Tool-Assisted Humanoid Locomotion

Transcription

1 Tool-Assisted Humanoid Locomotion Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Hongfei Wang, B.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 2016 Dissertation Committee: Professor Yuan F. Zheng, Advisor Professor David E. Orin Professor Vadim I. Utkin

2 c Copyright by Hongfei Wang 2016

3 Abstract Biped robot locomotion has been an active research area since the 1970s. With the advent of advanced digital signal processing, high speed computing, high frequency electronics and a powerful actuation, biped robots (such as Asimo by Honda, Atlas by Boston Dynamics and HUBO by KAIST, etc.) can reliably walk on level surfaces with handsome speed. Recent research has been focused on improving energy efficiency and stability performance on different terrain. However, when the terrain is challenging with slippery, unevenness and deformation, stable biped walking places a high requirement on the robot s power system. Until now, only the hydraulic system on Atlas is proved powerful enough to correct the disturbance brought by rough terrain. But for DC motorized humanoid robot, the tolerance on terrain roughness is usually limited due to limited power. The objective of this dissertation is to exploit a practical way to improve the traversing capabilities of the DC motorized humanoid robot without too many modifications to its existing design. On the other hand, medical rehabilitative robots have been widely studied in recent years. Beneficial from the mass production of robot modules and accessories, personal medical robots have become increasingly affordable. One crucial category of rehabilitative robots is the lower-extremity exoskeleton, which is designed to help paraplegics recover walking. The design of such exoskeletons (Rewalk, SuitX etc.) is to attach a pair of motorized legs onto a human and recover the leg functionalities. ii

4 However, such an exoskeleton needs to bear the body weight and to prevent it from collapsing. Consequently, the motors need to be powerful and the battery capacity needs to be large. To address these issues, we propose two new types of robotic devices for the rehabilitation of paralyzed people: the swing-through exoskeleton and the robotic walker Sparrow. The two rehabilitative robots we proposed are designed to reduce the power consumption in the corresponding tool-assisted locomotion. Different from the prevailing lower-extremity exoskeletons, we focus on the cooperation between robots and the human upper body. Through utilizing the human biochemical energy, the power requirement for robots is lowered. Analysis and simulation on the two types of locomotion are covered in the dissertation. Moreover, a prototype of the robotic walker and preliminary experiments are presented. In addition, this dissertation discusses robotic sensing using the inertial measurement unit (IMU). For the humanoid robot, an IMU is indispensable for whole-body motion planning. It provides the relative position and orientation between the robot and the environment. While for our proposed rehabilitative robots, the human and robot interaction (HRI) is the creative aspect. The IMU will provide sensing information on the human upper body. Then the rehabilitative robots can decide how to cooperate accordingly to fulfill the locomotion. A preliminary experiment on human motion detection is implemented. Inspired by the DARPA Robotics Challenge, we also perform degradation analysis of the DC motor due to radiation. Since the DC motor is the most common actuation in humanoid robots, we study the potential motion distortion brought by radiation. This will provide insight on designing robust locomotion in the irradiated environment. iii

5 This is dedicated to my parents iv

6 Acknowledgments I would like to take this opportunity to express my deep gratitude to my advisor Dr. Yuan F. Zheng, for his guidance and caring of my research. He is always there to offer insightful advices and guide me to the prospective directions. Moreover, he sets me an example to be positive and aggressive in life. During my Ph. D. study, I feel so lucky to learn so much from Dr. Zheng, which will benefit my whole life. A special thank goes to Dr. David E. Orin and Dr. Vadim I. Utkin for serving on my candidacy and defense committees and providing invaluable advice to my research. I also extend my gratitude and appreciation to Dr. Manoj Srinivasan, Dr. Dong Xuan, Dr. Wei Zhang and Dr. Hooshang Hemami, who have offered help during my study at OSU. Many thanks will go to my colleagues at The Ohio State University. I would like to thank Dr. Siyang Cao, Dr. Yiping Liu, Mr. Shimeng Li, Mr. Sihao Ding, Mr. Qiang Zhai, Mr. Fan Yang, Ms. Ying Li, Ms. Ankita Sikdar for creating an excellent atmosphere for doing research. Moverover, many thanks go to Mr. Bo Liu, Mr. Jingyin Gao, Mr. Shan Lu, Mr. Qi Hao, Dr. Zhicao Feng and Ms. Zixuan Guo for the friendship and shining memories over these years. In addition, I am grateful to the DASL group in Drexel University led by Dr. Paul Oh, who is now a professor at University of Nevada, Las Vegas. He was leader of our team DRC-HUBO in the DARPA Robotics Challenge (DRC). As a member of v

7 the team, I was able to research and experiment on the HUBO platform and get to know other researchers and state-of-the-art robots. Also, I would like to thank Dr. Youngbum Jun and Dr. Kiwon Sohn for their help during my stay at Drexel University. Special thanks will go to the Casey s, for their caring and support from the very time I landed in USA. Finally, I would like to thank my parents for their love and all they have done for me. vi

8 Vita December 29, Born - Zhumadian, Henan, China B.S. Electronics & Information Eng., Beijing Institute of Technology, Beijing, China Graduate Research Associate, Electrical & Computer Engineering Beijing Institute of Technology Beijing, China 2011-present Graduate Research Associate, Electrical & Computer Engineering The Ohio State University Columbus, Ohio, U.S.A. Publications Research Publications H. Wang, S. Li and Yuan F. Zheng, DARPA Robotics Grand Challenge Participation and Ski-Type Gait for Rough-Terrain Walking, Engineering, vol. 1, no. 1, pp , March H. Wang and Yuan F. Zheng, Crutch-Assisted Swing-Through Exoskeleton, Dynamic Walking, July H. Wang, S. Li, Yuan F. Zheng and P. Oh, Ski-type Self-balance Humanoid Walking for Rough Terrain, IEEE Intl. Conf. Robotics and Automation (ICRA), vol. 2, pp , vii

9 H. Wang, Yuan F. Zheng, Y. Jun and P. Oh, DRC-Hubo Walking on Rough Terrains, IEEE Intl. Conf. Technologies for Practical Robot Applications (TePRA), pp. 1-6, Yuan F. Zheng, H. Wang and et.al., Humanoid Robots Walking on Grass, Sands and Rocks, IEEE Intl. Conf. Technologies for Practical Robot Applications (TePRA), pp. 1-6, H. Wang, Shimeng Li, Yuan F. Zheng and L. Cao, Analysis of Radiation Effects on DC Motorized Manipulator, IEEE Intl. Conf. Control, Automation and Robotics (ICCAR) (in press), April Shimeng Li, H. Wang, Yuan F. Zheng and L. Cao, Performance Degradation Estimation of Robot in Highly Radioactive Environment: Servo Motor Control, Intl. Conf. Mechanical, System and Control Engineering (ICMSC) (in press), May Fields of Study Major Field: Electrical and Computer Engineering Studies in: Robotics and Control Systems Signal Processing and Communication Systems viii

10 Contents Page Abstract Dedication Acknowledgments Vita List of Tables ii iv v vii xii List of Figures xiii 1. Introduction Fundamentals Homogeneous transformation Forward and inverse kinematics Forward and inverse dynamics Stability margin DC motorized joint Position sensing: encoders Orientation sensing: IMU Related Works Tool-assisted locomotion in humanoid robots Tool-assisted locomotion in human beings Organization of this Dissertation Ski-Type Gait for Humanoid Robot Introduction Birth of Ski-Type Gait ix

11 2.2.1 Core strategies Cane-assisted walking for human beings Ski-Type gait Stability Analysis Assumptions in the modeling Step sequence choice Force/Torque Analysis Foot pedal contact model The parameters for analyzing the force/torque distribution Relationship of friction and joint torques Determining the joint torques Optimize the lower body energy consumption Implement of Ski-Type Gait Variables in cane length selection Relationship between L cane and L step Simulation and Experiment Conclusion Rehabilitative Robots for Human Tool-Assisted Locomotion Introduction Swing-Through Exoskeleton Review of passive dynamic walking Birth of swing-through exoskeleton Modeling and simulation Prototype design and preliminary experiments Sparrow: the Robotic Walker Birth of the Sparrow Prototype design and experiment Conclusion IMU sensing Introduction Dynamic Analysis of Human Motions SSP of different activities Dynamic analysis Relationship of θ UB with L(θ) and V x Impact in the transition between SSP and DSP Identify the dynamic differences Human Behavior Detection Sensing principles using mobile phone x

12 4.3.2 Distinguish static and dynamic states Experimental Results Conclusion Radiation Effects on DC Motorized Joint Introduction DC Motor Variation after Radiation DC motor model without load Flux density (B-field) damage Change of K e and K τ DC motor transfer function Manipulator Motion Performance Position control Manipulator motion Conclusion Contributions and Future Work Bibliography xi

13 List of Tables Table Page 4.1 Experiment result of human behavior detection U12M4T disk servo motor specifications Mean and quantiles of motor parameters after radiation xii

14 List of Figures Figure Page 1.1 Denavit-Hartenberg convention [1] PWM illustration [2] A 2-channel encoder installed on geared motor shaft An IMU chip Visualization of IMU sensing Crawling icub (left two pictures) and NAO (right two pictures) [3] Pole vault motion adopted by human [4] The enhancing exoskeleton: BLEEX [5] Rehabilitative lower extremity exoskeletons: Rewalk (left)[6] and SuitX (right)[7] HUBO2 (left) and DRC-HUBO (right) HUBO2 forward quadruped (left) and DRC-HUBO backward quadruped (right) Top view of one cane assisted walking showing variables Stability performance of one cane assisted walking Ski-Type walking concept xiii

15 2.6 Ski-Type modeling in top view Ski-Type gait of Crawl Ski-Type gait of Crawl Variables for force/torque analysis Hard point contact modeling for the foot pedal Relation of joint torques and (f F x, f F z ) Side view for lower body torque optimization Upper and lower extremity energy consumption under different Ski- Type configurations Variables for cane design Relationship between L cane and L step under three configurations HUBO Ski-Type gait on flat surface in OpenRAVE HUBO biped gait on grass HUBO Ski-Type gait on grass Swing-through gait with crutches [8] Three-link humanoid model for swing-through gait Joint angles in swing phase (left) and rotation phase (right) Zoomed in view of foot pedal in swing-through motion Ground reaction forces in swing-forward phase Knee joint of the swing-through exoskeleton Passive damping strut across ankle xiv

16 3.8 Robotic walker with passive pulling mechanism Front view of Sparrow Back view of Sparrow Electronic structure and associated control scheme of Sparrow Inverse pendulum model of human behavior Illustration of three activities Dynamic analysis of ż, z and F z θ UB under different initials Motion sensing using cellphones The half sinusoid shape Data before correlation Correlation result for dynamic states Marginal distributions of motor parameters Scatter plot showing pairwise correlation of K e, a and b DC motorized joint structure Step response with θ ref = 1 rad Step response with θ ref = PUMA-500 manipulator in our lab Simplified manipulator model Desired angular position of θ O, θ A and θ B Angle of joint O before and after radiation xv

17 5.10 Steady state error of joint O before and after radiation Angle of joint A before and after radiation Steady state error of joint A before and after radiation Angle of joint B before and after radiation Steady state error of joint B before and after radiation xvi

18 Chapter 1: Introduction Humanoid locomotion is the motion performed by a subject in the humanoid shape. It can be a human being, a humanoid robot or a hybrid system consisting of both a human being and robotic devices. Biped locomotion is the most common type of humanoid locomotion in daily practice. However, in case of some challenging terrain or people suffering injuries, the introduction of certain tools to help with the locomotion is the most popular approach. The tools utilized can provide more contact points with the ground to render the possibilities of dealing with these challenges. The tool-assisted locomotion in human beings appears in many cases. In mountain climbing, the terrain is usually rugged and bears characteristics of slippery and deformation. Biped walking in this case may not provide satisfying stability performance. Then trekking poles are introduced to extend the arms and enable ground contacts from the upper body. Locomotion with these additional contacts can be viewed as a variety of quadruped gait. Thus falling is less possible to happen. Another case is when a human carries heavy loads. With the help of a stick, a closed-chain system exists no matter one leg or the stick is in the air. Consequently, the load redistribution is possible between upper and lower bodies to alleviate the high torque required in legs. Also for people with impaired visual capabilities, a stick can help with the detection of terrain conditions. On the other hand, tools are helpful in case of human injuries. 1

19 When the leg cannot provide reliable contact with the ground, auxillary crutches can compensate the walking capabilities of the injured people. The synchronized crutches can be viewed as a substitute of the injured leg to provide contact with the ground. As for humanoid robots, the focus has been primarily on biped locomotion. The prevailing approach is to design gaits and controllers for stable and natural walking [9]. Few works have been done to implement tool-assisted locomotion on humanoid robots. The only related research is the crawling motion on small-size humanoid robots like NAO [3, 10]. With hands on the ground, the resulting quadruped gait provides improved stability. However, such crawling motion is not suitable for full-size humanoid robots like ASIMO [11] or HUBO [12]. The heavy weight of such robots can cause potential damage to the mechanical components. Enlightened by human walking with trekking poles, introducing two canes held by the hands for assistance is believed to be advantageous for humanoid robots especially in rough terrain walking. In [13], we call this Ski-Type gait and studied the stability improvement. Canes are designed and comparison experiments with biped gaits are performed on grass terrain. The results validate the benefits of introducing tools in improving stability. Lower-extremity prostheses and exoskeletons can also be categorized as tools to provide additional contact with the ground. Such prostheses are used to replace the missing leg and recover the original reliable contact with the ground. Lowerextremity exoskeletons are designed for people with limited control or strength in their legs. Suffering from the spinal cord injury, the paraplegic patients are incapable of controlling their lower body. Exoskeletons are attached to legs and thighs to make them move. 2

