Abstract. This paper reports the results of many projects undertaken in the support of a fivelink

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2 Abstract This paper reports the results of many projects undertaken in the support of a fivelink planar biped walking machine. The primary function of this research is to assist in the development of various walking gaits by addressing ongoing mechanical design issues pertaining to the planar biped, ERNIE. Experimentation is also a cornerstone of this research. This research focuses on difficulties confronted in the progression from ground walking to treadmill walking. The transfer of experience based knowledge gained from the work done with the biped walking mechanism is a main concern of this thesis. ii

3 Acknowledgements Upon the completion of a Bachelor s Degree in Mechanical Engineering at Ohio State University there are many people that had significant effect on my growth as a student, as a colleague, and as an individual. First and foremost, I would like to thank the advisers to my research, Dr. James Schmiedeler and Dr. Eric Westervelt. I have learned a great deal from both from a technical and personal perspective. Their constant availability, willingness to help, and desire to learn and teach has made this research very enjoyable. I value the experience I have gained working with all of the members of the Locomotion and Biomechanics lab at Ohio State University. I would also like to thank Tao Yang for his constant helpfulness and availability. Without Tao s constant help and attentiveness this research would not have been possible. Thanks to Gary Gardner, he has been very helpful throughout this research. I would like to thank my friends and family for their constant support and help throughout this research and throughout my life. Without my parents and brothers constant guidance and help I would not be in the position I am today. Thank you for all of your help. iii

4 Vita January 12, Born Fairview Park, OH, USA December 2004 June Product R & D Co-op Goodyear Tire and Rubber, Engineering Product Division, Marysville, OH June October Undergraduate Research Intern Ohio State University, Locomotion and Biomechanics Lab Columbus, OH June B.S. Mechanical Engineering The Ohio State University, Columbus, OH iv

5 Table of Contents Abstract... ii Acknowledgements...iii Vita... iv List of Figures...viii List of Figures...viii Introduction Background Motivation Objective Outline... 3 Robotics Overview of Documented Research in Legged Robotics Types of Biped Gaits Literature Review Asimo Rabbit BIRT ERNIE Overall Design Differences from BIRT Cabling System Control Links Overview ERNIE Design Changes Move and Setup in Scott Lab ERNIE Ground Walking ERNIE on the Treadmill Alternate Shank Gearhead problem v

6 3.4.1 Pin replacement Harmonic Drive Turnbuckle Experimental Results Procedure Walking Lessons Learned General Walking Lessons Ground Walking Lessons Treadmill walking Lessons Walking Experimentation Sensitivity analysis Overview Results across all simulated gaits Results: same gaits different configuration Gait m step height Gait m step height Results: same configuration different gaits Conclusion and Future Work Summary of Results Future Goals Recommendations References Appendix A (Write ups) Appendix B (CAD Drawings) Alternate Shank CAD Turnbuckle CAD Appendix C (Sensitivity Study Results) vi

7 List of Tables TABLE 1: ASIMO'S ACTUATED DOF (ADAPTED FROM [9])... 9 TABLE 2: RABBIT'S ACTUATED DEGREES OF FREEDOM (ADAPTED FROM [14]) TABLE 3: BIRT'S ACTUATED DEGREES OF FREEDOM TABLE 4: ERNIE ACTUATED DEGREES OF FREEDOM TABLE 5: LIST OF PERFORMANCE CHARACTERISTICS (TAKEN FROM [20]) TABLE 6: PHYSICAL PARAMETERS USED FOR THE SENSITIVITY STUDY OF A 5-LINK MODEL TABLE 7: NOMINAL PARAMETER VALUES TABLE 8: GAITS USED IN THE SENSITIVITY STUDY TABLE 9: SENSITIVITY STUDY: ACROSS ALL GAITS TABLE 10: SENSITIVITY STUDY: STEP HEIGHT M DIFFERENT CONFIGURATIONS TABLE 11: SENSITIVITY STUDY: STEP HEIGHT M DIFFERENT CONFIGURATIONS TABLE 12: SENSITIVITY STUDY: NORMAL CONFIGURATION DIFFERENT STEP HEIGHT TABLE 13: SENSITIVITY STUDY: ACTUATE FEMUR CONFIGURATION DIFFERENT STEP HEIGHT TABLE 14: SENSITIVITY STUDY: DIRECT DRIVE CONFIGURATION DIFFERENT STEP HEIGHT vii

8 List of Figures FIGURE 1: PHONEY PONY (CITATION)... 6 FIGURE 2: PLANES OF HUMAN BODY (TAKEN FROM [8])... 7 FIGURE 3: HONDA MOTOR COMPANY'S HUMANOID DEVELOPMENT (TAKEN FROM [9])... 8 FIGURE 4 : ASIMO WALKING DOWN STAIRS (TAKEN FROM [10])... 9 FIGURE 5: RABBIT WITHOUT STABILIZING BOOM (TAKEN FROM [12]) FIGURE 6: THREE LEGGED PLANAR BIPED, BIRT. (TAKEN FROM [15]) FIGURE 7: FRONT VIEW OF BIRT, SHOWING LEG SPLAY (TAKEN FROM [15]) FIGURE 8: SOLID MODEL OF BIRT'S TORSO. (TAKEN FROM [15]) FIGURE 9: ERNIE GROUND WALKING EXPERIMENTAL SETUP FIGURE 10: ERNIE SPRINGS FIGURE 11: ERNIE ON TREADMILL FIGURE 12: SINGLE TURN POTENTIOMETER (TAKEN FROM [17]) FIGURE 13: FERMUR LINK (LEFT) AND TIBIA LINK (RIGHT) (TAKEN FROM [16]) FIGURE 14: ASSEMBLED LEG FIGURE 15: SCOTT LAB SETUP, SAFETY LINE (LEFT) AND BOOM MOUNT (RIGHT) FIGURE 16: GROUND WALKING EXPERIMENTAL SETUP FIGURE 17: ERNIE SETUP ON TREADMILL IN SCOTT LAB FIGURE 18: TREDMILL SETUP (ABOVE VIEW) FIGURE 19: ALTERNATE SHANK FIGURE 20: DISASSEMBLED VIEW OF THE GEAR REDUCER FIGURE 21: RAISED CERAMIC PIN ON FINAL STAGE OF THE GEAR REDUCER FIGURE 22: GEAR REDUCER FINAL STAGE WITH STEEL PINS (LEFT), FINAL ASSEMBLY (RIGHT) FIGURE 23: HARMONIC DRIVE ISOMETRIC VIEW [19] FIGURE 24: HARMONIC DRIVE [19] FIGURE 25: ERNIE S TORSO FIGURE 26: TURNBUCKLE FIGURE 27: SPRING/TURNBUCKLE ON ERNIE FIGURE 28: SCHEMATIC OF A 5-LINK MODEL (TAKEN FROM [20]) FIGURE 29: SAMPLE OF METRIC VS. PARAMETER PLOT viii

9 Chapter 1 Introduction 1.1 Background Locomotion is the act of moving from place to place, an ability common to humans and animals alike that is necessary for their survival. A gait is defined as a particular way or manner of moving on foot. A human gait is the way every part of a human body works together in order to generate walking motion. Each person may have a unique walking gait. The majority of terrestrial locomotion falls into one of two categories: wheeled locomotion and legged locomotion. Wheeled locomotion, observed in man-made machines such as cars, is very stable and reliable and has many practical functions. A subcategory of wheeled locomotion is tracked vehicles, the primary advantage of which is the ability to more easily overcome unpredictable, adverse terrain. Legged locomotion is the focus of this thesis because of its advantages over wheeled locomotion. 1.2 Motivation Legged locomotion has many distinct advantages over wheeled and tracked locomotion. Wheeled and tracked vehicles are greatly limited by the terrain. A steep slope or rocky terrain can be a very large obstacle for a wheeled or tracked vehicle. A legged locomotion mechanism that is capable of robust walking can easily adapt to 1

