg bore weight during stance. Video was recorded with a digital SLR camera at 30 frames per second in the sagittal plane. Tracking points were placed on the shoulder, hip, knee, and ankle on both sides on the pilot. The video was analyzed using "Tracker: Video Analysis and Modeling Tool" [8], a free open source software package that enables post processing and point tracking of video. Knee flexion results were extracted by post processing testing footage as discussed in the Appendices in Section Data was smoothed in Matlab using a moving average filter with a span of five. Results for two different swing cycles are shown in Figure

120 [deg] [deg] time [s] Figure 11 8: Two Swing Phase Point Tracking Results Initial results support the viability of the passive knee concept. Adequate toe clearance was achieved with no toe scuff during early to mid swing. The knee consistently attained approximately 60 degrees of flexion. The small amount of knee flexion after full extension is due to a small amount of backlash that allows the knee to slightly flex on heel strike. These initial experiments validated the passive knee concept. 106

121 11.5 SWING MODEL TUNING AND VALIDATION The pendular dynamics of the knee are the central element in the design of a swing leg trajectory. To obtain accurate values for the inertial properties of the knee, an experiment was devised to isolate the pendular behavior of the swing knee. Experimental data will be collected that will provide all dynamic information for the swing leg system. Several inertial parameters for the knee and foot of the model will be tuned using a subset of the experimental data. Remaining data will be used to verify model performance KNEE PENDULAR DYNAMICS ISOLATION: EXPERIMENTAL PROTOCOL Experiments were conducted in the Berkeley Robotics and Human Engineering Laboratory. A T 1 incomplete SCI pilot donned the Passive Knee Exoskeleton and a harness that was connected to an overhead tether for safety. The pilot was then suspended in the air so that the his legs would hang limp with his feet approximately six inches (~15 centimeters) above the floor. A laboratory staff member stabilized the suspended pilot and provided other assistance as needed. Several images of the experimental setup during a test are shown in Figure Figure 11 9: Knee Pendular Dynamic Isolation Experimental Setup Tracking markers were placed on the hip, knee, and ankle of each leg. A high frame rate camera was positioned to capture footage in the sagittal plane. As the pilot was suspended in air, a series of steps were executed while footage was recorded at 10 frames per second. Testing footage was post processed to extract hip and knee angles throughout the step. Hip and knee angle data were filtered using a moving average filter with a span of five. Data was then segmented to use only the pendular periods so that knee parameters can be identified. Figure shows a plot of hip and knee angles during a sample swing cycle. 107