20 Since motion planning and designing robotic tools are the main parts of this dissertation, the basics of motion planning and robotic components are introduced in this chapter. 1.1 Fundamentals Homogeneous transformation A robotic system usually consists of multiple links. Each link can be viewed as a rigid body. The connection between links is called a joint, which enables the relative motion of the links connected to it. To represent the relative position and orientation between links, we use the homogeneous transformation for description. For each link, we define a coordinate system attached onto it. The relationship of any two three-dimensional coordinate system can be characterized by a 4 4 matrix H. H = [ ] n x s x a x d x R d = n y s y a y d y 0 1 n z s z a z d z (1.1) The translation of the origins of the two coordinate systems are denoted by vector d and the rotational relation is denoted by rotation matrix R. Based on the axis and angle of rotation, we have the following rotation matrix: cosθ 0 sinθ cosθ sinθ 0 R x (θ) = 0 cosθ sinθ, R y (θ) = 0 1 0, R z (θ) = sinθ cosθ 0 0 sinθ cosθ sinθ 0 cosθ (1.2) Usually the rotational relationship is not just one step rotation around a certain axis. In this case, we need apply the chain rule to get R. Suppose we rotate θ around X-axis in coordinate A to get coordinate B, then rotate φ around Z-axis in coordinate 3

21 B to get coordinate C. The rotation matrix from A to C is: A R C = R x (θ)r y (φ) (1.3) The choices of axes around which to calculate the rotation angles are not unique. Any combination of X,Y,Z as long as the circular neighboring are not the same. For example, XZZ is not a legal choice. Since there are infinite number of ways to attach a coordinate onto a link, the Denavit-Hartenberg convention is used formatting the way of attaching coordinate shown in Fig The parameters are used to define the following transforms: Figure 1.1: Denavit-Hartenberg convention [1] H x (a i 1 ) = 0 cosa i 1 sina i sina i 1 cosa i 1 0 (1.4)

22 cosθ i sinθ i 0 0 H z (θ i ) = sinθ i cosθ i (1.5) H d (d i ) = d i (1.6) a i H d (a i ) = (1.7) The homogeneous transform from link i 1 to link i can be calculated as cosθ i sinθ i cosa i 1 sinθ i sina i 1 a i cosθ i i 1 T i = H x (a i 1 )H z (θ i )H d (d i )H d (a i ) = sinθ i cosθ i cosa i 1 cosθ i sina i 1 a i sinθ i 0 sina i 1 cosa i 1 d i (1.8) Forward and inverse kinematics When a robot structure is given, we can attach coordinate systems onto the links according to the Denavit-Hartenberg convention. The forward kinematics equation of n links with joint angle θ i at each joint is given by 0 T n = n i 1 T i (θ i ) (1.9) i=1 Given the joint angles of θ i, the position and orientation of the link n can be calculated. This is called forward kinematics. On the other hand, if the homogeneous transform 0 T n is known, solving for the joint angles is the inverse kinematics problem. In forward kinematics, the solution is unique. While in inverse kinematics, the number of solutions depend on the constraints and degrees of freedom (DOF). The number of DOF is the same as the number of joint angles. The constraints in inverse 5

23 kinematics can be the position or orientation of a specific link. In the three dimensional world, the maximum number of constraints is three in position and three in orientation for one link. Consequently, if the DOF is greater than the number of constraints, multiple solutions may appear. In this case, we call the system redundant. Some other criteria should be applied to reduce the solution numbers Forward and inverse dynamics The dynamics captures the relationship between the force (torque) required and the motion of the robot. Typically, the dynamic equation of a robotic system is in the form τ = M(Θ) Θ + V (Θ, Θ) + G(Θ) (1.10) where τ is the vector of torque input. Θ, Θ and Θ are the vectors representing the joint angles, angular velocities and accelerations. Forward dynamics is the process of solving Θ given τ. The opposite problem of inverse dynamics is more useful in robotics applications. Through the inverse dynamics, the torque required for a desired motion is calculated. Then the corresponding actuation can be design to perform the motion. In this dissertation, our robot design relies on this to choose the appropriate hardware in our application Stability margin In quasi-static locomotion, stability margin is the common criterion used for evaluating the stability. If the supporting area is denote by region R and center of mass (COM) is denoted by point C. For quasi-static locomotion, we have C S. The 6

24 stability margin S min is defined as follows: DC motorized joint S min = min P C, where P R P The DC motor usually bears the following dynamic models: dω m dt = (τ m K d ω m )/J m U = (R + dl dt )I + U e U e = K e ω m τ m = K τ I (1.11) (1.12) (1.13) (1.14) where ω m is the motor angular velocity, U the input voltage, I the current, U e the back-emf voltage, τ m the output torque, K d the damping coefficient and K e the back-emf coefficient. J m is the motor inertia, R and L are constants denoting the motor equivalent resistance and induction. K τ is the output torque coefficient. To get the model of DC motorized joint, we need to include the load and reducer. Suppose the speed reduction ratio is n, we have the whole joint model as follows dω m = (K τ I Kω m )/J (1.15) dt U = (R + dl dt )I + K (1.16) eω m K = K d + 1 n 2 K L (1.17) J = J m + 1 n 2 J L (1.18) where K L and J L are the damping and inertia from the load, respectively. In application, we adjust U to tune the motor performance. The transfer function of DC motor from the input voltage U to the output angular position θ m is G m (s) = θ m(s) U(s) = K τ s(ljs 2 + (KL + RJ)s) + (K τ K e + RK) (1.19) 7

25 Figure 1.2: PWM illustration [2] Pulse width modulation is the method of adjusting effective input voltage by digital circuits. The digital switches quickly turn on and off to determine the output as shown in Fig The time percentage of the on state within one period is called the duty cycle. When the duty cycle is zero, the output voltage is zero Position sensing: encoders Figure 1.3: A 2-channel encoder installed on geared motor shaft There are five fundamental types of position sensing elements that are used in robots: potentiometers, linear variable differential transformer (LVDT), resolvers, 8

26 absolute optical encoder and incremental optical encoder. Potentiometers use mechanically variable resistors and have a relative short life. LVDT and resolvers require AC supply and are expensive. So optical encoders are the common choice in non-industrial robot applications. Absolute optical encoders use multiple concentric rings of binary code to denote the absolute value of position. It is accurate and keeps the position reading even with power-off. However, the cost is high due to the expense of photolithography. The most widely used position sensor is the incremental optical encoder. It is usually installed on the motor shaft. The advantages are its simple structure and low costs. Fig. 1.3 shows a 2-channel encoder installed on a geared motor shaft. If the encoder channel number is m, then the resolution of the encoder is m. The most common encoders have channel number of 2, 3 or 4. The resolution seems to be low with the small number of sensing channels. However, the speed reducer between the motor shaft and load will increase the effective resolution of position sensing. With a speed reduction ratio if n, the position sensing resolution at the load side is 360 n 2 m. To get the absolute position, we need to calibrate the encoder to set the zero reference position Orientation sensing: IMU For floating based robots like humanoid robot and wheeled robot, their base link is not fixed onto some reference frame like the ground. Depending on the motion of the system, their relative position and orientation with respect to the ground usually changes. The inertial measurement unit (IMU) is one typical device of this kind shown in Fig

27 Figure 1.4: An IMU chip Figure 1.5: Visualization of IMU sensing 10

28 The IMU can measure the three axis linear and angular accelerations with respect to the coordinate system fixed to itself. Moreover, it can measure the magnetic flux. Combining the readings of accelerometers, gyroscopes and magnetometers, the changes in position and orientation are provided. In practical applications, the IMU is fixed to a certain link. Given the initial position and orientation reading, the homogeneous transform of this link in the ground frame can be updated based on the readings. Similar to the incremental positional optical sensing, the IMU needs calibration in initialization to provide accurate absolute orientation sensing. Fig. 1.5 shows the visualization sensing result from the IMU chip shown in Fig Related Works Tool-assisted locomotion in humanoid robots To overcome the stability problem of biped locomotion, researchers hope to use quadruped locomotion as the solution, which has been well studied on four-legged robots. References [14,15] presented quadruped gaits for walking on slopes, and the famous Little-Dog showed impressive traversing capabilities over rough terrains [16]. A recent study focused on stability of quadruped walking by taking trunk stiffness/body flexibility into consideration [17 19]. Human adults quadrupedal locomotion was studied to adapt the output of central pattern generators as a function of different environmental constraints [20]. Some of the latest efforts made humanoid robots crawl like human beings, of which research is still in its initial stage. Niimi et. al. presented the crawl motion following certain strategies on a robot designed as the human skeleton [20]. And infant crawling gait was reproduced on the NAO robot platform shown in Fig. 1.6 [3]. In 11

29 2013, Lowe et. al. developed a new architecture based on motor primitives which was applied to NAO to perform a crawling task [10,21]. All these humanoid crawling research used small-sized robots like NAO to mimic infant s motion and the terrain was smooth. Only in 2013, the learning strategy for crawling was simulated in multiple environments including rough terrains [22]. Such humanoid crawling can improve stability performance only for some small size robots, and the limbs are usually contacting the terrain directly. But for full size humanoid robots, the weight is much greater, and the force/torque applied to the limbs may cause damages to the system [23]. Also when the robot needs to stand up to perform biped walking or hand operations, the transition from crawling to standing will be challenging. Moreover, the space between the torso and the ground is limited in the crawling posture. So collision with obstacles may take place. Figure 1.6: Crawling icub (left two pictures) and NAO (right two pictures) [3] Tool-assisted locomotion in human beings In real life, different kinds of tools are adopted to help improve the locomotion capabilities of human beings. Generally, the tools are classified into two categories based on the applications involved: the enhancing and the rehabilitative types. Based on the tools adopted, various humanoid locomotion are developed accordingly. 12

30 Figure 1.7: Pole vault motion adopted by human [4] Figure 1.8: The enhancing exoskeleton: BLEEX [5] 13

31 The enhancing tools are usually used by people without impaired motion capabilities. The environment can be so challenging that it s beyond human limits. One example is to get over a wide gap or tall obstacle. In this case, a pole can be used to perform the pole vault motion shown in Fig The pole functions as a long equivalent leg to provide greater rotation radius. Consequently, the swinging distance is enlarged and obstacles are overcome. Some other enhancing tools aim to augment human strength in certain applications. BLEEX is one such robotic tool developed by the Berkeley Robotics and Human Engineering Laboratory shown in Fig. 1.8 [24,25]. By wearing this device, most of the weight is carried by the device instead of human legs. Also it moves harmonically with human legs in biped locomotion such as walking and running. Consequently, human efforts can be heavily reduced or equivalently human strength is enhanced. The rehabilitative tools are usually adopted by people with impaired functionalities in visual or appendicular skeleton. The most basic tool of this kind is the cane used by blind people. Canes enables the sensing of terrain conditions and thus impaired vision is compensated. Other modern enhancing tools are the emerging field of prostheses and exoskeletons. Prostheses are robotic devices designed to replace the missing human limbs and recover its functionality. Exoskeletons are attached to human body and help with the locomotion. Based on the limbs they compensate, prostheses and exoskeletons can be classified as lower-extremity and upper-extremity types. Since we focus on humanoid locomotion, only lower-extremity rehabilitative devices are discussed. 14

32 For lower-extremity prostheses, the shape usually resembles the human legs and the key challenge is to control its motion through human neural network. The corresponding locomotion is the same as normal people. While in applications of lowerextremity exoskeletons, the subject usually suffers from spinal injuries and has no control of the body from the waist down. As a result, the prevailing design of lowerextremity exoskeleton is to attach a robotic device and perform the required motion from the waist down. ReWalk is the most famous product of this type approved by the U.S. Food and Drug Administration (FDA) [6]. SuiX is another competitor aiming to lower the cost and make it affordable to more people [7]. Fig. 1.9 shows the two prevailing exoskeletons. Figure 1.9: Rehabilitative lower extremity exoskeletons: Rewalk (left)[6] and SuitX (right)[7] Both Rewalk and SuitX share some similar disadvantages. The first is that the exoskeleton is designed to replace the human lower body. Thus hip, knee and ankle joints need to be actuated. To keep from collapsing, the device needs to power all 15

33 the joints. The corresponding power consumption is huge and the battery capacity requirement is high. Moreover, the joint module is expensive due to the high cost of speed reducer. So price of lower-extremity exoskeleton following such design is high. Rewalk is $70,000 per set and even SuitX costs $40, Organization of this Dissertation The rest of this dissertation is organized as follows. Chapter 2 introduces the Ski-Type gait for humanoid robots to deal with rough terrains. Through the stability analysis and force/torque study, we get the sense of how to configure the Ski-Type walking wisely. In the experiment, Ski-Type gait is proved to be more stable compared with traditional biped walking. Chapter 3 presents the tool-assisted locomotion applied in gait rehabilitation. To reduce the energy cost of current prevailing lower-extremity exoskeletons, we propose two robotic devices to realize this goal: the swing-through robot and the robotic walker Sparrow. Through modeling and simulation work, we figure out the hardware requirements to build the prototype. The corresponding experimental results show that our ideas are valid. Chapter 4 describes the human motion detection using the inertial measurement unit (IMU). Through dynamic analysis of different human behaviors, we propose a fast and accurate way for detecting human motion states using the single IMU on the cellphone. Through communication between the robot and IMU sensing, the cooperation between human and robot will be more natural and comfortable. Chapter 5 discusses the radiation effects on DC motors. As the common actuation source in humanoid robot, we merge the radiation effects into DC motor model and 16

34 simulate its effects on the DC motorized joint performance. The result provides us insight of how robot joint will behave under irradiated environment. Then tools to compensate the DC motor degradation can be developed accordingly. Chapter 6 summarizes the dissertation in tool-assisted humanoid locomotion. Future research of pushing forward the application of these robotic devices and the corresponding locomotion is discussed. 17