10 different environments and situations. Most wheeled vehicles lack the ability to adjust to adverse terrain. Legged locomotion only requires a small secure area for the placement of the foot, called a footfall. Having a small footfall enables a legged locomotion mechanism to achieve more robust walking than wheeled or tracked vehicles. The ability granted by legged locomotion to go virtually anywhere motivates the imitation of legged locomotion in mechanical form. Because many parts of every day life have been designed to be easily accessible by humans, biped robotic mechanisms are a natural progression in the search for assistive robots. A personal assistant biped robot could be used by the elderly to complete everyday tasks, in a hospital to perform a range of tasks, or for entertainment purposes. Biped robots could replace humans in hazardous environments, such as search and rescue operations. Prosthetic development for human users is another possible application of biped robotics. It is difficult to measure the energy consumed by a living organism. However, the energy consumption of a machine can be easily calculated from the supplied current. Because of this, legged locomotion can assist in prosthetics development and reduce the iterative processes and human subject testing. 1.3 Objective The purpose of this research is to support the development of stable walking gaits at a variety of walking speeds with a five-link biped walking machine named ERNIE. A primary objective of this research is to make design changes to the existing mechanism and to develop innovative solutions to mechanical problems as they arise throughout this 2

11 research. All mechanical design changes made to ERNIE must be robust and durable in order to withstand the forces generated during high intensity walking. Experimentation is also a significant part of this research. Experiments take significant time to organize, set up, and run properly. This work supports the entire experimentation process. Developing and performing the experiments and analyzing the results is a crucial part of this research. From these experiments, valuable data can be collected and analyzed to determine the future of this research. 1.4 Outline This thesis is organized into four sections. Section 2 discusses the development of legged robotics and the current state of biped locomotion. Section 2 also discusses the developments of the Locomotion and Biomechanics Lab at Ohio State University in the field. Section 3 addressed all of the design changes that have been made to the biped planar walking machine. Section 4 discusses the experimental results. Section 5 concentrates on a sensitivity analysis that addresses the physical parameters of the system and how changing these parameters changes a number of quantitative metrics. Section 6 summarizes this work and elaborates on the future for this research. 3

12 Chapter 2 Robotics 2.1 Overview of Documented Research in Legged Robotics The study of the locomotion of animals dates back at least as far as 350 B.C with Aristotle s paper titled On the Gait of Animals [1]. Gravity powered toys were being constructed as early as These toys functioned by trading off potential energy for kinetic energy while accounting for losses in energy due to impact forces. This section will introduce biped gaits and discuss the development of actuated biped robots Types of Biped Gaits Biped gaits are divided into four categories. Each type of gait generates motion through various foot-ground contact patterns. The four categories of biped gaits are walking, running, skipping, and hopping. The gaits are composed of different combinations of double support, single support, and flight periods. A walking gait is composed of single support periods and double support periods. The two legs move separately, exactly out of phase. During single support, the stance leg is in contact with the ground, while the swing leg is moving. In double support, as the stance leg and former swing leg prepare to switch roles in preparation for the next step, both legs are in contact with the ground [2]. 4

13 A running gait is composed of single support periods and flight periods. Like the walking gait, the two legs of the biped function exactly out of phase. A flight period occurs when neither leg is in contact with the ground. The single leg stance period and flight period alternate repeatedly to achieve a running gait [2]. Hopping is composed of periods of double support and periods of flight. During a hop, both legs operate in phase, working together to generate movement, which is realized in the flight period. There are no single support periods, and during double support periods, both legs are stance legs. Animals, such as kangaroos, use hopping gaits to achieve high-speed locomotion [2]. The final gait is the less commonly used skipping gait. A skipping gait is executed with various combinations of double support, single support, and flight periods. This research focuses exclusively on walking gaits with the future goal of developing running gaits Literature Review Phoney Pony, an electric-actuated quadruped shown in Figure 1, was the first computer-controlled legged machine to walk [2]. Phoney Pony was designed and built at the University of California by Frank and McGhee in Because Phoney Pony was the first computer-controlled legged walking machine, it is credited as being the origin of motor-actuated walking mechanisms. 5

14 Figure 1: Phoney Pony (citation) Researchers at Waseda University have been researching humanoid bipeds since In 1973, Wabot-1 was constructed and is believed to be the first full-scale anthropomorphic biped to have the capability to execute a static walking gait. Waseda University has developed several prototypes with their walking legs, called WL or Waseda leg, technology including their most recent humanoid robot, the Wabian-2 [3]. Since the development of Wabot-1, significant efforts have been made to duplicate human joint structure in the hopes of developing the capability to precisely recreate human walking with a machine. Recent examples of attempts to mimic human joint structure are evident in HRP-2 [4], Johnnie [5], ASIMO [6], and QRIO [7]. Increasing the degrees of freedom (DOF) of the joints gives these robots the ability to closely duplicate some aspects of human walking. To demonstrate degrees of freedom the human shoulder can be approximated as a three-degree-of-freedom joint. The human shoulder can rotate forward or backward in the sagittal plane (1) and up or down in the coronal plane (2) and can twist (3). These planes are shown in Figure 2. The human hip 6

15 can be modeled as having three degrees of freedom as well. The human knee is usually modeled with only one degree of freedom, rotation in the sagittal plane. Increasing the degrees of freedom increases the versatility of the robot, but it also adds a great amount of complexity in the actuation. An actuator is needed to control most, if not all of the degrees of freedom. Increasing the DOF greatly increases the design complexity as well as the necessary complexity of control scheme. Figure 2: Planes of human body (taken from [8]) 7

16 2.1.3 Asimo Honda Motor Company developed ASIMO, shown in Figure 4, which stands for Advanced Step in Innovative Mobility. ASIMO is frequently used as an example for humanoid walking mechanisms because it is well known for its remarkable technological ingenuity. Honda Motor company has been involved in the development of humanoid locomotion since 1986 [9]. Figure 3 shows the progression of Honda Motor Company s Humanoid development program. Figure 3: Honda Motor Company's humanoid development (taken from [9]) 8

17 Figure 4 : ASIMO walking down stairs (taken from [10]) Table 1: ASIMO's actuated DOF (adapted from [9]) Head Arm Hand Leg Neck Joint Shoulder Joint Elbow Joint Wrist Joint 2 DOF 2 DOF x 1 head = 2DOF 3 DOF 1 DOF 1DOF 5 DOF x 2 arms = 10 DOF 5 fingers (grasping) 1 DOF 1 DOF x 2 hands = 2 DOF Hip Joint Knee Joint Ankle Joint 3 DOF 1 DOF 2 DOF 6 DOF x 2 legs = 12 DOF 9

18 ASIMO is an anthropomorphic biped that is 1.2 m (approx ) tall and weighs 52 kg (114.6 lbs). With 26 actuated joints, detailed in Table 1, ASIMO is capable of duplicating many human motions and actions. Powered by a 38.4 V, 10 amp-hour Nickel Metal Hydride (Li-ion) battery pack, ASIMO is capable of walking km/h. ASIMO is actuated by servomotors with harmonic drive gear reducers [9]. Harmonic drive gear reducers are discussed in detail in Section in relation to this research. ASIMO uses a zero moment point (ZMP) control strategy. Many bipeds use the ZMP control strategy to perform stable walking gaits. The ZMP is the position of the foot ground contact where the entire reaction force must be applied to counteract the moments generated by the gravitational force and the inertia of the biped [11]. ASIMO is a magnificent feat in engineering and is responsible for incredible technological advances. However, to advance any research, the shortcomings must be recognized, and once recognized, an effort should be made to improve on those shortcomings. ASIMO can mimic many human motions, but when walking, ASIMO does not mimic a human s natural walking motion. Additionally, ASIMO has large feet, as can be seen in Figure 4. Because of these large feet, stability is more easily achieved from a control perspective. This research attempts to control a more simply actuated biped with point feet Rabbit RABBIT is a biped robot with similar applications to that of ERNIE, the focus of this research. The basics of RABBIT s construction and intended use are similar to those of ERNIE. Both are five-link biped mechanisms that are meant to test various control 10

19 strategies. RABBIT was designed and built by ROBEA, a project group of the French research agency CNRS, the Center for National Science Research. [12] Figure 5 shows RABBIT without the stabilizing boom. RABBIT was designed with skate wheels aligned with the frontal plane. Because the boom stabilizes the robot in the frontal plane, the skate wheels eliminate radial loading of the shanks. This skate wheel concept will be discussed in relation to this research in Section 3.4. RABBIT uses brushless DC motors to actuate each of the joints. Table 2 shows RABBIT s actuated degrees of freedom. Coupled to the brushless DC motors by means of timing belts are harmonic drive gear reducers. The use of harmonic drive gear reducers located at the joints on RABBIT is a significant design difference from ERNIE. The hip motors are mounted within the torso, while the knee motors are mounted on the upper femurs, near the torso. A significant achievement with RABBIT by Morris at al. [13] was the ability to transition from a walking gait to a running gait where 6 consecutive steps at a running gait were achieved. The use of harmonic drive gear reduction does not allow for compliance during torque transmission from the motors to the joints. Low compliance is beneficial from a control standpoint because it allows for very precise control over the joints. From a hardware perspective, low compliance causes very high impact forces to be transmitted through the mechanism during running gaits, which can cause damage to the components over time. 11

20 Figure 5: RABBIT without stabilizing boom (taken from [12]) Table 2: RABBIT's actuated degrees of freedom (adapted from [14]) Leg Hip Joint Knee Joint 1 DOF 1 DOF 2 DOF x 2 legs = 4 DOF 12

21 2.2 BIRT BIRT, a planar biped, was designed and built by Dunki-Jacobs, Schmiedeler, and Westervelt at Ohio State University s Locomotion and Biomechanics Lab to test various control strategies [15]. BIRT, shown in Figure 6, is an acronym that stands for BIped Robot with Three legs. BIRT functions as a biped because the outside legs are slaved together using control. This means that the robot is stabilized in the frontal plane because the two outside legs work as one. BIRT behaves as if it were a five-link planar biped. Table 3 shows the actuated degrees of freedom. Six Maxon EC 40, 120 watt brushless DC motors with integrated planetary gear reducers are used to actuate the three single-degree-of-freedom hip joints as well as the three single-degree-of-freedom knee joints. All of the motors are mounted on the torso in order to save energy. By placing the motors in the torso, the moment of inertia of the femur and the tibia can be reduced along with the overall weight of each of these links. This, in turn, saves energy because there is less mass that needs to be moved by the motors. The femur and the tibia are made primarily of carbon fiber and some aluminum where necessary to reduce the weight and moment of inertia of the links. 13

22 Figure 6: Three legged planar biped, BIRT. (taken from [15]) Table 3: BIRT's actuated degrees of freedom. Leg Hip Joint Knee Joint 1 DOF 1 DOF 2 DOF x 3 legs = 6 DOF 14

23 Many lessons were learned from experience with BIRT that helped Bockbrader in the design of the five-link biped ERNIE [16]. The remainder of this section focuses on design issues and experience gained with BIRT and how these experiences were helpful in the development of ERNIE, which will be discussed in Section 2.3. The first of these issues was the observed leg splay, which is shown in Figure 7. After construction and cable tensioning, it was observed that neither of the outside legs was parallel to the middle leg nor perpendicular to the ground. From visual inspection, the center leg appears to be perpendicular to the ground, as it should be. Figure 7: Front view of BIRT, showing leg splay (taken from [15]) 15

24 The cause of the leg splay is the hip joint design and cable system. Figure 8 shows a solid model of BIRT s torso. The solid model clearly shows that the knee and hip driving cable on both of the outside legs are on the same side of the single torso mounting point for the hip axis. Because the knee and hip driving cables are both under tension, this loading causes bending of the hip axle and the leg splay shown in Figure 7. To prevent leg splay, an aluminum plate was added on the right and left side of the torso of BIRT so that both the knee and hip cable tension are evenly supported over the two aluminum plates to prevent the bending load. The leg splay issue on BIRT emphasized the importance of strong joints and evenly distributed loadings. Figure 8: Solid model of BIRT's torso. (taken from [15]) 16

25 Because BIRT was designed to be a planar biped by slaving the two outside legs together, there was an inherent problem. If the two outside legs were not perfectly in phase, errors would arise and a rocking motion in the coronal plane would develop after several steps. Because all of the joints have only 1 degree of freedom to control the motion in the sagittal plane, the mechanism has no way of correcting the motion in the coronal plane. This problem motivates an alternate approach to constrain a biped robot to the sagittal plane. 2.3 ERNIE The design of this planar, five-link mechanism came directly from Dunki-Jacobs BIRT [15]. Like BIRT, this mechanism was designed to be a testbed for various control schemes. The experimental setup of ERNIE during a ground walking test is displayed in Figure 9. The design will be explained later in this section. Bockbrader designed this mechanism to be very similar to BIRT with two exceptions explained in the following section. The following sections outline the overall design of this planar biped, and complete details on the design of this biped can be found in [16]. 17

26 Figure 9: ERNIE ground walking experimental setup Overall Design Differences from BIRT The first design difference between BIRT and this mechanism is that this mechanism was designed so that it could execute a running gait. A running gait is characterized as having periods of flight and periods of single support. BIRT was not capable of running, nor was it intended to be. The design of ERNIE focused on the development of a mechanism that was capable of walking as well as running. Because of the dynamics of running, there are larger accelerations and decelerations at the joints when compared to walking. Running gaits require that the joints, specifically the knee joints, are capable of producing much higher torques than walking gaits. This means that the motors on ERNIE must be capable of supplying the higher torque necessary during running. It was realized that the motors may not be able to supply the instantaneous 18

27 torque necessary to execute a running gait and that it would be important to have an additional means of applying torque at the knee joints. Figure 10 shows the linear springs on the mechanism stretching over the femur and connecting to the tibia to apply extra torque at the knee joints. Figure 10: ERNIE springs As discussed in Section 2.2, BIRT was constrained to be planar by a third leg. The gantry that supported BIRT made it difficult to safely perform experiments. The design of ERNIE addressed the problems encountered during experimentation with BIRT by implementing a carbon fiber boom. The boom is mounted securely to the wall by means of a universal joint, which allows this mechanism to remain planar as it walks in an arc (Figure 9). This simple and reliable setup made tests easier and safer. Another difference is that ERNIE has point contact feet whereas BIRT has line contact feet. BIRT s feet are cylindrical and perpendicular to the walking direction while ERNIE s feet are hemispherical. Point contact feet are very different from many other 19

28 anthropomorphic bipeds such as ASIMO. ASIMO has large feet (Figure 4), which make achieving stability much easier when compared to point contact feet. The feet of this mechanism, clearly shown in blue in Figure 11, are aluminum covered by a racquetball cut in half. The racquetball dampens impact forces, adds compliance to the system, and increases the coefficient of friction between the foot and the walking surface. All of these characteristics are important to ensure long life of the hardware and successful tests. 20