35 Chapter 2: Ski-Type Gait for Humanoid Robot 2.1 Introduction In 2011, the Fukushima nuclear power plant suffered severe damage due to the tsunami triggered by the Tohoku earthquake. When the plant was hit by the tsunami, three of the plant s six nuclear reactors melted down. Due to grave risks to human health, caused by high radiation, rescue and aid workers are not expected to go into such disaster sites. The alternative is sending robots to perform a timely and effective response to minimize the impacts of such accidents. However at that time, even the most advanced humanoid robots, such as ASIMO from Honda, for example, can do almost nothing helpful in the rescue. Other wheeled or tracked robots have limited traversing capabilities in the complex environment of a power plant. This historic event provided the urgency behind DARPAs decision to push forward robotic technologies, and particularly in humanoid robots. In 2012, DARPA announced a grand challenge program focused on the humanoid robots called the DARPA Robotics Challenge (DRC) [26]. The goal of the DRC is to advance the current state-of-the-art in humanoid robots. To simulate the potential tasks encountered in the rescue, eight tasks are specified in DRC: Vehicle Driving, Rough Terrain, Ladder Climbing, Debris Cleaning, 18

36 Door Opening, Wall Breaking, Valve Turning and Hose Installation. Out of the eight events in the competition, Wall Breaking and Hose Installation emphasize accurate hand manipulation while maintaining balance. In the other events, balancing in biped locomotion is a major challenge. Some teams designed robots with different structures such as CHIMP [27] using tracks for motion, and RoboSimian using four legs for walking [28]. The purpose of such design is to avoid the challenges of biped locomotion, while other participating robots like SCHAFT and Atlas have to prevent themselves from falling in various kinds of environments. Consequently, Rough Terrain is the most crucial task for all the teams which use the humanoid structure. As a member of the team DRC-HUBO, we were responsible for Rough Terrain walking. To deal with the stability challenges, we proposed a different approach which is called a Ski-Type gait in this dissertation. This chapter is organized as follows. Section 2.2 shows the birth of the Ski-Type gait when dealing with rough terrain using our biped robot. We compared different possible solutions and finalize the Ski-Type approach. Section presents the development of Ski-Type gait including stability analysis and joint force/torque analysis. Further, we simulate the Ski-Type motion and implement it in our experiments. Section 2.7 concludes the chapter. 19

37 2.2 Birth of Ski-Type Gait Core strategies Some of the teams in the DRC designed their new robot specially for the competition, while our team focuses on the gait development and corresponding algorithm design for the existing platform to accomplish the events. This is a more appealing approach since it will expand the motion capabilities of existing biped robots without re-designing for specific tasks. In this part, we introduce briefly the platform and how we develop the Ski-Type gait. Figure 2.1: HUBO2 (left) and DRC-HUBO (right) The humanoid robot platform of our team is HUBO2, which is a full-sized humanoid robot developed by KAIST (Korea Advanced Institute of Science and Technology). It has 40 degree of freedom (DOF), weighs 45 kg and is 1.25 m tall. It has two force/torque sensors on each ankle joint and an IMU on the waist. In summer 20

38 2013, the motors were upgraded to be more powerful and the arms were enlarged for better hand manipulation, which is the DRC-HUBO as shown in Fig To improve the balancing capability of humanoid robot, we present the idea of enlarging the supporting area as our strategy. To realize the goal of larger supporting area, we think of various ideas which are stated in detail in the following parts. The first natural attempt is to enlarge the foot pedals. Obviously, the supporting area will be enlarged in this way. However, the disadvantages are numerous. Firstly, the width of the foot pedals cannot be increased significantly; otherwise, the pedals will step on each other and no steps can be taken. So increasing the length of the foot pedal is the only option. Unfortunately the lengthened foot pedal will increase the torques on the lower body joints while taking steps. Moreover, the clearance will be reduced by the long foot pedal. In case of stepping over obstacles, a collision is more likely to occur, which is fatal to the system. Another disadvantage is that the larger foot pedal requires more landing space on the ground, and introducing more complexity in foothold planning. Through the analysis above, we give up the approach of increasing foot pedal size. Since multiple-legged robots usually have much better stability performance than biped robots, we examined the feasibility of turning our humanoid robot into a quadruped-mode locomotion. In biped walking, the only supporting area is one foot pedal while taking steps which limits the stability performance. On the other hand, quadruped walking enables as much as four points to touch the ground in a gait cycle. In this way, the supporting area is enlarged more efficiently compared with enlarging foot pedals. To perform quadruped walking, there are two candidate solutions: leaning forward and backward as shown in Fig

39 Figure 2.2: HUBO2 forward quadruped (left) and DRC-HUBO backward quadruped (right) In our early experiments on HUBO2, we attempt to make HUBO2 bend backward for quadruped walking. When the legs fold heavily, the arms can touch the ground. However, the folded legs limit the locomotion capability. As a result, we go back to lean the torso forward with unfolded legs as depicted on the left of Fig The short arms, however, still cannot touch the ground [29]. In addition, the delicate design of the hands does not allow any contact with the ground. Let alone supporting the body. In DRC-HUBO, the arms are extended and a spike is added on each hand to touch the ground without damaging the hand as we suggested. Backward quadruped walking is tested shown on the right in Fig On a flat surface, quadruped walking works well but the heavy torque on arms frequently causes system failure after around twenty minutes operation. Moreover, the torso is much lower than in biped walking and the clearance of steps is limited. In our test of stepping over wood bars, collision is unavoidable in the case of a 20 cm square bar. 22

40 As shown by these attempts, the DRC-HUBO performing quadruped walking still does not meet our expectations. So we propose to use some tools to aid walking instead of making permanent changes to the mechanical design. First of all, we study human walking with the aid of a cane Cane-assisted walking for human beings Usually human beings can perform biped walking very stably relying on strong muscles and biological sensing feedback in the legs. When the legs suffer some injuries, it turns out to be difficult keeping balance using the two legs only. In order to overcome the difficulties caused by injuries, the cane is invented to help people walk. Since humanoid robot is not stable executing biped locomotion in rough or uneven environments, it can be viewed as leg-injured human beings. Consequently, looking into cane-assisted walking by human beings will shed some light on designing reliable cane-assisted gaits for humanoid robots. According to [30, 31], the cane is usually held at the contralateral side of the injured leg. Here are some variables for specifying the gait. L fw and L fl are width and length of the foot pedal, L LFR F is the distance between the centers of the two foot pedals, L LFLcane is the distance between the left cane and the center of the left foot pedal along the y-axis, and L step is the step length. The variables are shown in Fig Some reasonable assumptions are made as follows: L fw = 2L fw L step = L fl L LFLcane = L LFR F = L fl 23

41 Projection of the center of mass (COM) is at the center of un-injured foot pedal (left foot in this case) at the initial posture. Figure 2.3: Top view of one cane assisted walking showing variables The gait and supporting region when L f w = 0.1 m is shown in Fig. 2.4 (a)-(h). Starting from the initial posture, the cane is the first to move forward, and the COM is within the left foot. Then the right leg moves forward by the same distance as the cane, while the COM moves forward in the supporting area formed by the left foot and the cane tip. Then the right foot swings forward by the step-length with the COM in the supporting polygon formed by the cane tip and right foot. After three steps of motion, it is back to initial posture. From the stability margin curve in Fig.2.4 (lower right corner), the minimum stability margin is 0.5L fw, which is greater than that of biped walking with the same walking parameters but without cane. One may notice a sudden change of the 24

42 a b c y/m 0.2 y/m 0.2 y/m x/m x/m x/m d e f y/m 0.2 y/m 0.2 y/m x/m g x/m h x/m stability margin (S min ) curve y/m y/m S min /m x/m x/m step index Figure 2.4: Stability performance of one cane assisted walking stability margin. That is due to the lifting and dropping of the cane tip bringing in instant change of the supporting area. So by introducing a cane to assist walking, the stability performance is improved. People use trekking pole in mountain climbing mainly for the improved stability. Moreover, when the uninjured leg is swinging in the air, the cane can help alleviate the weight cast on the injured leg. Then the leg strength is effectively augmented. Elder people using a cane in walking is one such application. 25

43 2.2.3 Ski-Type gait For the human cane-assisted walking, the gait is asymmetric with only one cane held at the uninjured side. For humanoid robot, we introduce two canes held in both hands for two reasons. It is called Ski-Type gait due to its visual similarities with skiing motion, which is shown in Fig The benefits of using two canes instead of one are twofold. First, the gait can be symmetric which will make the gait planning less complicated. And secondly the robot can be more stable with two canes providing more contacts with the terrain. Some related research has focused on developing robots to function as a cane for walking assistance called cane-robot [32 35]. But in our work, the cane is an ordinary stick not a robot and to be held by robot hand to assist walking. Figure 2.5: Ski-Type walking concept To perform Ski-Type gait, two canes are held in hands. With the redundant joints on arms and hands, touching the ground by the canes is feasible and the gait becomes quadruped. Although the wrist joint is not very powerful due to the small motor size, 26

44 we can distribute the torques among the arm joints to respect such limits due to the redundancy. In the Ski-Type gait, the arm can be viewed as a 3-link limb, while the leg is considered a 2-link module (foreleg and thigh). So the gait becomes a special case of the quadruped walking. However, it bears many advantages in addition to the stability provided by quadruped walking. First of all, humanoid robots are usually required to perform manipulating tasks. That is, hands must hold some tools for the purpose. It is exactly the case in the DRC events as Wall Breaking and Hose Installation. Consequently, frequent transitions between quadruped and biped states are required. In either forward or backward quadruped walking, the transformation into biped standing will cost huge energy without using the canes. While the Ski-Type gait can facilitate a simple transition to the functions of the hands. The canes can be simply dropped when the hands need to perform a manipulating task, and be grasped when the robot needs to negotiate difficult terrains. The robot may still gain better stability when one hand manipulates and the other holds the cane. Another benefit of the Ski-Type gait lies in the flexibility of where the hands hold the canes. By holding different places, the effective cane length changes accordingly. That is equivalent to the variation the robot leg structure. Such flexibility enables the robot to transform to configurations dealing with different scenarios. One example is the height of the center of mass (COM). For long canes, the COM is high, and the robot is able to ensure a large clearance from the ground. A short cane, on the other hand, enables a low COM which provides better stability at the cost of small clearance. 27

45 From the discussion above, we conclude that the Ski-Type gait is a simple and effective solution to take the challenges of difficult terrains, while requiring almost no modifications to the original structure of the humanoid robot as well as providing more flexibility and stability in the gait. 2.3 Stability Analysis Assumptions in the modeling In the Ski-Type gait, there are numerous configurations available for planning the leg and cane motions because of the redundancy. However, based on our experience on HUBO2 and experiments of human beings performing the Ski-Type gait, we model the top view of the gait for stability analysis as shown in Fig Figure 2.6: Ski-Type modeling in top view 28

46 Shown in Fig. 2.6, we place the COM on the front edge of foot pedals. This is to shift the COM towards the back of the supporting area at initial posture. The purpose is to let the legs sustain more weight than the canes, since the legs are more powerful than arms. Such an arrangement can prevent potential damages to the arms. Another consideration is the sequence of the COM shift. In traditional quadruped walking, there is no obvious difference between arms and legs. So the COM moves forward whenever a limb swings forward [36]. In the Ski-Type gait, we place the COM near the feet. If the COM moves when the arm is in motion, the force/torque on the other supporting arm will significantly increase, which may damage/crash the arm. So we shift the COM only when the leg is in motion. This consideration provides additional benefit. When the canes are equipped with sensors for detecting the terrain for a solid touching, the risk of fall can be reduced because of no COM shift in the process. Moreover, we assume no lateral COM sway throughout the gait. This is possible because of the enlarged supporting area by introducing the canes. Recall that in the biped locomotion, the COM has to shift laterally to maintain the support by the landed leg. No lateral sway also reduces energy consumption by the robot Step sequence choice The step sequence is the next factor to be determined in designing the Ski-Type gait. Since we propose to perform quasi-static walking, the gait should be crawl like. If the leg moves following the arm motion on the same side, the gait is called Crawl-1. If on the opposite side, it is called Crawl-2 [13]. To determine which of the two gaits should be selected, we calculate their minimal stability margin (S min ) in a walking cycle under the same initial configurations and the step length. 29

47 As shown in Fig. 2.6, the parameters affecting the stability are listed as: L fw : width of the foot pedal. L fl : length of the foot pedal. L LF RF : length between the centers of the two foot pedals along the y-axis. L LC RC : length between the two cane tips along the y-axis. D COM : length between the COM and the cane tips along the x-axis at the initial posture. According to the assumption for the position of the COM, D COM = L fl. L X : length between the cane tips and the center of the foot pedal along the x-axis. L step : step length. Due to the lateral symmetry in the Crawl-1 and Crawl-2 gaits, the supporting area and the COM position are shown for only one half of the cycle. To obtain the numerical result, values need to be assigned to the variables. Based on the mechanical dimensions of the HUBO2 robot, we set L fw = 0.1 m and L fl = 0.2 m [12]. By our experiments of human walking with two canes, we obtain the sense of how far to reach out the canes, how wide to separate the canes, and what to be the step size. Then based on the height of HUBO2, we set the following parameters to be nominal values of the Ski-Type gait: L LC RC = 0.6 m, D COM = 0.2 m, L X = 0.4 m and L step = 0.2 m. Fig. 2.7 shows the COM and the supporting polygon when the right cane moves and then the right foot swings for Crawl-1. Fig. 2.8 shows the COM and the supporting polygon when the right cane moves and the left foot swings in Crawl-2. For 30

48 (1) (2) y/m TT Line y/m TFR Line x/m (3) x/m (4) y/m y/m TFR Line x/m (5) x/m S min of Crawl y/m S min /m x/m Figure 2.7: Ski-Type gait of Crawl-1 31

49 (1) (2) y/m TT Line y/m TFR Line x/m (3) x/m (4) y/m y/m x/m (5) x/m S min of Crawl 2 y/m S min /m x/m Figure 2.8: Ski-Type gait of Crawl-2 32

50 better illustration, we name the supporting edge formed by the cane tips as the TT- Line, and the edge on the right formed by the cane tip and the foot as the TFR-Line. By checking the COM and the supporting area, we conclude that the change of the TT-Line does not affect the stability margin since the COM is placed far from the canes. However, the TFR-Line is the edge closet to the COM, meaning that it is the most crucial edge affecting the stability. In the two S min curves (on the right of the third row of Fig. 2.7 and Fig. 2.8), there are obvious jumps when the end-effectors (canes and foot pedals) swing. That is the result of a sudden change in the shape of the supporting polygon. In both Crawl-1 and Crawl-2, when the right cane swings forward, the stability margin is minimal. This agree with our observation that TFR-Line will cast most significant effects on S min. In Crawl-1, the TRF-Line is much more inclined compared with that in Crawl-2. So the supporting polygon of Crawl-1 results in smaller stability margin. Through the analysis, the Crawl-2 step sequence outperforms Crawl-1, resulting in greater S min and thus provides better stability for the robot. This conclusion is different from the optimal step sequence in [36], in which the arms are treated as legs and the contacting points are all treated as point-contacting. While humanoid robots have foot pedals and only the cane tips can be viewed as points. So we conclude that Crawl-2 is the better step sequence for the Ski-Type gait under this configuration. 2.4 Force/Torque Analysis In this part, we analyze the force/torque distribution in the Ski-Type gait. Since there are many different walking patterns in terms of speed and foothold positions, we perform the analysis on the initial posture for generality. Because of the symmetry at 33

51 the initial static posture, we ignore the force/moment components around the x-axis. Fig. 2.9 shows the modeling for the force/torque analysis. The points on O to E represent the joints of ankle, knee, hip, shoulder, elbow and wrist, respectively. The point F is the contact point of the cane tip with the ground. Thus a closed-chain system is formed. 0.9 z /m θ lean (p B x,pb) z O D B f P z C A E L cane f F z 0 f P x f F x F 0.1 P L x x /m Figure 2.9: Variables for force/torque analysis Foot pedal contact model There are three types of contact conditions including hard point contact with friction [37], soft finger contact, and rigid contact [38]. Hard point contact with friction indicates that a reaction force normal to the contact surface and two friction forces exist but not any moments. The soft finger contact and the rigid contact allows for one or three moments along with the three forces, respectively. In our case, we 34

52 choose the hard point contact model for the foot pedal contact. For better illustration, we introduce an effective contact point P as shown in Fig A zoomed-in view of the foot pedal following the hard point contact model is shown in Fig Since the effective contact point P can be anywhere along the foot pedal, the distance from P to the rear end of the foot pedal should be less or equal to the foot pedal length. To be stable, the point P should be supported by the terrain O z / mm 50 f P z 0 L P P f P x x / mm Figure 2.10: Hard point contact modeling for the foot pedal The parameters for analyzing the force/torque distribution Based on Fig. 2.9 and Fig. 2.10, the parameters for analyzing the force/torque distribution in the initial posture are listed below: (p B x, p B z ) : the position of the hip joint. θ lean : the angle between the torso link and the positive z direction. L x : the distance from the cane tip to the ankle joint along the x-axis. 35

53 L cane : the cane length. L P : the distance from the ankle joint to the effective contact point P along the x-axis. (fx F, fz F ) : the contact force at the cane tip. (fx P, fz P ) : the contact force at the effective contact point P on the foot pedal. µ : the static friction coefficient. m : the total mass of the system. g : the gravitational acceleration. As illustrated in our previous work, the parameters of (p B x, p B z ), θ lean, L x and L cane will significantly affect the valid motion pattern in the Ski-Type gait, resulting different stability performance. In our force/torque distribution analysis, these parameters are also crucial variables. The remaining parameters (f F x, f F z ), (f P x, f P z ) and L P are used to describe the solution of the force/torque distribution. The final issue before the analysis is the physical values of the links. For consistency with our previous work, mass and length of each link as well as joint torque limits are based on the HUBO2 humanoid robot available in our laboratory Relationship of friction and joint torques In this part, we use a specified ratio as the measurement of joint torques. Instead using the absolute torque values, we scale all the torques by the quantity mg, which is the torque generated by whole body gravity at effective 1 m. By evaluating using this ratio, it eliminates the effects between different robot systems. 36

54 wrist torque elbow torque f F x f F x f F z f F z shoulder torque hip torque f F x f F x fz F fz F knee torque ankle torque f F x f F x fz F fz F Figure 2.11: Relation of joint torques and (f F x, f F z ) Before studying the relationship by changing (fx F, fz F ), the Ski-Type parameters need to be chosen. As shown in Fig. 2.9, the configurations are: L x = 450mm, L cane = 650mm, θ = 30, µ = 0.6 and (p B x, p B z ) = (0, 460mm). The torque distribution when (fx F, fz F ) changes is shown in Fig The axis value is the ratio of contact force with respect to the quantity mg and the torque value is also a ratio as stated before. The region of (fx F, fz F ) is triangular because of the friction constraint. From the wrist torque figure, it is shown that as f F z increases, the torque applied on the wrist joint will gradually decrease to zero and change the direction. This is 37

55 the reason that f F z will compensate part of the torque caused by gravity of the cane. However, if f F z is fixed, the positive f F x will generally increase the load on wrist and the negative f F x will help to decrease the torque. When (f F x, f F z ) = (0, 0), the wrist torque is low because the cane orientation is close to vertical and the mass portion of cane length is small. After scaling, it is much smaller. The other five joint behave differently from the wrist joint. The torque will decrease with the increase of f F z and the increase of f F x. The only difference within this five torque with the relationship of (fx F, fz F ) is their sensitivity of the two contact variables. For the change in fz F, the ankle and hip joints are the most sensitive since their distance from point F is the greatest along the x-axis. The shoulder and wrist joints are the least sensitive to fz F. In our Ski-Type configuration, the wrist joint is close to point F along x-axis so the torque barely changes once f F x is fixed. If the wrist joint (point E) is vertically above the cane tip (point F), f F z will not affect the wrist torque at all. This is the reason we set the cane to be vertically touching the ground in our previous study. Similarly, the sensitivity of joint torques with respect to f F x can be concluded. It should be positively related to the distance from the joint to the cane tip. As shown in Fig. 2.9, excluding the ankle joint, all the other five joint are relatively high above the ground, so they should change significantly as f F x changes. This inference is verified in Fig

56 2.4.4 Determining the joint torques For the closed-chain system, the joint torque solution is not unique because of the redundancy. At the initial posture, we have the following equations: { f F x + f P x = 0 f F z + f P z = mg which are satisfied regardless of the position of the effective point P. Consequently, if the force pair (f F x, f F z ) are variables, the joint torques will vary correspondingly. For generality, (f F x, f F z ) will be scaled by mg and expressed as a ratio. For f F z, the minimum is 0 because the contact point cannot provide force pointing downwards without a hinge. The upper bound ratio is set to be 1 since foot pedal is not hinged either. Moreover, the force pair should follow the friction constraint. In summary: { 0 f F z /mg 1 f F x µf F z. Another constraint is that the effective point P should lie within the foot pedal. That means L P L fl. Also each resulting joint torque need to be within the limits. Since the joint torques depend on the value of (fx F, fz F ) in the system equations. To obtain an optimal solution, we choose to minimize the total torques required. For the posture shown in Fig. 2.9, the total torque is minimized when the cane forces are (fx F, fz F ) = ( 0.042mg, 0.202mg) and µ = 0.6, and the corresponding joint torques are within the limits Optimize the lower body energy consumption From the force/torque analysis above, we can see the solution for all joint torques are not unique. For the closed-chain system, we can perform optimization according 39

57 to certain rules. In the previous part, we only optimize the sum of all joint torques for the initial static posture. Now a generalized optimization problem is proposed in the Ski-Type walking. Since the friction force pair (fx F (t), fz F (t)) will determine the corresponding unique solution for joint torques, we view (fx F (t), fz F (t)) as the time dependent variables. Here the assumption of quasi-static motion still holds throughout the Ski-Type motion, so we have the following constraints: fx F (t) + fx P (t) = 0 fz F (t) + fz P (t) = mg fx F (t) µfz F (t). 0 τ (t) τ max τ (t) = InverseDynamics(fx F (t), fz F (t), θ(t), θ(t), θ(t)) where θ is the vector of all joint values and τ is a N 1 vector storing all joint torques. N is the total number of joints. It can be calculated through the inverse dynamic function of system. One thing to notice is that under the quasi-static assumption we have θ = θ = 0. Finally the cost function is in the form of C = T t 0 Aτ (t)dt (2.1) in which A is a 1 N weight vector, t 0 and T are the starting and ending time of the motion of interest. To minimize one particular joint torque, we can set the corresponding weight in A as 1 with all other elements as 0. For the Ski-Type walking, we introduce the canes to help alleviate the burden on legs. It is necessary to investigate how to configure the Ski-Type gait to benefit the lower body best with respect to the upper body joint specifications. So we perform analysis on minimizing the lower body total torque in the Ski-Type gait. For the Ski-Type motion, we have the following assumptions. First of all, the hip joints 40

58 only shift forward with the leg swing on the same side. Secondly, the wrist joint is mechanically locked while the elbow joint is free. Under this assumption, the Ski-Type gait resembles the elder people walking with axillary crutches. The way canes are held in this way is more friendly to distribute burden onto upper body since the wrist joints are usually weak in both human beings and humanoid robots. Also this is the way we attach canes onto HUBO to perform experiments. Finally, the sustaining leg on the ground should be straight without knee bending. This assumption guarantees that the knee torque is not huge when bearing the body weight. The gait snapshots are shown in Fig Comparing Fig and Fig. 2.9 we can see the arm are modeled as a 2-link system instead of a 3-link system. The reason is that canes are mechanically locked onto the forearm, leading to the elimination of wrist joints in Fig Excluding this difference, all the other configurations and variable definition are same as those in 2.9. Moreover, the blue and red bar models represent the left and right side of the subject, respectively. Figure 2.12: Side view for lower body torque optimization For each intermediate time step of the motion, we minimize the leg energy consumption by tuning the variables (fx F (t), fz F (t)). By summing all the intermediate results, we get the final result of one cycle of Ski-Type motion under certain specifications. As discussed in 2.4.2, the Ski-Type gait is configured by many variables. 41

59 Consequently it is difficult to determine one universal optimal configuration. However, we are interested in how the specification variables affect the load distribution. So we perform the following two studies with L x and θ lean as the only varying Ski- Type specification variable, respectively. The result of upper and lower extremity energy consumption is shown in Fig Figure 2.13: Upper and lower extremity energy consumption under different Ski-Type configurations From the left plot with θ lean = 9 in Fig. 2.13, the leg energy cost is concave with L x in the range of 0.20 m to 0.26 m. This means for a fixed step in the Ski- Type walking, there is an optimal configuration which minimizing the total torque applied on the legs. In the right plot of Fig. 2.13, the leg energy cost is also concave as θ lean increase from 6 to 20 with fixed cange length of m. While in both cases, the upper body energy cost monotonously increases with the increase of L x or θ lean. The reason is that as L x or θ lean increase, the upper body tends to lean forward more which leads to more burden on the arms. However, depending on the 42

60 differences among the subject performing Ski-Type gait, the curves in Fig may differ in large scale. However, similar analysis procedure can be applied to guide the configuration of Ski-Type gait according to different optimization standards. 2.5 Implement of Ski-Type Gait In the initial setup for the Rough Terrain task, there are several wood bars to step over. To avoid collision with such obstacles, a certain step size is necessary. In our Ski-Type gait, the three contacting points while taking steps will limit the available step size because of the kinematic constraints imposed on the Ski-Type gait. Since the cane length will directly change the kinematic structure, we need to determine the cane length in the light of the available step size. To do so, an additional aspect to consider is the trajectory of the foot and the cane tips. We assume the curve governing their motion trajectories to be sinusoid for smoothness in both position and speed, which can be modeled as follows: z = H max sin(π T ), (2.2) where H max is the maximum lifting height in one step, T stands for the total time of one step and z is the height of foot pedal or cane tips. Moreover, we assume that the foot pedal to be leveled to ensure the clearance of the ground. This sinusoid trajectory pattern is also available on the HUBO2 platform Variables in cane length selection In the force/torque analysis, the parameters for configuring the Ski-Type gait are defined and shown in Fig In this section, we further make p B x = 0 and introduce θ ankle to decide the hip position. Since the thigh and leg are of the same length, the 43

61 θ lean 0.5 y /m θ ankle L cane L x Lstep H max x /m Figure 2.14: Variables for cane design hip joint is always over the ankle joint. In conclusion, we fix the following parameters for determining the step size, which the robot is able to take, and the corresponding cane length as shown in Fig θ lean : the angle between the torso and the y-axis. This can be used to tune the COM position with respect to the supporting area. θ lean : the angle between the leg and the z-axis. L cane : the effective cane length held in the hands. L x : the distance from the cane tip to the ankle joint along the x-axis. L step : the step size. H max : the maximum lifting height in one step. 44

62 2.5.2 Relationship between L cane and L step To determine the valid step size in the Ski-Type gait, an inverse kinematic (IK) solver is introduced to calculate the joint values. Once the cane length and the step pattern are fixed, the IK solver provides the joint values throughout one step. If the joint values are all within the limits, the corresponding step size is feasible with that cane. According to the dimensions of HUBO2, the joint limits are set to be: Ankle pitch: Knee pitch: Hip pitch: Shoulder pitch: Elbow pitch: step range / m step range / m step range / m step range / θ ankle =40 o L / m cane step range / θ ankle =30 o L cane / m step range / θ ankle =20 o L cane / m Figure 2.15: Relationship between L cane and L step under three configurations. To determine the step size range for each corresponding cane length, some of the variables need to be assigned. We set θ Lean = 30, L x = 0.30 m. For each fixed cane length, the step size increases and the trajectory follows Eqn The maximum step 45