29 Figure 11: ERNIE on treadmill Table 4: ERNIE actuated degrees of freedom Leg Hip Joint Knee Joint 1 DOF 1 DOF 2 DOF x 2 legs = 4 DOF 21

30 2.3.2 Cabling System The torque is transmitted from the motors to the joints by means of a cable/pulley system. The actuated degrees of freedom of ERNIE are shown in Table 4. The motors with integrated gear reducers are mounted on the torso. The right and left hip motors output shafts are fixed to a pulley which simply transmits the torque to another pulley that is fixed to the hip axis. The knee torque transmission is more complex. The most simplistic design for the mounting of the knee motor would be to mount the motor directly at the knee axis or on the femur link itself. Both of these designs would yield a higher femur mass and a higher femur rotational moment of inertia; therefore, the knee motors are located on the torso. The output shaft of the knee motor is fixed to a pulley, and the knee cabling runs down to the hip axis. To transmit the knee motor torque over the hip axis without affecting the hip torque, an idler pulley is used at the hip axis. The cables from the knee motor pass around the idler pulley and then down through the center of the carbon fiber tubing that makes up the length of the femur link. A pulley on the knee axis receives the cabling through the femur and transmits the toque to the knee joint. The knee and hip cable/pulley system is mirrored for both legs of the mechanism. 22

31 2.3.3 Control This section provides a simplified overview of the control system. This mechanism functions time invariantly. Time invariance means that ERNIE does not perform any movements based on a given time line. All motions that ERNIE makes are a function of the configuration of the robot, which makes walking more robust. ERNIE used hybrid zero dynamic (HZD) control to create dynamic gaits. HZD control uses feedback to impose constraints based on the mechanism s configuration [14]. MATLAB and dspace create a closed loop control system for this mechanism. Feedback from the system gives the configuration of ERNIE to the dspace computer which in turn communicates with MATLAB. The motors are controlled by the dspace computer through the off-board amplifiers. Feedback of the mechanism configuration comes from two different sources: the motor encoders and the potentiometers at both hip joints and both knee joints. Potentiometers are variable resistors, illustrated in Figure 12. The motor encoder readings are used for the control because they have very high resolution and very low noise so that the control scheme has the most accurate configuration possible. Figure 12: Single turn potentiometer (taken from [17]) 23

32 Potentiometers are zero-order measurement devices, meaning that the voltage drop across the potentiometer is directly proportional to the joint angle; however, the signal from the potentiometers is noisy, which is undesirable because noise leads to poor control. Force Sensitive Resistors (FSRs) are used at the feet to sense the moment of ground contact. The point of ground contact is used to determine the point at which the stance and swing legs switch. Unlike BIRT, ERNIE only has four actuators. Because of their high power density, the Maxon line of brushless DC motors was selected to actuate ERNIE. The Maxon motor selected was the Brushless DC EC 45, 250 W, product number Integrated planetary gears with a ratio of 91:1 were selected to increase the torque and step down the speed necessary for the joint control Links ERNIE is a five-link planar biped. The full details of the design of each link of this mechanism can be found in [16]. The five-links are the torso, the left femur, the right femur, the left tibia, and the right tibia. The torso serves as the mounting link for the motors and the motor electronic connectors. The femur and tibia lengths are identical. Each femur is made of two pieces of carbon fiber tubing connected at each end by aluminum forks. The tibia is made of two concentric pieces of carbon fiber connected to an aluminum fork at one end and the foot at the other end. 24

33 Figure 13: Fermur link (left) and tibia link (right) (taken from [16]) Figure 14: Assembled leg 2.4 Overview This design overview summarizes how the mechanism functions as a whole and how the different systems coordinate with each other to perform successful walking gaits. The following section will discuss mechanical concerns and design changes that were introduced here. 25

34 Chapter 3 ERNIE Design Changes 3.1 Move and Setup in Scott Lab A new Mechanical Engineering building, Scott Laboratories, was constructed and completed in 2006 during the work of this thesis. In order to continue experimentation and to move the research forward, a stable setup for both ground walking and treadmill walking was required. The setup in Scott Lab needs to be safe and secure for ERNIE, easily accessible for experimentation, and flexible to accommodate any future changes. The wall mount, which connects to the boom of ERNIE by means of a universal joint, needs to be securely attached to the cinder block wall. Also, a safety line is required to protect ERNIE from damage if a fall occurs during experimentation. The setup in the new lab required some consideration to keep the electrical components (amplifiers, circuitry and dspace computer) and the control computer close to ERNIE for ease of experimentation. To attach the wall mount and the safety line to the wall, wood 2x4s and Unistrut metal framing were used. The completed mounting system is shown in Figure 15. The purpose of the 2x4s was to construct a stable mounting structure on top of the cinderblock wall in order to bypass electrical conduit and a window sill that were in the way on the only cinderblock wall in the lab. The U-shaped Unistrut was used to give the system extra flexibility while retaining its strength. The use of Unistrut makes it possible to easily convert the system from ground walking to treadmill walking as necessary to 26

35 continue experimentation. During all walking the carbon fiber boom is to be parallel to the ground. To move from ground walking to treadmill walking the universal joint, shown on the right in Figure 15, is raised so that the boom is parallel to the ground. The Unistrut allows for this adjustment of the boom (right) and the safety line (left). Figure 15: Scott Lab setup, safety line (left) and boom mount (right) 27

36 3.2 ERNIE Ground Walking Ground walking is a necessary step in this research in order to move forward to treadmill walking. Ground walking is safer for the mechanism because there is no moving treadmill and the mechanism is closer to the ground. Ground walking is used as a learning tool to develop the most stable walking possible so that when moving forward to the treadmill experiments, which are more dynamic and risky, the experimenters have confidence that ERNIE is safe. Ground walking has certain limitations. Based on the current setup, shown in Figure 16, ERNIE is restricted by the carbon fiber boom to motion in the sagittal plane which also restricts the walking path to a semicircular arc. The setup for ERNIE ground walking is a concrete floor with a rubber mat that covers the walking path of ERNIE in order to increase the friction between the feet and the ground during contact. For legged locomotion, slippage at the ground, due to a low coefficient of friction, is a recurring problem [18]. The walking surface was changed to increase the coefficient of friction in the direction of walking while minimizing that in the direction perpendicular to the walking. Minimizing the friction in the direction perpendicular to the walking allows the feet to slide in that direction and rotate small amounts, both of which are desirable for ground walking because of the discrepancy caused by the planar constriction of the boom. 28

37 Figure 16: Ground walking experimental setup There were many results from the ground walking experiments. The two most important results of the ground walking experiments were the development of stable ground walking gaits to be tested on the treadmill and experience. The experimenters gained considerable experience with gait development and the optimization process as well as problem diagnosis. Problem diagnosis is an important aspect that relates the physical problem causing some sort of instability during experimentation to the gait design process and will be discussed in Section 4.2. Ground walking is limited because of size constraints. Depending on the step length specified by the control system, a ground walking experiment will last only steps. Ground walking was used as a safe learning tool. 29

38 3.3 ERNIE on the Treadmill Treadmill walking has many benefits over ground walking. The treadmill allows for longer experiments. Longer experiments more clearly display stability. Ground walking experiments, on the other hand, do not last long enough to clearly show stability, nor do they capture enough data to yield accurate analysis. On the treadmill, any number of steps can be achieved. This allows for long data sets to be captured for analysis. The future goal of running with ERNIE would not be possible on the ground because of the size limitations of the given setup of ERNIE. Therefore, a treadmill is used to allow for unlimited steps during experimentation. Moving from ground walking to treadmill walking is a considerable change that brings about new problems and concerns that need to be addressed. The ground properties have a great effect on the stability of walking. The two primary ground properties that changed when moving to the treadmill are the coefficient of friction and the stiffness of the ground. The coefficient of friction between the foot and the ground would ideally be as high as possible. If there is not enough friction between the feet and the ground, there will be slippage. Slipping is bad because it is unexpected from a control perspective. Slipping is an instability that leads to the robot falling over. The change in ground stiffness is also very important to the repeatability of the walking. A softer surface, such as carpet, will absorb more of the impact at touchdown, and therefore, the system will lose energy. A harder surface, such as concrete, will not absorb as much of the impact, and therefore, will return much of the energy at touchdown back to the mechanism. For similar reasons, the harder surface results in shaper impact 30

39 loads on the robot, so here is greater potential for damage. If the energy lost at touchdown is not properly accounted for, the walking performance will be greatly affected. Figure 17: ERNIE setup on treadmill in Scott Lab The treadmill can be located at any place along the arc of the boom. Figure 18 shows the setup from an above view. The treadmill was placed in a location so that the arc through which ERNIE walks is maximized based on the treadmill length. The figure shows that because of the boom, ERNIE will walk through a circular arc while the treadmill is linear. This concern will be addressed by means of an alternate shank discussed in Section

40 Ernie s feet Walking Direction Front of Treadmill Carbon Fiber Boom Cinderblock Mounting Wall Figure 18: Tredmill setup (Above view) 32

41 3.4 Alternate Shank During treadmill walking experiments, it became apparent that there was an inherent problem in the difference between the path of the mechanism during a walking experiment and the linear path of the treadmill. The original foot-ground contact design for the mechanism is a machined piece of hemispherical aluminum covered by a racquetball. There are several concerns with the original design that motivated the design of an alternate shank. It was observed during experimentation that both of the belts of the treadmill were buckling. The friction between the racquetball feet and the treadmill belt surface was high enough that the foot would not slide perpendicular to the treadmill belt running direction. In this case, slipping perpendicular to the running direction of the treadmill belt is beneficial, while slippage in the running direction of the belts is not beneficial. The belt would buckle and move from its intended position due to the frictional force. Treadmill buckling could lead to permanent damage to the belts. In addition, the radial forces placed on the mechanism are undesirable and could cause damage to the mechanism over time. From a control perspective, frictional force between the foot contact and the ground are undesirable. The friction force could force the mechanism to stay in the center of the treadmill. The friction forces that were observed are stabilizing forces because they stabilized the mechanism from extreme movements toward the front or back of the treadmill. Artificial confidence in the effectiveness of the control would lead to erroneous results. 33

42 This design was to address the buckling treadmill belts and stabilization forces. The control of the mechanism occurs only in the sagittal plane; therefore, the alternate shanks were designed so the mechanism could roll small amounts in the frontal plane. Roller skate wheels were used because they are readily available, can withstand impact forces and have a satisfactory amount of compliance. Figure 19 shows the alternate shanks. Figure 19: Alternate shank The design of the alternate shanks was adapted from the shank design established by Bockbrader [16]. The alternate shanks were designed using the concentric carbon fiber tubing developed by Bockbrader in the original design. The overall length, 34

43 including the wheel, of the shank was maintained. An inline skate wheel was used because of its availability, its ability to withstand impacts, and its compliance. The Outside diameter (OD) is 3, the Inside Diameter (ID) is 0.950, and the width of the wheel is 1. The skate wheel rolls in the frontal plane. The ball bearings for the wheel are the matching Element inline skate wheel bearings. The bearings have an OD of 0.965, an ID of 0.310, and a width of Because the robot is stabilized by the boom in the frontal plane, the rolling of the wheel will not affect the walking motion. Detailed drawings of the designed parts are shown in the Appendix B. The carbon fiber tubing, circular spacers, upper shank plug and lower shank plug are assembled using Loctite brand 9460 Hysol epoxy adhesive. The Force Sensitive Resistors are used to sense ground contact as they are used in the original design. 3.5 Gearhead problem As detailed in Section 2.3.3, ERNIE is actuated by four brushless DC motors with integrated planetary gear reducers. The four motors, 2 hip motors and 2 knee motors, are identical and have identical gear reducers. The three-stage planetary gear reducer can be seen partially disassembled in Figure 20. Some problems were encountered during ground walking experiments as the left knee motor was not functioning properly. The joint would move in a very choppy, inconsistent manner, or it would not move at all. 35

44 Figure 20: Disassembled view of the gear reducer After disassembly of the gear box, it was clear that the problem was caused by an interference between the final two stages of the gear reducer. One of the pins about which a planet gear rotated had become loose and moved from its intended position. This problem was most likely caused by the high impact forces and vibrations to which the biped was exposed during each walking step. Ceramic pins, high in strength and low in weight, were only used on the final stage. The intended position was such that the top face of the pin would sit flush with the gear. As shown in Figure 21, the ceramic pin identified had moved from its intended position. Because the raised ceramic pin had the same diameter as holes in the middle stage of the gear reducer, the middle and final stages interlocked. The interference caused the left knee joint to function in a manner different from that specified by the control program, which is a clear problem. 36

45 Raised Ceramic Pin Figure 21: Raised ceramic pin on final stage of the gear reducer The first attempt to fix this problem was to have the ceramic pins removed and press fit into place again. This solution worked for some time, but after a number of cycles, the pins began to interfere again. Two solutions were considered. The first solution was to replace all of the ceramic pins with steel pins of the same size held in place by a set screw. The other solution explored was the replacement of the planetary gear reducers by harmonic drives. 37

46 3.4.1 Pin replacement The performance of the gear reducer is critical to the overall performance of the robot. Therefore, a reliable solution to this problem was necessary to move forward with confidence. This solution was important because the gear reducer moves at more than 5000 rpms and has to endure impact forces and constant vibrations. The solution was to replace the ceramic pins with comparable metal pins. To ensure that these pins would stay in place, a small notch was placed in the side of each of the pins. This notch functions as a resting place for a set screw that keeps the pins from moving. Figure 22 shows the final stage of the gear reducer without the gears but with the new metal pins and set screws. The set screw bores are cut at an angle rather than radially to the carrier to increase the number of engaged threads to increase holding force. A small amount of Permatex Threadlocker, Medium Strength (Blue), was used to hold the set screws, so they would not be loosened by the impact forces and vibrations during walking. This solution has solved the recurring problem of the moving pins. Set Screw Figure 22: Gear reducer final stage with steel pins (left), final assembly (right) 38

47 3.4.2 Harmonic Drive An alternative to the planetary gear reducers was explored in the meantime. This alternate solution was the use of harmonic drives. Harmonic drives have many desirable characteristics. Because the pin replacement solution successfully solved the problem, harmonic drives were not implemented, but are a very interesting possibility to discuss as a possible design change. The three main components of a harmonic drive are the circular spine, the wave generator, and the flexspline. The circular spline, which functions much like a sun gear of a planetary gear train, is the structural casing of the harmonic drive. The wave generator, clearly shown in Figure 24, is an elliptical shaped disc that rotates relative to the circular spline. The flexspline is a non-rigid cylindrical cup with external teeth to interface with the circular spline. The flexspline fits over the wave generator. The gear reduction is achieved because the flexspline has a slightly smaller pitch diameter than the circular spline. Therefore, the high rotational velocity at the input, the wave generator, is reduced to a lower angular velocity at the output, the flexspline. 39

48 Figure 23: Harmonic drive isometric view [19] Figure 24: Harmonic drive [19] This solution demands considerable design changes. To make change in the gear reduction method, the pros and cons of each method must be considered, and the necessary design changes explored. Harmonic drives have excellent position accuracy, high torque capacity, compact size and zero backlash. RABBIT, discussed in Section 2.1.2, utilizes harmonic drive gear reducers on the joints [12]. Torque is transmitted from the motors to the harmonic drives 40