63 size is calculated with each corresponding cane length. Also we check the relationship under three different conditions, where the ankle joint values are 20, 30 and 40, respectively. The results are shown in Fig and a few observations are made: 1. As θ ankle decreases, the COM height increases. So the reasonable L step range shifts to the right, meaning that longer canes are needed to take steps. 2. When θ ankle is decreasing, the maximum achievable step length decreases. Moreover, when θ ankle = 20, there is a flat part around L cane = 0.80 m. That happens when the COM is relatively high and L cane is large enough. Previously we assume that the canes vertically touch the ground. However, the arms of HUBO2 are short and the elbow joint cannot bend backward because of the mechanical constraints in the design. So L step cannot increase as the canes become longer to around 0.80 m. 3. At the rightmost part of the curves, there is a steep drop. The reason is that in such ranges, the elbow joints are heavily bent at the initial position. Consequently, canes cannot be lifted following the sinusoid curve as limited by the elbow joint constraint. Based on the observations as shown in Fig. 2.15, we choose L cane = 0.75 m out of the following considerations. First, as θ ankle changes, the height and the valid L step ranges change accordingly. The L cane value of 0.75 m can promise a large step size for all the three scenarios of θ ankle. Secondly, 0.75 m is around the height of the torso, which makes a comfortable posture for the HUBO2 robot to hold the canes. 46

64 2.6 Simulation and Experiment To validate our design of the Ski-Type gait, we performed simulation in the Open- RAVE simulator, which is a robot simulator developed by Rosen Diankov of the CMU Robotics Institute. Based on OpenRAVE, Robert Ellenberg from the Drexel University developed some supplementary packages for simulation dealing with the HUBO2 model [39]. The simulator involves a physics engine for dynamics; therefore, the result is close to real-robot operation. Fig shows the snapshots of simulation, in which the HUBO2 robot performs the Crawl-2 Ski-Type gait. Based on the result of the cane length design, we attach two canes of 0.75 m to the robot hands. Figure 2.16: HUBO Ski-Type gait on flat surface in OpenRAVE. Succeeding in the simulation, we performed experiments on grass. The softness and slippery of the grass constitute one kind of the rough terrain conditions. So Figure 2.17: HUBO biped gait on grass 47

65 Figure 2.18: HUBO Ski-Type gait on grass the grass can ideally test the stability performance of biped and Ski-Type gaits. In our analysis, we assume no lateral sway in the Ski-Type gait. While in experiment, we found adding the lateral sway will alleviate the arm torque on the side of the swinging leg, which reduce the possibility of system failure because of the limited torque. So we introduce the same lateral sway in Ski-Type as in biped walking for better comparison. The experimental result of biped and Ski-Type gaits is shown in Fig and Fig In the biped walking, the COM sways left and right to keep balance while taking steps. When HUBO2 sways to its right with the left foot swinging in the air, the grass under the right foot pedal is compressed because of the pressure, and the foot pedal tilts to its right. Consequently, the actual COM position differs from the reference COM position, which makes S min smaller. Since the motion is open-loop, the COM error cannot be killed and HUBO2 will sway to the other side. As a result, oscillation of the COM occurs as HUBO2 taking steps as shown in Fig After three steps, HUBO2 falls because of the oscillation. While in the Ski-Type gait, the supporting area is not just the foot pedals. It is much larger by using cane tips and foot pedals alternately. When HUBO sways to its right, S min will also decrease because of the deformation of the grass, but the 48

66 Ski-Type gait provides much greater S min values to ensure stability. Furthermore, the three supporting points at any time forms a triangle, which will prevent the oscillation from growing. Moreover, the shared weight will cause less deformation under the foot pedals and COM disturbances are smaller compared with the biped gait. The experimental results verify that the Ski-Type gait is more stable than the biped gait. 2.7 Conclusion In this chapter, we propose the new Ski-Type for humanoid robot. By adding two canes held in hands, more contacts with grounds are provided. Beneficial from this redundancy, more motion choices are available ensuring stability. Moreover, the canes can be dropped or picked up easily for hand operation. Through the stability analysis, we conclude the Crawl-2 gait is a better step choice in the Ski-Type gait. The force and torque analysis shows that it is possible to tune the force-torque distribution within the close-loop system. What s more, the simulation and experiment results validate that Ski-Type gait is more stable than the traditional biped walking dealing with terrain roughness. 49

67 Chapter 3: Rehabilitative Robots for Human Tool-Assisted Locomotion 3.1 Introduction According to [40], there are around 236,00 to 327,000 persons suffering the spinal cord injury (SCI) in the US only. As mentioned in Section 1.2.2, current prevailing rehabilitative lower-extremity exoskeletons are expensive. So making lower-extremity exoskeletons affordable for more people is quite promising. In this chapter, we propose different designs from the current lower-extremity exoskeletons to aid humanoid locomotion. This chapter is organized as follows. In Section 3.2, we present a robot to enable a new swing-through gait instead of normal biped locomotion which borrows the idea from passive walker to reduce actuations. In Section 3.3, we show the robotic walker we designed to help people with SCI or other walking disabilities to walk. Section 3.4 concludes the chapter. 50

68 3.2 Swing-Through Exoskeleton Review of passive dynamic walking Research on legged locomotion partly originates in understanding the fundamentals of its mechanics and the traversing capabilities of corresponding practical machine. Based on the relationship of zero-moment point (ZMP) and supporting area, locomotion can be categorized as dynamic and static motion. If the ZMP is always within the supporting area, the motion is static; otherwise, it is dynamic. Adaptive Suspension Vehicle (ASV) is one typical static walker [41]. In dynamic biped motion, early works focus on the trajectory planning for different terrains [42, 43]. While recently, many researches target at the modeling of the robot for better motion planning and how to minimize the energy consumption by applying various types of controllers [44 46]. Although tremendous efforts have been made on dynamic biped locomotion for smooth motion under various scenarios, the gait is still not as efficient as human. Even for the state-of-art humanoid robot ASIMO, the energy consumption is roughly 20 times the energy (scaled) that a human uses to walk on flat surfaces [47]. The reason is that the high-gain feedback, and therefore the considerable joint torques are cancelling out the natural dynamics of the machine to follow a desired trajectory. In [48], a passive dynamic walker is proposed to walk downslope without any actuation. Among the work of improving energy efficiency in legged-robot locomotion, [48] has pushed it to the extremity in respecting the natural dynamics of biped locomotion. Through detailed and elegant analysis, it is proved to be possible to walk downslope driven by gravity only. In the modeling discussed above, the leg is only rigid body without knee joints. To avoid collision of the swinging leg, small 51

69 motor is attached to bend foot pedals in the air. However, the author investigates the possibility of fully passive knee joint to solve this problem. The passive walking gait demonstrated in [48] is impressive but it still bears some disadvantages. First of all, the only power source is the gravity. So such fully passive machine can only walk down a slope. Such characteristic limits the application of this work. Second, to achieve stable cyclic walking, the gait configurations are highly dependent on the setting of the terrain. The disturbances of both environmental and systematic parameters are investigated in [48]. As shown in the derivation of the system dynamics, there are some approximations and linearization applied relying on assumptions like small slope etc. So once the environment is fixed, the stable gait is fixed. Such inflexibility of gait choice is also a disadvantage. Moreover, in the support transfer stage, the inelastic model may not perfectly capture collision features. Some negative work is done to make the system deviate from the cyclic states. As seen in the experiment, usually after some steps the passive walker collapses. As seen in [48], the fully passive dynamic walker can only walk downslope since the gravity is the only power source. Since walking on level surface is the most common biped locomotion in practice, one may want to realize the level biped gait under the framework of passive walker. Although biped walking on level surface has been researched long before the work in [48], they are not competitive in energy efficiency compared with the passive dynamic approach. In [47], actuation is added to substitute the gravity to power the system walking. Reference [49] shows three actuated passive walkers developed by Cornell, Delft and MIT, respectively. An apparent feature of these robots is their human like structure. In the Cornell robot, actuation is added in the ankle joints. To make up for the 52

70 energy losses due to dissipation in collision when walking at constant speed, the ankle actively extends when triggered by the feet hitting the ground. This is realized by pulling the heel by the motor. The hip joint is unpowered and knee joints are passive with only latches. An interesting design is the synchronization of arms and legs. In the Cornell biped robot, the arms swing forward with the opposite side leg. This agrees with the strategy in human locomotion. Besides the structural improvements, the efficiency of the human, humanoid robot and actuated passive walkers are compared in [47]. After scaling, the Cornell biped walker is almost as efficient as human being. This means the passive dynamic strategy outperforms the traditional biped walking which follows generated trajectories through controllers. However, there are still some problems to be solved in extending the work of actuated passive robots. Firstly, the knee joint is not actuated which makes it challenging to stand still. Without some mechanical designs to lock the knee joints in case of standing, the robot will collapse. Also in case of walking upslope/upstairs or there are some obstacles blocking the way of the swing leg, ankle actuation only is not enough for such scenarios. So we consider that actuation in the knee joints should be advantageous Birth of swing-through exoskeleton As rehabilitation attracts more and more attention and various devices have been developed for different patients, robots should be put into practice to help people with impaired walking capabilities. One popular research is the lower-extremity exoskeleton to aid walking. Current approach of controlling the motion of such exoskeleton is using controllers to follow some trajectories. Just an resembling of the development in 53

71 humanoid robot locomotion, the framework of passive walking should be introduced in the locomotion related exoskeletons. One benefit is the high energy efficiency. Since most prevailing lower exoskeletons requires large battery to power the system, the mobility of its application is limited. If the actuated passive walking is realized by such exoskeletons, this problem will be solved. The crutch-assisted swing-through gait is one possible solution of such trials shown in Fig Figure 3.1: Swing-through gait with crutches [8] In our exoskeleton design for performing the swing-through gait, active knee joint is proposed to enable the possibility of standing and ensure leg clearance in more complex cases than level walking. Similar to the extension of foot pedal of Cornell biped, the slightly bent leg can provide such push-up through knee joint motion. When the crutches are holding on the ground, through proper motion of knee joints, a pole-vaulting like motion is achieved to swing over obstacles. So active knee joint will provide more flexibility compared with active ankle joint only. However, the ankle joint needs some special design for our robot. Initially we propose no ankle joint and design the foot pedal to be semicircular. But such design will harm the stability in standing still. So we propose some passive mechanical device to control 54

72 the ankle joint, which is adding a damper across the leg and heel. Such device can absorb energy when heel hitting the ground and help the body rotate forward when swinging forward the crutches. Moreover, it can help lock the ankle joint when foot is in the air. In the MIT robot, there are two springs linked to the foot pedal. These springs function similarly with our proposed ankle joint design Modeling and simulation In the practical swing through gait of a person with a pair crutches, the motion of hip joint is very small. Shoulder and knee joints are most crucial in fulfilling the motion. So we use the following three-link humanoid model to analyze the twodimensional motion in the sagital plane. Link-1 denotes the human leg. Link-2 is the human trunk with thighs. Link-3 denotes the synchronized crutches and arms on them. The ground coordinate system is shown to the right in Fig. 3.2 with its origin as O. For better illustration, the link ends are denoted as A, B, C, D. τ 1 and τ 2 are available at B and C, denoting the knee and shoulder joints, respectively. The motion can be separated into two phases based on either A or D is on the ground without slippery. So we need to derive two sets of dynamic equations due to the structural difference. Figure 3.2: Three-link humanoid model for swing-through gait 55

73 Figure 3.3: Joint angles in swing phase (left) and rotation phase (right) When the crutch tips are fixed on the ground in the swing phase, the dynamic equation is in the form of 0 τ 2 = M 1 (Θ) Θ + V 1 (Θ, Θ) + G 1 (Θ) τ 1 where Θ = [θ 1, θ 2, θ 3 ] T. When the crutches are swinging in the air, the dynamic equation is in the form of 0 τ 1 = M 2 (Φ) Φ + V 1 (Φ, Φ) + G 1 (Φ) τ 2 where Φ = [φ 1, φ 2, φ 3 ] T. Since the motion is periodic, the two phases above should occur alternatively. The relation between the two phases depends on the transition conditions like collision model and double support-phases. In general, the two sets of angles we defined can be easily transformed based on the following joint angle relationship in degrees: φ 1 + φ 2 + φ 3 + θ = 180 φ 1 + θ 1 + θ 2 + θ 3 = 180 φ 2 + θ 3 = 0. 56

74 Figure 3.4: Zoomed in view of foot pedal in swing-through motion In the swing-through motion with our exoskeleton, one key problem to solve is the clearance of the legs when swinging forward. In the model derivation shown above, the foot pedal are modeled as a dot without any length. This is not true in practice, so we add the foot pedal to the human model same as Fig The zoomed in view of the knee and ankle joint are shown in Fig θ crutch and θ knee are same as θ 1 and θ 3 in Fig Since the potential users may have no control of the ankle, we model the ankle joint to be fully passive. When the torso swings over the crutch tips, the ground reaction force on the foot pedal will change accordingly. Friction is proportional to the ground reaction force, which prevent the motion if feet are dragging on the ground. Through dynamic analysis, we hope to find the minimum ground reaction force to obtain a good understanding of when to trigger the knee motion for swinging leg forward. The result is shown Fig From the simulation result, we can see that the ground reaction force is concave throughout the swing phase. If the ankle joint is fully passive, knee bending around the minimum ground reaction force is desired. The reason is that overcoming the dragging friction from foot pedals is most possible with only knee bending from the swing-through exoskeleton. 57

75 Figure 3.5: Ground reaction forces in swing-forward phase Prototype design and preliminary experiments To develop the prototype of swing-through exoskeleton, the most crucial part is the knee joint. With the assumption of perfectly elastic collision during the phase transition, the knee joint should be around 5 Nm to bend the leg for swinging forward based on the analysis in Section In most joint design of humanoid robots, speed reducer is usually used with a DC motor for actuation. The benefits are threefold. First of all, the rotational speed of the DC motor is usually much higher than the requirement of actuated joint. The speed reducer connecting the motor output and robot link reduces the rotational speed by ratio of n. Moreover, as the speed is reduced, the effective output torque is multiplied by the same ratio. The third benefit 58