49 by means of a timing belt. Because the reduction occurs at the joint, the compliance would be drastically reduced, leading to very precise joint angles. The planetary gear reducers have excellent position accuracy, high torque capacity and are compact, simple and inexpensive. Because of the cabling system necessary when planetary gear reducers are used, there is some compliance in the system. Some compliance is desirable in this mechanism to protect the components from potential damage from the high impact forces. The first design change to ERNIE would be in the torso. Because the torso was designed for the original motors with an inline gear reducer configuration, as shown in Figure 25, considerable design changes would be necessary to mount the motors in such a way that they will correctly interface with the very different design of harmonic drives. Figure 25: ERNIE s torso 41

50 Because the harmonic drives would be placed directly on the joint, the hip and knee motors would have to be mounted such that the output shafts of the motors would be outside of the torso. In addition to changing the mounting position of the motors, the idler pulleys would have to be moved outside of the torso. These design changes would likely result in a larger torso. Also, because the timing belt would be connected to the output shaft of the motor, the belt would be moving at a very high speed, which could be dangerous for the experimenters and for possible damage to the robot itself. 3.6 Turnbuckle One of the series of experiments done with ERNIE, which will be discussed in Section 4.2.3, was the analysis of the effect that adding springs to the knees had on the system from an energy cost perspective. During this experimentation, it became necessary to develop a simple, reliable means to frequently change the offset angle of the springs. The spring offset is defined as the angle of the tibia relative to the femur at which the linear spring becomes in tension. Prior to the experiments, gaits were developed, and part of this development was the optimization of the spring offset. Limited options were considered, and the means of adjustment of the spring offset was selected to be a turnbuckle. The difficulty in this design was that the turnbuckle would have to be very short and have a very short adjustment length. There was no commercially available turnbuckle that was suitable for this application. The turnbuckle, pictured in Figure 26, was made of steel with #10-32 threads. It has a fully extended length of and a compressed length of The 0.5 overall change in length corresponds to a Ө spring-offset = 15. Nuts are used to tighten down on each side of the 42

51 turnbuckle body to keep the body from moving during the dynamic loading seen during experimentation, which would change the offset angle. Detailed drawings of the turnbuckles are shown in Appendix B. During experimentation using the turnbuckles, it was discovered that because of the dynamic loading, the turnbuckle would periodically vibrate loose and therefore not maintain the desired spring offset angle. To address this problem, Teflon tape was wrapped onto the threads to maintain contact and friction between the threads on the turnbuckles screws and the threads on the turnbuckle body. Figure 27 shows the spring and turnbuckle system on the mechanism. Figure 26: Turnbuckle 43

52 Figure 27: Spring/Turnbuckle on ERNIE 44

53 Chapter 4 Experimental Results 4.1 Procedure Performing experimental testing with ERNIE was a large portion of this research. Effort was made throughout this work to achieve stable walking at a range of speeds under different conditions. The starting point and growth period for knowledge was ground walking. During ground walking, the robot walks through a circular arc on a high friction mat placed on the ground. The ground walking tests provided a secure option for experimentation. During treadmill walking, the boom of the robot only moves through small oscillations as the treadmill belts moves below the robot. The following sections address the lessons learned during experimentation and diagnosis issues that were confronted by this research. The motivation behind this section is to relay concepts learned from experience in experimentation. 4.2 Walking Lessons Learned There were many goals in the initial ground walking experiments aimed toward developing stable, natural-looking walking gaits. Important experience diagnosing and solving problems was gained at this stage. Section discusses the experience applicable to all types of walking experimentation. Section addresses issues 45

54 confronted specifically during ground walking experiments, while section deals with treadmill walking General Walking Lessons As discussed in Section 2.3.3, ERNIE has many available measurement devices that can deliver the current configuration of the mechanism. Either the potentiometers at each of the joints or the motor encoders could be used to control the robot. Both of these measurement devices have a downside. The potentiometers are simple, cheap and durable, but they have a very noisy signal. The motor encoders are very accurate, but the position reading of the motor is not the exact position of the joint due to compliance in the transmission cables. Initially, the potentiometer readings were used in the control programming to yield the mechanism configuration. Using the potentiometers to determine the mechanism configuration, ERNIE s joints move with very jerky movements. Because of the high frequency noise in the potentiometer readings, the links would shake at a high frequency. A low-pass filter was used in an attempt to filter out the high frequency noise, but all filters were unsuccessful in giving a smooth signal and therefore did not give adequate experimental results. The mechanism configuration is now obtained from the motor encoders. To minimize error in the configuration due to compliance, the transmission cables are maintained at a high tension. The cable tension is a very important aspect of all types of walking, ground or treadmill. If the cable is not properly tensioned, the high impact forces cause the joints to exceed their desired angle. Throughout experimentation, it was observed that the cable tension was not as high as it should be or had loosened over the course of many tests. 46

55 The low tension in the cables was most noticeable in the knee joints during touchdown. As the swing leg foot touches down under high impact forces, the knee joint flexes beyond the desired position of the knee joint. In this case, the cables should be under greater tension. The proper cable tension is a critical parameter to successful walking in all environments because with a higher cable tension, the motors have greater control over the joints. There is a limit to the cable tension. A very high cable tension can transfer the impact forces to the body and can lead to component damage. Therefore, the cable tension should be set through experimentation at a value high enough to have a manageable compliance from a control perspective but enough compliance to protect the mechanism from a hardware perspective. The best cable tension is determined through experimentation. The cable tension is controlled by two nuts on the upper femurs for the hip cables and two nuts on the upper tibias for the knee cables. To check the cable tension, the user would pinch the cables together. There is no cable tension measurement, and therefore adjusting the cable tension requires experience and experimentation. An issue separate from, but potentially diagnosed as cable tension is the hyperextension of the knee joint during walking. Hyperextension of a human knee occurs when the tibia moves beyond the physical limitations of the knee cap, muscles and tendons. Figure 28 shows the generalized schematic of a 5-link mechanism. Hyperextension occurs when q 3 is positive. Because the goal of this research is to create motions that are comparable to human walking, hyperextension is undesirable. Hyperextension is also undesirable from a control perspective because it causes a loss of 47

56 angular momentum. Through experimental experience, it has been observed that hyperextension occurs when the desired knee angle of the stance leg for a specific gait is too close to the singularity position, which occurs when q 3 is 0º. During experimentation, hyperextension of the knee joints should be monitored to ensure that it is not occurring. Hyperextension of the knee can be avoided during the gait design by ensuring that q 3 does not get to close to the singularity. Figure 28: Schematic of a 5-link model (taken from [20]) A frequent problem during experimentation was the feet. Some relative movement within the feet to sense touchdown of the feet with the Force Sensitive Resistors (FSR) is necessary. Too much movement causes energy loss, leading to instability. Therefore, it is critical to routinely tune the FSR value during experimentation. To sense foot touchdown, the derivative of the force reading from the 48

57 FSR is taken. This reading is an impulse. While the motors are Servo to Start or in the initial position, the robot is rocked back and forth without switching stance and swing legs from one leg to the other. From the saved data during this experiment, the magnitude of the minimum FSR reading can be established so that the initial impulse is read as the touchdown and any small perturbation in the signal is not falsely read as the touchdown of that foot. Throughout experimentation, Loctite was used on the four screws that hold each of the hemispherical feet to the tibias. These screws are to be handtightened to allow for the proper reading from the FSRs, but during a long stretch of experiments, the screws can be vibrated loose, and therefore, they should constantly be monitored Ground Walking Lessons One of the first and most critical issues addressed during this research was the coefficient of friction between the racquetball foot and the ground. If this coefficient is not high enough, the stance foot will slip, and this instability will cause the robot to fall. To achieve the best possible walking, the friction at the ground should be as high as possible. Therefore, the ground walking surface was changed to provide maximum friction in the direction of walking. The surface increased the coefficient of friction and prevented slipping. Prior to the surface change, it was noted throughout many experiments that foot slippage was never good. Foot slippage either caused an immediate fall or lead to a fall within a few steps. Therefore, the foot-to-ground contact should be observed closely to ensure that the foot is not slipping. The treadmill belts are a textured surface and do not result in slipping for most gaits. 49

58 4.2.3 Treadmill walking Lessons Switching from ground walking to treadmill walking is difficult because all of the difficulties of ground walking are still present and new difficulties are added by the treadmill. The primary difficulty that changes from ground walking to treadmill walking is the problem of keeping ERNIE centered on the treadmill surface. The treadmill has a safe walking surface length of 1.58 m (approx. 62 inches). With a step length of 0.2 m (approx. 8 inches), a few steps will move ERNIE very close to the front of the treadmill. Likewise, at a walking rate of 0.4 m/s, the treadmill can move ERNIE to the back of the treadmill quickly. The control approach attempts to keep ERNIE in the middle of the treadmill during treadmill walking experiments. The position of ERNIE horizontally on the treadmill was determined from the integral of the analog speed input over time. It was discovered through experimentation that this approach caused a problem within the control because the treadmill did not move at exactly the input speed. An encoder was placed on the treadmill to give accurate position and speed measurements. The current position of the robot relative to the treadmill is determined from the treadmill encoder and the encoder reading from the U-joint at the wall. 4.3 Walking Experimentation Most of the experimentation during the work of this thesis concentrated on developing stable, consistent walking gaits at various speeds. The first step was to develop consistent, stable walking gaits on the ground. Successful ground walking was achieved. The next step was to move from ground walking to treadmill walking. 50

59 Treadmill walking presented some complications that were very different from ground walking, as was discussed in the above sections. Successful treadmill walking was achieved. With reliably stable gaits successfully tested on the treadmill, this research expanded in scope to address other experimental testing. The use of springs on the mechanism for running gaits continues to be a concern. The next step in experimentation was to test the energy savings of springs at the knee joints. This is done by optimizing two gaits at the same walking rate, one without springs and one with springs. Both gaits are tested, and the walking cost is measured from the data collected during experimentation. This is done for gaits at a range of achievable walking rates. The comprehensive results of this series of experiments are yet to be determined, but after a preliminary comparison of successful walking experiments with and without springs it is observed that the springs save energy at all speeds. More energy is saved at higher walking speeds. The complete results of this study will be determined after the completion of this thesis. 51

60 Chapter 5 Sensitivity analysis 5.1 Overview This research continues and expands the scope of a sensitivity study begun by Adam Dunki-Jacobs at Ohio State University. The sensitivity study concentrates on the effects of design changes to an existing five-link biped walking mechanism on its stability, walking cost, fixed point location, walking rate, and maximum ground reaction force (GRF) ratio [20]. A generalized schematic of a five-link model consistent with ERNIE is shown in Figure 28. The sensitivity study was conducted by simulating walking in a simulation program called SHS sim. SHS sim was developed by E.R.Westervelt and B. Morris. The purpose of this program for this work is to simulate walking gaits and gather data concerning many different metrics of walking. After the simulation is complete, results are returned to be analyzed. Table 5 lists the five performance characteristics considered by this sensitivity study. Table 5: List of performance characteristics (taken from [20]) 52

61 There are thirteen physical parameters that characterize an actuated five-link planar biped. These thirteen parameters are shown in Table 6, the values of these parameters vary throughout the study but are based off of BIRT. The goal of this sensitivity study is to consider each of the parameters and determine which of these parameters are most influential on the performance characteristics of the biped. This sensitivity study is intended to drive and/or validate design changes to ERNIE. Table 6: Physical parameters used for the sensitivity study of a 5-link model (taken from [20]) Simulations were carried out on six different gaits designed for BIRT. Therefore, the nominal parameter values are from the physical setup of BIRT. In order to remain consistent with the sensitivity study performed by Dunki-Jacobs, gaits for BIRT were used. This sensitivity study considers the same gaits, parameters, and metrics used by Dunki-Jacobs, but differs in the method of quantifying the sensitivity values. Some of the nominal parameter values used in this study differ from the values used by Dunki- 53

62 Jacobs. Because BIRT and ERNIE are conceptually similar, the results from this study directly apply to ERNIE. This study was designed so that it could be easily applied to different gaits. Using this same methodology developed here, ERNIE s gaits could be tested to verify that the same trends. Parameter Table 7: Nominal parameter values Configuration Normal Actuate femur Direct Drive Hip Rotor Inertia Knee Rotor Inertia Torso Length Femur/Tibia Length Torso Mass Femur Mass Tibia Mass Distance from Hip to Torso COM Distance from Hip to Femur COM Distance from Knee to Tibia COM Torso Inertia about COM Femur Inertia about COM Tibia Inertia about COM The six gaits selected, listed in Table 8, were chosen because they matched the gaits used by Dunki-Jacobs. The reason for selecting these gaits was to give a range of different configurations of the robot and different walking gaits or walking motions. Table 8: Gaits used in the sensitivity study No. Configuration Gait change (step height) 1 Normal Knee actuator on femur Knee actuator on femur Normal All Joints directly driven* All Joints directly driven* * Actuators on both the knee and hip joint 54

63 The different configurations change the values of many of the parameters that are shown in Table 6. The change in the step height, or the ground clearance of the swing leg during its motion, changes the gait. The goal of this sensitivity study is to discover (1) dominant trends that apply across all of the gaits chosen, (2) dominant trends that apply when only the configuration is changed, and (3) dominant trends that apply when only the gait is changed. The study is performed by incrementally changing one of the thirteen parameters independent of the others and measuring the effect that the change has on the stability, walking cost, max GRF, walking rate and fixed point location. Each parameter is changed by +/- 1%, +/- 2%, +/- 3%, +/- 4%, +/- 5%, +/- 10%, +/- 15% and +/- 20% of the nominal value of that parameter, determined from the existing physical system. The simulation is run for each parameter at the nominal value and at each of these variations from the nominal, and data is generated. The data quantifying the stability, efficiency, max GRF, walking rate and fixed point location is gathered and sorted to be analyzed. The five performance characteristics are analyzed for each gait. A plot of the results is made comparing the percent change from the nominal parameter value (x axis) to the percent change from the nominal performance characteristic (y axis). A sample of this plot is shown in Figure 29. The sensitivity value is the slope of the linear fit line to the discrete values collected from the simulation. In the sample case in Figure 29, the sensitivity value is The sensitivity value is unitless % change, to allow for % change direct comparison of the sensitivity values of a parameter or metric. The larger the magnitude of the sensitivity value, the more influential that parameter is to that metric. The R 2 value shown in Figure 29 is a numerical value that indicates the accuracy of the 55

64 linear fit to the discrete points. If the R 2 value is 1, the linear fit is perfect. If the R 2 value is not close to 1, less than 0.8, special considerations should be made concerning that sensitivity value. Figure 29: Sample of metric vs. Parameter plot The sign of the slope of the linear fit can be negative or positive. The sign of the sensitivity value has a meaning as well as the magnitude of the value. The percent change of the metric is calculated by: percent change of metric = [ Nominal metric value] [ New metric value] [ Nominal metric value] Therefore, a positive sensitivity value indicates that as the parameter value is increased from the nominal value, the performance metric value will decrease and as the parameter value is decreased, the performance metric will increase. Conversely, a negative slope 56