76 accompanied by the speed reducer is the reduced requirement of joint accessories. One example is the optical encoder mentioned in Section Since precise position control depends on high resolution encoders, putting the encoder onto the motor shaft can reduce the resolution requirement by the speed reduction ratio of n. In our application of the swing-through exoskeleton, the robotic joint should be attached along the leg. So we choose the harmonic drive instead of gear box as the speed reducer. The harmonic drive is more compact in size. After choosing the DC motor and speed reducer for our knee joint, another thing is the electronics for controlling the motor motion. In our case, we use the Arduino micro-controller and matching motor board to power the motor. Fig. 3.6 shows the whole knee joint attached on the knee brace. The knee brace we use in our prototype is off-the-shelf product with motion range setting. This mechanism can limit the motion of knee joint with some mechanical device. It can help prevent from collapsing in case of motor failure. Figure 3.6: Knee joint of the swing-through exoskeleton In our preliminary experiment, the swing-through exoskeleton is tested on myself. The testing results indicate that the performance highly depends on the timing of 59

77 knee bending. With the force sensing information and the timing of discussion in Section 3.2.3, we manage to swing forward in most cases. However, the landing case has some problems. When the human upper body behaves similarly to the desired motion, the landing is acceptable. If the human motion deviates heavily from the desired motion, the landing impact is huge and will damage the system. Since the landing time is almost instantaneous, sensing based impact control will be difficult and increase the costs of our device. So we think some ankle joint mechanism should be added to make the motion smooth and comfortable. Figure 3.7: Passive damping strut across ankle In normal swing-through locomotion with only crutches, human ankle joint tends to push down to drive the swinging and cushion the impact in landing phase. During my post-op of Anterior Cruciate Ligament (ACL) reconstruction, traversing long distance with the crutches usually results in the sour of my ankle. Enlightened by the ground reaction force analysis and my experience, a fully passive ankle joint is proposed to help perform swing-through gait better and reduce the burden on ankle joints. We propose a passive damping strut across the rear part of foot. It can store energy in landing and push the rear part of foot pedal to help take off as shown in Fig

78 3.3 Sparrow: the Robotic Walker Birth of the Sparrow In Section 3.2, we conclude that the upper body motion will directly affect the performance of swing-through gait with crutches. The reason is that the swing-through gait is relatively dynamic which depends on timely and accurate cooperation between human upper body and the exoskeleton. This requirement may be uncomfortable for potential users liker elder people. In daily life, it is also the case that elder people prefer sitting on wheelchair to using crutches. To eliminate this disadvantage, we propose an robotic walker aiding the biped locomotion. In practice, walkers are used to bear some body weight for people with impaired strength or balancing in legs. The walker provides additional supporting on the ground and thus balancing becomes easier. The walker aided locomotion can be viewed as a variety of quadruped walking. With the help of walker, the motion can be quasi-static. When leg is about to swing, the supporting leg and walker forms a large supporting area on the ground. Thus the stability is highly improved as discussed in Section As a result, people who use the walker have much longer time to perform the desired leg swing. Moreover, the slowed-down motion reduces the landing impact which may cause potential damages. On the other hand, the introduction of walker lead to the possibilities of load redistribution. This is benefit from the closed loop formed by human body and walker as discussed in Section 2.4. However, for people who has no control of their body from the waist down, performing leg swing is still challenging. Sparrow is the robotic walker we developed aiming to help both paraplegic people and those who has impaired lower-extremity capabilities in walking. It consists of 61

79 three parts to help recover humanoid locomotion. First of all, the frame similar to the traditional walker provides the support for hands to alleviate the load on legs. By controlling the upper body posture, people can actively distribute the body weight between upper body and legs. Also through leaning to the left or the right, ground reaction force on both legs can be tuned. When the left leg is about to swing, leaning to the right can make the swinging easier and ensure clearance with the ground. This lateral swing pattern also exists in the normal biped walking. The second part is the knee braces. It is the most crucial part of our design. The knee braces should be attached onto human legs. Through certain mechanical lock design, the motion range permitted is limited. When the knee motion tends to cross the limits, mechanical lock will stop the motion going any further. This design is will prevent collapse even without any actuation in the knee joint. So the power consumption for sustaining body weight is omitted similar to the case in Section 3.2. If we lock the knee joint, the thigh and leg become a rigid link without any knee motion. The third part of the robotic walker is effective hip joints. For people with no control of their lower extremity, leg swing is the only challenge left given the previous two parts of design. Since the hip rotation is the key in walker-assisted motion, we need some design recovering the functionality of hip joints. It should connect human legs and the walker frame. When stepping forward is desired, it pulls the legs forward. When a certain leg is on the ground, it will release as upper body moves forward. So the pulling mechanism behaves effectively as hip joints. The first solution is using some energy storing components like a spring. When the walker is pushed forward, the distance between the walker and stance legs increases. Energy is stored 62

80 in the spring. Since the body weight is mainly on the legs, the friction on the foot pedals is enough to fight the pulling force. When leg swing is desired, human can shift the upper body to tune weight distribution. Consequently, the reduced ground reaction force leads to friction reduction. Then the pulling force will drive the leg forward. To stop the leg swing, leaning back towards the swinging side can kill the leg motion. Through the walker motion and human body leaning, the passive pulling mechanism store and release energy periodically to drive the leg swing. Thus the hip joint functionality is recovered Prototype design and experiment In the discussion above, the pulling mechanism is the key in performing walkerassisted locomotion successfully. So we perform analysis to figure out the details of it. Fig. 3.8 shows the side view of walker-assisted walking with fully passive pulling mechanism. We will analyze the leg swing phase with walker fixed on the ground. The black frame represents the walker. The blue and red part denote the left and right side of human beings. In Fig. 3.8, only one pulling device connecting the walker and blue side leg due to the symmetry. The human model is based on my height, weight and human segmentation data. In our optimization problem, the variables are specifications of the passive pulling mechanism: pin position on the walker, rest length and stiffness. We hope to minimize the swinging foot speed at the time of landing. However, the walking parameters like step length, foot pedal height and leg swing time differ in different scenarios for various people. The corresponding optimal configurations of the passive pulling mechanism will change accordingly. But once the hardware is deployed, it s specification is fixed. 63

81 Figure 3.8: Robotic walker with passive pulling mechanism Moreover, the constant stiffness coefficient is not ideal in this application. During the initial swinging phase, the gravity will help rotate the leg forward and pulling force required is small. While the leg swing over the vertical position, the gravity will slow down the swing angular speed. At this time, the desired pulling force is greater but the force from the passive mechanism is smaller due to the reduced length. So we look for alternative ways to meet the various pulling requirements for different person. Our solution is using two motors to drive the strings connecting the walker and human legs. Through simulation, the maximum torque for leg pulling in the swinging phase is 10 N m. Since the pulling point on the leg is between the knee and ankle joints, the effective force to fight against the friction is enough even 25 % of body weight is on the swinging side. In one step, the change in rope length is smaller than 0.5 m. The required output speed of motors should be within 500 RP M. Geared motor and pulley system are adopted for pulling the legs. Through the strings connecting knee braces and the walker frame, people can shift the center of mass in 64

82 cooperation of the leg swing. Moreover, the knee braces have locking mechanism to prevent collapsing. In the leg swing phase, the walker needs to be stable on the ground. This originally depends on human operation. However, we demand the shift of center of mass for leg swing which also need posture adjustment from human. To alleviate the responsibilities of potential users, the front wheels of the walker are actuated by two geared DC motors. The benefits are twofolds. First of all, the walker depends on electric power to move forward. Thus the energy consumption from user is reduced. Secondly, the walker is more stable and flexible when people take steps. Since the wheels are controlled by DC motors, close loop speed control can ensure the walker at desired state. Thus unexpected walker motion can be eliminated in the leg swing phase. Also turning becomes easier with the actuated front wheels. Fig. 3.9 and Fig shows the snapshot of our prototype. The electronics of Sparrow consists three main parts: the power system, the central controller and the distributed controllers. To drive the motors and process the corresponding encoder information, we use the Arduino as the distributed controller board. Position control are designed based on the geared motor we choose. To enable the communication between the electronics, we use an Raspberry Pi as the central processing unit. The Raspberry Pi is a full-size computer with fast processing capabilities and more memories than the Arduino board. ROS is installed on the Raspberry Pi as the operating system for Sparrow. The distributed controllers like Arduino function as nodes in ROS, under which the real-time communication is realized. The rated voltage for Arduino, Raspberry Pi and geared motor are 5 V, 3.3 V and 12 V. 65

83 Figure 3.9: Front view of Sparrow Figure 3.10: Back view of Sparrow 66

84 So we have two batteries providing 12 V and 3.3 V output. The 5 V input for Arduino can be drawn from the motor shield with 12 V input. Fig shows the electronic structure and associated control scheme of Sparrow. The highest layer is the ROS running on Raspberry Pi. The second layer is the distributed controllers such as Arduino and IMU sensors. The lowest layer is the functional components. The communication between the first and second layer are based on ROS messages between nodes. The message contains the customized information of the system denoted by black arrows in Fig The blue arrows denote the encoder reading of geared motor. Based on the desired position and encoder sensing of the current position, Arduino can determine the corresponding PWM input to drive the motors (represented by red arrows). Moreover, the colors of rectangles refer to the rated operating voltage: black (3.3 V), blue (5 V) and red (12 V). Figure 3.11: Electronic structure and associated control scheme of Sparrow 67

85 In the preliminary experiment, we test the performance of Sparrow on people with no walking disabilities. The knee locking is proved to be harmless to leg swing. Also the body shift to ensure clearance is small which requires little energy from human. Moreover, the pulling mechanism makes the subjects feel relaxed in the hip joints, which is promising for potential users suffering ACL. 3.4 Conclusion In this chapter, we present two new design of lower-extremity exoskeletons: the swing-through exoskeleton and the robotic walker Sparrow. The idea of the two designs is to reduce the actuation in exoskeleton and rely on more cooperation between human and robotic devices. The crutches in swing-through exoskeleton function as an effective leg and a dynamic swing-through gait is enabled. The testing shows that more components like damping ankle joint is required to perform comfortable and natural swing-through motion with our exoskeleton design. On the other hand, the robotic walker we proposed enables a more static locomotion type. Thus the cooperation between human and robot is much easier to realize. The experiment shows the potentials in recovering legged motion for people with impaired capabilities in the lower-extremity. Moreover, the simplicity of the design makes it attractive for an effective device affordable for more potential users. 68

86 Chapter 4: IMU sensing 4.1 Introduction In humanoid robot, the IMU is usually attached to the trunk of the robot. The reason is that arms and legs are constantly in motion while trunk remains stationary in most cases. In both biped and the Ski-Type walking, we monitor the IMU reading to plan motion and check states of the robot. In case the robot is tilting or falling unexpectedly, the readings of the IMU can provide real time warning and trigger the emergency mechanism to reduce the damage to the robot. In the application of exoskeletons, the deployment of IMU is similar to that of humanoid robot. For exoskeletons like ReWalk or Suitx, the IMU updates the states of human torso and determines the motion to perform accordingly. Since the legs are attached onto by an equivalent biped legged system, the joint readings can provide status of the human legs. While in our design of the Sparrow robotic walker, no legged robot device is attached to human. We emphasize to compensate the joint rotation capabilities instead of replacing the legs. So no accurate joint information can be gathered of human legs. However, the potential user of the Sparrow walker usually suffer from SCI, who has no feeling and control of their legs. In their training to cooperate with 69

87 the robot, it is difficult without the knowledge of their legs. Moreover, the pulling mechanism needs sensing feedback to tune its pulling forces. Consequently, we attach two IMUs on the thighs of the user to update position and orientation of the legs. As mentioned in the previous chapter, the knee has a very small range motion so only one IMU is required for each leg. With the help of IMUs, the pulling forces can be tuned based on the desired motion and leg status sensed. Additionally, in the training procedure, the feedback of legs status makes it easier for the subjects to perform upper body motions harmonically with the walker. This chapter is organized as follows. Section 4.2 shows the dynamic analysis of normal walking, stumbling and fall with the IMU information from the torso. Section 4.3 presents the detection designing and experiment result with the IMU on cellphones. Section 4.4 concludes this chapter. 4.2 Dynamic Analysis of Human Motions To understand the dynamics of normal walking, stumbling and fall, the first issue is to choose models for the motions. One possible approach is using separate models for each of the three activities, which are as accurate as possible to model real human motion. The other approach is to choose one model which is universal for all of them. The model should at least reveal the differences of these motions to some extent such that detection is possible. Conceptually, all the three activities can be divided into SSP and DSP and no perfect modeling for fall and stumbling has been developed to simulate the dynamics. So we propose to adopt the second approach and choose a model which can be used for all the three activities. 70

88 Normal walking has been well studied and many modeling has been done and realized to make humanoid robot walk [46, 50, 51]. In our research, only one inertia sensor embedded on the mobile phone is deployed, so it is not possible to depict both motion and orientation of the body. Instead we can just measure the data of one point of interest. The most reasonable way of deploying the motion sensor is to attach it to the waist, which is the approximate center of mass (COM) position [52], therefore, we focus on the COM trajectory modeling. 1 M V x M Fx 0.8 Fz 0.6 y /m L(θ) 0.4 θ Z O X 0.5L step x /m Figure 4.1: Inverse pendulum model of human behavior According to [52], the typical COM trajectory when people walk normally is a curve which is the intersection of two perpendicular planes. The horizontal and vertical planes are both sinusoid shaped. Moreover, people evolve into the walking pattern to minimize the COM displacement in order to save energy. Since we care most the status of the COM instead of how to configure the joint values of legs, one link inverse pendulum modeling is adequate for our purpose. Also the most significant 71

89 feature of the human motions lie in the vertical plane and the SSP is symmetric about the position where the COM is just above the supporting foot. So in our study only the side view is explored. Fig. 4.1 shows the model for the half cycle of the SSP before the next landing. The parameters are defined as follows: M : the motion sensor position, which is the approximate COM position. O : the contact point of the supporting leg. L(θ) : the effective length of the supporting leg. θ : the angle point M rotated during SSP. M : the COM position at the end of SSP. 0.5L step : half of the step length. V x : the horizontal linear velocity when M is above O. There are some assumptions about the model. First of all, L(θ) is changing for different θ in normal walking. Generally speaking, when θ increases, L(θ) becomes longer to reduce the vertical COM displacement [52]. Also the link is massless. This is because we measure the motion of the COM which is equivalent to the whole body mass. Moreover, the leg force exerted on the COM is along the link and can be decomposed as F x and F z as shown in Fig To describe the motion of point M, x(θ) and z(θ) are the instant position of the COM along the x-axis and y-axis, respectively. Since the length of the link L(θ) is a function of θ, it is more reasonable to express the positions as function of θ instead of time. According to Newton equation, the acceleration equations are derived: F x = mẍ(θ) (4.1) 72

90 F z mg = m z(θ) (4.2) where m is the mass and g is the gravitational acceleration. Also at the initial position shown in Fig. 4.1, the horizontal speed is V x. Based on our assumption, two more equations are: F x = x(θ) F z z(θ) = tan θ (4.3) SSP of different activities x 2 (θ) + z 2 (θ) = L 2 (θ). (4.4) Figure 4.2: Illustration of three activities 73

91 To understand the dynamics for each activity shown in Fig. 4.2, the parameter values need to be considered. For better illustration, θ N, θ S and θ F are the θ values at the end of the SSP for normal walking, stumbling and fall, respectively. First of all, L(θ) and L step will vary for different people in normal walking. Even for the same person, L step is not constant corresponding to different speed of gaits. In normal walking, even though L step for each individual is different because of the L(θ), it is reasonable to assume that by the end of the SSP, θ N is a stable parameter. Here we do not make assumption that θ N is constant, but is with small variance for different speeds in normal walking. Fall is one kind of severe abnormal behavior which has been well studied. Basically it is a free fall process before contacting the ground. We focus on the scenario that the swinging leg is somehow blocked by obstacles so that the balance is lost. In this case, the swinging leg never landed until θ F 90. Different from a fall, if a person succeeds in landing the swinging leg on the ground to regain balance, it is a stumbling. In this sense, θ S < 90. On the other hand, although the swinging leg lands before falling, the rotating angle throughout the SSP should be greater than that in normal walking, that is θ S > θ N. In conclusion, the rotating angle in the SSP until landing can differentiate the three activities. In general, the following relationship holds: θ N < θ S < θ F 90. (4.5) To obtain the dynamic differences among the thee motions, how the velocity and acceleration change with θ in our model needs to be investigated. 74

92 4.2.2 Dynamic analysis Based on the discussion in the previous parts, both linear velocity and acceleration are functions of θ. While for a fixed θ, only the initial state determines the dynamics. Since the COM is about 55% of the whole body height above the ground, L = 1 m which is the approximate COM height for people of 1.8m high. As to the horizontal linear speed, it is reasonable to set V x = 1 m/s for normal walking. Based on these parameters, Fig. 4.3(a)-(b) show the result of ż, z and F z as functions of θ. 0 (a) ż θ / o 0 (b) z/g θ / o (c) Fz/mg θ / o Figure 4.3: Dynamic analysis of ż, z and F z In Fig. 4.3(a), the initial ż is zero and increases as θ becomes larger. In Fig. 4.3(b), the y axis shows the ratio of z to the gravitational acceleration g for better illustration. We can see z/g at initial position is some negative value. This is the reason that V x 0 so that the centrifugal force makes F z < mg. As θ increases, z/g approaches to 1. In conclusion, see both ż and z increase with θ. 75

93 Another important aspect is that the curves in Fig. 4.3(a)-(b) both cut off at the same value of θ. Fig. 4.3(c) which shows how F z change with θ will explain this phenomenon. Since the force is a function of the mass m, we use the ratio of F z /mg as measurement. When θ increase, the speed becomes greater and the centrifugal force decreases F z. At some θ, F z will become zero. Based on the assumption in our modeling, F z can only be some non-negative value. So when F z decreases to zero and θ further increases, the COM enters the free fall stage. Here we denote the upper bound of θ before entering into the free fall stage as θ UB. From the analysis above, we can see that the existence of θ UB divides the SSP into to stages. The first stage can be analyzed using our model. The second stage is a free fall process with the velocity when θ = θ UB as the initial and last until the impact occurrence. Obviously, the value of θ UB will affect the dynamics of the whole SSP. So an investigation of θ UB is indispensable Relationship of θ UB with L(θ) and V x Through our analysis, the values of the initial COM height and velocity will affect θ UB. In Fig. 4.3, the parameter are chosen as follows: L(θ) = 1 m and V x = 1 m/s. However, people with different heights have different effective L(θ). Even for the same person, the walking speed will differ meaning V x will fluctuate. The range of L(θ) is chosen as 0.8 m to 1.2 m denoting people 1.45 m to 2.18 m high, and V x is set to be 0 m/s to 2 m/s. The relationship is shown in Fig. 4.4 and some comments are made: A smaller V x can provide larger θ UB, because the centrifugal force is smaller at the same θ. 76

94 A greater L(θ) can also result in greater θ UB because of the reduced centrifugal force required. Within the range of our setting, θ UB is always greater than 10. The maximum value of θ UB is around θ UB / Vx m/s L height m 10 Figure 4.4: θ UB under different initials The results agree with the common sense in daily life. When people walk faster, the reaction force on the supporting leg during the SSP is smaller. Thus θ UB decreases. In case a person is stumbled by obstacle, equivalently the V x is increased so the chances of entering the free fall state is greater because of the speed increase along with the θ UB reduction Impact in the transition between SSP and DSP Succeeding the SSP, the swinging foot will have an impact with the ground and becomes DSP for all three activities. This impact procedure is the transition between 77

95 SSP and DSP. Since the time duration of the impact is very small, the instant magnitude of the impact force is very huge and can be viewed as infinite. In [53, 54], the collision of manipulators with the environment is mathematically modeled and how the collision changes states of the system is studied. Similarly here we model the collision problems as follows: ż(t 0 ) is the vertical linear velocity just before the impact. t is the duration of the impact. ż(t 0 + t) is the vertical linear velocity right after the impact. Γ δ denotes the generalized constraint force along the z-axis in the collision. The collision procedure along the z-axis can be modeled as: m(ż(t 0 + t) ż(t 0 )) = t0 + t t 0 Γ δ dt (4.6) Since the magnitude of an impulse namely Γ δ shown in Fig. 4.2 tends to infinite as t 0, the right side of Eq. 4.6 converges towards a finite quantity. Thus we further denote T δ = t0 + t t 0 Γ δ dt (4.7) and T δ is called the generalized impulsive force. Then Eq. 4.6 comes m(ż(t 0 + t) ż(t 0 )) = T δ (4.8) where ż(t 0 + t) ż(t 0 ) represents the linear velocity change immediately before and after the collision. Eq. 4.8 is a general form for impulsive based impact formulation. In our study, we propose to use it for analyzing the transition between the SSP and 78

96 the DSP. In normal walking, stumbling and falling down, the vertical linear velocities are all zeros after collision, which means ż(t 0 + t) = 0. Thus we get mż(t 0 ) = T δ. (4.9) Based on Eq. 4.9 we can compare the impulse differences in the three activities. First of all, the magnitude of the impulse is proportional to the magnitude of ż(t 0 ). The greater the speed before the impact, the higher the impulsive force will be generated. Since ż(t 0 ) denotes the vertical velocity just before the impact, we can use another form to express it. In the dynamic analysis applying our model, we use θ as the variable instead of time to describe the system. To keep consistency, ż(t 0 ) should be expressed as ż(θ N ), ż(θ S ) and ż(θ F ) for the three corresponding activities Identify the dynamic differences Until now we have modeled and analyzed the locomotion dynamics of normal walking, stumbling and fall. In this part, we will investigate the differences for seperating them based on our previous studies. First of all, θ SSP is around 8 in normal walking [52], which means θ N 8. This value implies that the free fall period will never appear in normal walking by comparing it with θ UB in Fig Referring to the result in Fig. 4.3, we can conclude that z(θ N ) should be at most around 0.5g and T δ is nor very large because ż(θ N ) is small according to Eq Also in normal walking people are conscious about the landing so T δ is not a large value. In stumbling, the value of θ S will differ significantly in different stumbling scenarios. If a person lands the swinging foot much later than normal walking, θ S will be a large number. In our setting, a conservative assumption is θ S 1.5θ N. If θ 1.5θ N, 79

97 we just consider it a hard step instead of stumbling. To determine ż(θ S ) and z(θ S ), one factor to notice is whether the SSP consists of the free fall stage. Based on our discussion, if a person is stumbled, the effective V x is increased. By looking at Fig. 4.4, θ S will make the SSP close to or experience a short time in the free fall stage. Consequently, z(θ S ) is close to g, and T δ will be a great value because of the large ż(θ N ). In a fall, although θ F will not be close to 90 in practice, it is much greater value than θ N. What s more, θ UB is around 20 according to Fig. 4.4, so the free fall stage will be definitely experienced in a fall. So z(θ F ) g as well, but ż(θ F ) is much greater than normal walking and stumbling. In conclusion, stumbling and fall will show a much higher peak in acceleration because of the impulse by unconscious impact compared with normal walking. On the other hand, before the impact both stumbling and fall experience a free fall like stage. But in a fall the duration is much longer than stumbling. 4.3 Human Behavior Detection Sensing principles using mobile phone In recent years, the widespread popularity of smart phones stimulates the research on this platforms and beneficial from the rapid development of micro-electromechanical systems (MEMS) and smart phones have become more powerful with more sensors onboard. Much research in human activity classification has been performed based on the motion sensor on cellphones [55 59]. Among the previous work, most of the focus is on extracting statistical features like mean, variance etc. and designing classification algorithms [60, 61]. The sensor has been mounted at wrist [62], waist [63] 80

98 and chest [64,65]. In our research, we use the motion sensor integrated in the Google Nexus for data collecting. Fig. 4.5 shows how motion sensing on mobile phone is implemented [66]. Figure 4.5: Motion sensing using cellphones First of all, the motion sensor is fixed with the cellphone. The frame which is attached to the phone is shown on the left in Fig While the frame attached to earth is shown on the right. The two coordinates are called local and world frame, respectively. Generally the orientation of the local frame is not stationary in the world frame, but the data measured by the motion sensor is with respect to the local frame. To obtain the motion measurement in the world frame, the relationship between the local and world frames need to be computed. R shown in Fig. 4.5 denotes the rotation matrix from the local to the world frame. Based on the gravitational force and earth s magnetic field sensed in the local frame, R can be computed accordingly. Based on the computed R, the six components from the 3-axis accelerometer and 3-axis gyroscopes (a x, a y, a z, θ x, θ z, θ z ) can be translated into the linear and angular accelerations with respect to the world frame. In our research, we focus on the linear acceleration sensed along the z-axis in the world frame, namely the (a z ) Earth. 81

99 The sampling frequency is an important consideration. According to [66], there are three working modes for the motion sensors and we choose the fastest sensing rate to get more sensing data. Through experiment, the rate is about 50Hz for the acceleration sensing. For detection purpose, a moving window is needed to segment the sensing data. Usually the window length in the time domain is of fixed length. Previously, the length is determined based on the average motion duration. In our approach, we propose to use the correlation approach to process the acceleration data. The effective window length is determined according to the user behavior at the initial sensing stage. We assume that the person will not fall or stumble at the very beginning of sensing and at least two normal steps are performed. Based on the two steps, we set the model length to be the length of the two peaks in acceleration. In this way, the length contains all the data points for a normal step. If abnormal behavior appears then the correlation model can provide the difference by comparing correlation result with normal step Distinguish static and dynamic states There are four basic states of the human: standing, normal walking, stumbling and falling down. Since we propose to use correlation for classification, the choice of the model is important. As discussed in the previous part, the length of the correlation model is determined by initial two normal steps. Here are several considerations for choosing the model shape. Firstly, the sensing data is of acceleration with noise and traditionally a low pass filter should be applied to process the data. So the correlation model should have such low pass characteristics. Secondly, in the impulse-based 82

100 impact analysis, the impulse is some quantity of integration over time in Eq. 4.7, so the correlation result should reflect the linear velocity. Consequently we choose the half sinusoid model for performing correlation as shown in Fig t Figure 4.6: The half sinusoid shape By comparing the correlation result with zero, standing and dynamic states can be separated. But for the three dynamic states of normal walking, stumbling and fall, how to distinguish them according to the correlation result needs to be considered Normal Walking Stumbling Fall z m/s Sample Index Figure 4.7: Data before correlation Fig. 4.7 shows the raw sensing data of z before correlation. For both stumbling and fall, the great positive acceleration is from the impulse illustrated in Section II. Among the three stumblings, it is obvious that the first two generate greater impulses. This is the reason that in such stumbling, θ S is greater than the third. Based on our 83

101 analysis in Section II, its associated negative acceleration peak before the impulse should be greater as well because of the larger θ S. This is validated in Fig While in a fall, both peaks are greater than those in a stumbling. One thing to notice is that after the impulse related peak, an abnormal negative peak appears in both stumbling and fall. This is caused by the structure of MEMS motion sensor on the mobile phone. In the motion sensor, there are two springs attached to the movable microstructure. When a huge impulse is applied, the spring will generate an opposite reaction force. Since impulse will disappear very fast, the reaction force of the springs will cause a negative overshoot, the overshoot will be killed in short time depending on the structure of MEMS. So the negative peak and the following associated positive peak in stumbling is the result of the MEMS structure instead of the SSP. correlation result Normal walking Stumbling Fall lags Figure 4.8: Correlation result for dynamic states Fig. 4.8 shows the correlation result corresponding to Fig The correlation result reflects the piecewise average velocity to some extent and some comments are listed: The MEMS caused negative peaks are eliminated through correlation because the oscillation die out fast. 84

102 The impulses in stumbling and fall lead to the peaks in the correlation result. And the peak value are much greater than that in normal walking. Based on these positive peak values, we can detect whether the motion is normal walking. The positive peak of a fall is smaller than that of a stumbling. In Fig. 4.7, the peak for the fall is the highest. However, after correlation it becomes lower. There are two reasons for the discrepancy. Firstly, the impulse duration is short, its neighboring negative data will be included in the correlation. Secondly, there are two huge negative peaks on its both sides. The SSP caused negative peak in a stumbling is much smaller than a fall. This is because the average velocity before the impact in a fall is much greater than in a stumbling. According to these comments, we can draw the approach to distinguish the three activities. First, use the positive peak value to decide whether it is normal walking. In the domain of abnormal behavior, if the positive peak denoting the impulse is much greater than the SSP related negative peak, it is a stumbling; Otherwise, it is a fall Experimental Results To test our algorithm, we choose two male adult with height of 1.75 m and 1.85 m for experiment. Since we use the first two normal steps for determining the model length and the correlation peak in normal walking, both of the subjects are required to take initial two steps with normal, fast and slow speed and then continuously record for 40 s. The experimental results are shown in Table

103 Table 4.1: Experiment result of human behavior detection Subject Initial V x Standing N S F Slow 100% 95% 100% 100% A(1.75m) Normal 100% 98% 95% 95% Fast 100% 100% 90% 90% Slow 100% 95% 100% 100% B(1.85m) Normal 100% 98% 95% 95% Fast 100% 100% 90% 90% In the experimental result, we conclude the height of the subject has no effect on the detecting performance. That is because we use online individual customized model for detection. However, the initial walking speed will affect the detection. When initial two steps are slower, the reference peak value for normal steps after correlation will be lower. Consequently, some hard steps will be judged as abnormal and detection accuracy for normal walking is lowered. While on the other hand, the performance for detecting abnormal behavior including stumbling and fall is better because of the lower normal peak. 4.4 Conclusion We use human locomotion model and impulsive based impact model to analyze the dynamics of the COM. Based on our analysis and simulation result, we develop the correlation based abnormal behavior detection method. The correlation model is determined based on the first two normal steps at the beginning of recording. The experiments are performed on two subjects with different heights and initial walking speeds. The detection result has validated our algorithms. 86

104 Chapter 5: Radiation Effects on DC Motorized Joint 5.1 Introduction Robots have played a significant role in modern daily life. Tedious and replicated jobs like assembling and house cleaning have been taken over by different kinds of robots. However, some operations are still highly dependent on human beings like rescue. The hazarded environment usually cast great threat on human health especially in the radiation sites like nuclear power plant. Confronted with the worldwide energy shortage, nuclear power plants have become the solution selected by many countries. Unfortunately, the associated problem is that the devastating pollution increases the difficulties of rescue when accident happens. The demand of substituting human beings with robot to perform timely and efficient rescue is a new challenge in robotics. The first challenge of robot rescue under radiation is to maintain the motion and manipulation capabilities. Inspired by Fukushima Daiichi accident, DARPA has held the Grand Robotics Challenge (DRC) to mimic the rescue sites. Humanoid robots are the focus since the plant is designed for easy human-shape access. Tasks like rough terrain and ladder climbing emphasize the motion, while valve turning and wall breaking aim at the manipulation. However, the competition is held in normal outdoor environment. The second crucial problem is the radiation damage to the 87

105 robot modules. Both electric and mechanical components can malfunction due to the high dose radiation. In 2007, NASA initiated a related project called the Radiation Hardened Electronics for Space Environment (RHESE) for development of radiation hardened electronic components [67]. Generally, the radiation effect on electrical circuits in robotic systems has been well studied [68 70]; however, the radiation effect on the performance of robot motor system has never been well studied before. A robot joint usually consist of DC motor, speed reducer and associated controller. In our previous work, performance of the DC motor under radiation is studied including the demagnetization of the permanent magnet [71]. An open loop forward PWM drive without load is presented. In this chapter, we will extend the study to the whole DC motorized joint module to see how it will impact the performance and the motion of a DC motorized manipulator. This chapter is organized as follows. In Section 5.2 the DC motor modeling merging the radiation effect is presented. In Section 5.3, motion of manipulator with position control is studied. Section 5.4 concludes the chapter. 5.2 DC Motor Variation after Radiation DC motor model without load According to the structure and working principles, DC motors can be categorized as brushed or brushless DC motor. Although the performances of different types of motor vary in large scale, the dynamic models capturing their behaviors are all similar. To get a quantitative result of the radiation degradation on DC motors, we pick the U12M4T servo disc motor with specifications in Table

106 Table 5.1: U12M4T disk servo motor specifications Specifications Symbol Values Unit Peak Torque T p 852 N-cm Rated Output P n 254 Watts Rated Voltage U n 40.4 Volts Rated Current I n 8.71 Amps Nominal Speed n 6000 RPM Rotor Inertia J m 1.84 Kg-cm 2 Back EMF Constant K e V-sec/rad Torque Constant K τ N-m/Amp Resistance R 0.75 Ohms Inductance L <100 uh Damping Constant K d 1.4 N-cm/kRPM Recall the DC motor dynamic models: dω m = (τ m K d ω m )/J (5.1) m dt U = (R + dl dt )I + U (5.2) e U e = K e ω (5.3) m τ m = K τ I (5.4) where ω m is the motor angular velocity, U the input voltage, I the current, U e the back-emf voltage, τ m the output torque and K d, J m, R, L, K e, K τ are defined in Table 5.1. The value of K e, K τ are the same due to the following relation: τ m = K τ I = U e I/ω m = K e ω m I/ω m = K e I (5.5) K e and K τ are highly dependent on the magnetic field (B-field) intensity of the permanent magnet within the motor Flux density (B-field) damage In our previous work, the permanent Nd-Fe-B magnets within the motor suffer handsome loss of magnetism after irradiated with fast neutrons [71]. Moreover, the 89

107 ferromagnetic materials are affected by neutron radiation and charged particles (protons and electrons) [72 76]. Consequently, the induced demagnetization in the DC motor is studied. We model the flux density (B-field) change as δ = B 0 B B 0 = k r ε, where ε N(µ, σ 2 ) (5.6) in which δ denotes the B-field change in percentage; B 0 and B are the B-field intensity before and after radiation within in the motor; k r is the coefficient of absorbed radiation dose; ε follows normal distribution N(µ, σ 2 ) with µ the average and σ 2 the spatial variance of particle energy. The modeling of B-field change above leads to two inferences about the radiation effects. First of all, the absorbed dose significantly affects the degradation level. Here we assume the dose is linearly related with the B-filed change with the coefficient k r. The second is that radiation degradation in B-field is not deterministic. That means two same motors under exactly the same radiation scenario may result in different B-field degradation. However, once the radiation degradation is done, the change in B-field is no longer random. The normal distribution is chosen to capture the stochastic radiation effect. In Eqn. 5.6, we decouple the radiation dose and normal distribution parameters, meaning µ and σ 2 are not functions of k r. Although k r may statistically affect µ and σ 2, Eqn. 5.6 fits well with our limited radiation experimental results of the permanent magnets Change of K e and K τ K e and K τ are linear functions of the B-field intensity. When the circuit containing the current rotates within in the B-field, the B-filed intensity is actually changing slightly. When circuit is right in the center of the B-field, the intensity is the greatest. 90

108 Otherwise, it drops as the circuit is away from the center. So K e and K τ are not truly constant. However, in practical applications, the motor usually rotate fast and the slight change in B-field is blurred. Thus K e and K τ are constants due to the averaged B-field intensity. The radiation will lead to B-field change as discussed in the previous part, we can derive that the effect on K e and K τ also follows normal distribution K e = K τ = k r ε 1, where ε 1 N(µ 1, σ 2 1) (5.7) Since K e and K τ are parameters describing the averaged B-field, we have µ 1 = µ and σ 2 1 < σ DC motor transfer function Transfer function of DC motor from input voltage to the output angular position is usually characterized as follows: G m (s) = θ m(s) U(s) = K τ s(lj m s 2 + (K d L + RJ m )s) + (K τ K e + RK d ) From Table. 5.1, L is very small, so Eqn. 5.8 can be simplified as θ m (s) U(s) = b s(s + a) a = K ek τ + RK d RJ m b = K τ RJ m (5.8) (5.9) (5.10) (5.11) a and b are the zeros and poles of the system, respectively. Before radiation, the transfer function is G mn (s) = 5780 s(s ) (5.12) 91

109 After radiation, a and b become stochastic and dependent on each other as functions of K e and K t. We perform a Monte Carlo estimation to get the approximate distribution of a and b. The radiation parameters are chosen as: k r = 1, u 1 = 0.03, σ1 2 = Fig. 5.1 shows the simulated marginal distribution of K e, a and b. It is shown that a follows similar distribution with K e due to their linear relationship shown in Eqn The marginal distribution of b is kind of screwed left compared to the normal distribution. Actually it is a chi-square distribution as indicated in Eqn Figure 5.1: Marginal distributions of motor parameters In statistical analysis, it is usually valuable to check the behavior at the mean and certain extreme conditions. Performing analysis within a 95 % confidence interval of random parameters is a solid approach. From Fig. 5.2, we can see the parameters of a and b are correlated. Since both of them are one-to-one functions of K e when K e > 0, the 95 % confidence interval of K e defines the corresponding confidence interval for aand b. As k r = 1, u 1 = 0.03, σ1 2 = 0.05, the mean, the upper and lower 95 % quantiles of K e, a and b are in Table 5.2. These means and quantiles can provide quantitative degradation extend of DC motors due to radiation. Even though the radiation effects 92

110 on DC motors are stochastic before radiation, we can use the quantiles to evaluate the motor performance in extreme cases, predicting the worst cases that could happen. Figure 5.2: Scatter plot showing pairwise correlation of K e, a and b 5.3 Manipulator Motion Performance Position control For most DC motorized joint, the load is not directly attached to the output shaft. A speed reducer usually combines the motor output shaft and load. By introducing the speed reducer, the load capacity is significantly increased. Also the radius torque 93

111 Table 5.2: Mean and quantiles of motor parameters after radiation Parameter Mean 2.5 % quantile 97.5 % quantile K e (K τ ) a b applied on the motor shaft is highly reduced, which protect the motor from potential damage. Moreover, some sensors are attached to the motor shaft to enable feedback control. Since position control is the most common control mechanism for manipulators, position sensor is applied to update the angular position. Incremental optical sensors are widely used due to their low cost and robust performance. Through integral of the sensed pulses, the angular position is updated. The optical sensors are usually installed on the motor shaft. Since the output angular speed is reduced, the effective sensing resolution at the load end is multiplied by the speed reduction ratio. Consequently, two or three channels optical sensor is adequate for practical applications. Fig. 5.3 shows the structure of DC motorized joint module for position control. Figure 5.3: DC motorized joint structure 94

112 θ ref is the reference angular position. θ m and θ are the actual angular position of motor shaft and load end, respectively. The speed reduction ratio is denoted as n and we have θ = θ m /n. U is the voltage input of motor and output of the controller. When PID controller is applied, U is determined by the following equations t de(t) U(t) = k p e(t) + k i e(t)dt + k d 0 dt e(t) = θ r ef(t) θ(t) θ(t) = θ m (t)/n (5.13) (5.14) (5.15) To study the radiation effects on the position control of DC motorized joint, we choose n = 100. We compare the performance with the following models: G(s) = θ(s) U(s) = K τ /(nrj m ) s(s + (K e K τ + RK)/(RJ m )) t de(t) U(t) = k p e(t) + k i e(t)dt + k d 0 dt e(t) = θ r ef(t) θ m (t)/n (5.16) (5.17) (5.18) Before radiation, the open-loop joint module transfer function is G n (s) = 57.8 s(s+59.67). After radiation, the mean, 2.5 % and 97.5 % quantiles of the corresponding transfer functions are: G rm = s(s ), G rl = 30.8 s(s ), G ru = s(s ) (5.19) In consideration of the overshoot, steady error elimination and settle time, we set the PID coefficients to be: k p = 40, k i = 8.62 and k d = These coefficients are constant throughout the analysis in this part. Because once the PID controller is designed, it will not change after radiation. For better comparison of the result, we set the reference position to be constant 1 and the initial position to be 0. Fig. 5.4 shows the step responses of position control before and after radiation. The G rm behaves almost the same with G n. However, the step responses of G rl and G ru are far away from G n. This means after radiation, the close-loop performance 95

113 Figure 5.4: Step response with θ ref = 1 rad Figure 5.5: Step response with θ ref = 1 96

114 may differ significantly. In the I and P curves of Fig. 5.4, the values are dramatically greater than the motor specifications. The reason is that we set θ ref = 1 rad directly. In practice, the reference angle should be broke down into several intermediate reference points for smooth motion. The negative P is because the large back-emf leads to opposite sign of U and I. To further check our PID controller design, Fig. 5.5 shows the results when θ ref = 1, which is a more realistic setting. In this case, I and P are within the limits of motor specifications. Moreover, all the θ is regulated at θ ref within 0.6s and G ru has a relative long setting time. Another thing to notice is that there is an obvious overshoot in the response of G rl. From the P curve of G rl, we can see it cost the most power. That means it is the least efficient case and the controller will behave aggressively to realize the position control. Consequently, the overshoot is most likely to occur in G rl Manipulator motion We further study the radiation effect on the robot motion. Since manipulator is a common tool equipped on the rescue robot, we use a manipulator and analyze the radiation degradation. The 5 degree-of-freedom (DOF) manipulator is the most common type like the PUMA-500 in our laboratory shown in Fig Excluding the two DOF on the gripper, there are three DOF on the manipulator arm. We will focus on the motion of 3 DOF robot arm. Fig. 5.7 shows the simplified manipulator model we use in this section. Point O represents the waist joint and A is the shoulder joint. Point B and C are the elbow and wrist joint, respectively. The parameters of this model for simulation are: 97

115 Figure 5.6: PUMA-500 manipulator in our lab Figure 5.7: Simplified manipulator model 98