65 indicates that as the parameter value is increased, the metric value will increase and as the parameter value is decreased, the metric value will decrease. By understanding the sensitivity values and their meaning, design trade-offs could be made to the parameters to maximize performance. 5.2 Results across all simulated gaits The first aspect of this study is to compare all of the gaits simulated and identify the dominant parameters for each of the metrics. It was hoped that the results would clearly show dominant parameters for the different metrics. Appendix C contains a sample spreadsheet of all of the sensitivity values. This spreadsheet is compressed and shown in Table 9. For simplicity, only the parameters with the highest sensitivity values are displayed, and the actual sensitivity values are not given, only the signs of the sensitivity values. The sign of the sensitivity value column indicates the sign of the sensitivity value for the six gaits simulated. Most of the sign values are consistent, but the asterisks on three of the parameters indicate the number of the sensitivity values from the six simulated gaits that do not agree with the majority. Table 9 shows that of the thirteen parameters that characterize this five-link walking biped, there are some recurring dominant parameters. The femur/tibia length, torso mass, and distance from hip to torso COM consistently appear as the dominant parameters. Therefore, these parameters have the greatest effect on the metrics. Of all of the dominant parameters shown in Table 9, there is a strong sign agreement for each parameter sensitivity value for the different metrics. This means that for all of the gaits simulated, changing any of these parameters will have a predictable effect, increasing or decreasing that particular metric. 57

66 Table 9: Sensitivity study: across all gaits Metric Fixed point location Max grf Stability Walking cost Walking rate Across All Gaits Parameter Sign of Sensitivity Value 1. Femur/tibia length (negative) 2. Torso mass (negative) 3. Distance from hip to torso COM (negative)* 1. Femur/tibia length (positive) 2. Distance from hip to torso COM (negative)* 3. Distance from knee to tibia COM (negative) 1. Torso mass (negative) 2. Distance from hip to torso COM (positive) 1. Femur/tibia length (negative) 2. Torso mass (negative)** 3. Distance from hip to torso COM (negative) 1. Femur/tibia length (negative) 2. Torso mass (negative) 3. Femur mass (positive) 4. Distance from hip to femur COM (positive) 5. Tibia mass (positive) * 1 disagreement in sign ** 2 disagreements in sign 58

67 For example, the three most dominant parameters for the walking cost metric are the femur/tibia length, torso mass, and distance from hip to torso center of mass (COM). Each of these sensitivity values is negative. Therefore, according to this sensitivity study if any of these parameter values are increased, the energy cost of walking will increase. Likewise, if any of these parameter values are decreased, the energy cost of walking will decrease. It is of interest to identify if any of the metrics is greatly affected by the parameter values or if there are metrics that are not affected by the parameter values. From the sensitivity value, it was determined that of the five metrics, the stability is least affected by changes in any parameter value. It can be observed that throughout the entire study, the sensitivity value pertaining to stability is consistently at least an order of magnitude smaller than the rest of the sensitivity values. Design changes can be motivated by the benefits indicated by these metrics. If one metric were more important than the rest, that metric could be the primary concern of a system redesign parameter. The relative size of the sensitivity values can also be considered. For example, assume that the primary metric being considered is walking cost with a secondary concern on the stability metric. For example in all gaits tested the femur/tibia length has a large negative sensitivity value pertaining to walking cost and a small negative sensitivity value pertaining to stability. Decreasing the femur/tibia length will have a greater effect on the walking cost. As the femur/tibia length is decreased, the walking cost and the stability will both decrease, but the walking cost will change a more significant amount than will the stability. 59

68 The observations from this aspect of the study are meant to be broad, across the board observations. These trends continue to be the dominant trends throughout the remainder of the sensitivity study. The next sections are more specific and analyze the effect of specific changes and any trends that can be identified from the results. These sections compare the same data used in the sensitivity study across all gaits; however, the results are organized in a different way, so that any trends that coincide with a particular change can be identified more easily. 5.3 Results: same gaits different configuration The results developed in this chapter are meant to build on top of each other. This section seeks to identify trends as the gait is kept constant and the robot configuration is changed. The data is shown in Table 10 and Table 11. Section discusses trends that can be identified only for the walking gait with a m ground clearance of the swing leg for the three different configurations. Section discusses trends that can be identified only for the walking gait with a m ground clearance of the swing leg for the three different configurations Gait m step height The results from a gait with a swing leg step height of m are show in Table 10. From these results conclusions can be drawn. The first conclusion is that the stability metric has a consistently higher sensitivity value in the direct drive configuration than in either of the other two configurations; therefore, if the robot joints were actuated by 60

69 motors located at the knee and hip joints, the stability would be more sensitive to changes in torso mass and changes in the distance from the hip to the femur COM. The walking rate metric has a negative sensitivity value for each of the configurations. This means that as the femur/tibia length is increased or the torso mass are increased, the walking rate will increase. This intuitively makes sense because with longer legs and no change in the rotational inertia of the legs, the mechanism will be able to walk at a faster rate and with more mass in the torso; there will be greater angular momentum which would result in a faster walking rate. 61

70 Table 10: Sensitivity study: step height m different configurations Same gait Different Configuration Metric Parameter Sign of Sensitivity Value Fixed Point location Step Height: m Actuate Direct Normal Femur Drive 1 Fermur/tibia length neg neg pos 2 Torso mass neg neg pos 3 Deistance from Hip to Torso COM neg neg neg Max grf Stability 1 Distance from Hip to Torso COM neg neg neg 2 Femur/tibia length neg pos pos 3 Distance from Knee to tibia COM neg neg neg 1 Torso Mass neg neg neg 2 Distance from Hip to Femur COM pos pos pos Walking cost 1 Femur/tibia length neg neg neg 2 Torso mass neg neg pos 3 Distance from Hip to Torso COM neg neg neg Walking rate 1 Femur/tibia length neg neg neg 2 Torso mass neg neg neg neg or pos means the value is approximately twice as large as the other values for a particular metric. neg or pos means the value is considerably more than twice as large as other values for a particular metric. 62

71 5.3.2 Gait m step height The results from a gait with a swing leg step height of m are show in Table 11. From these results conclusions can be drawn The dominant trend across the configurations for this gait is that the sensitivity value of the max GRF is consistently greater in the normal configuration than in the actuate femur and direct drive configuration. This is reasonable because the torso mass is highest in the normal configuration and the high step height of the swing leg in this gait would logically cause a greater Max GRF. Consistent with Section 5.3.1, the stability metric has a higher sensitivity value in the direct drive configuration; therefore, if the robot joints were actuated by motors located at the joints, the stability would be more sensitive to changes in torso mass and distance from the hip to the femur COM. Also consistent with Section 5.3.1, the sensitivity of the femur/tibia length and torso mass pertaining to the walking rate metric are negative in all configurations. Another observed trend associated with the walking rate metric for this gait is that the sensitivity value is consistently greater in the direct drive configuration than any of the other configurations. 63

72 Table 11: Sensitivity study: step height m different configurations Same gait Different Configuration Metric Parameter Sign of Sensitivity Value Fixed Point location Step Height: m Actuate Direct Normal Femur Drive 1 Fermur/tibia length neg neg neg 2 Torso mass neg neg neg 3 Deistance from Hip to Torso COM pos neg neg Max grf Stability 1 Femur/tibia length pos pos pos 2 Distance from Knee to tibia COM neg neg neg 3 Distance from Hip to Torso COM neg pos neg 1 Torso Mass neg neg neg 2 Distance from Hip to Femur COM pos pos pos Walking cost 1 Femur/tibia length neg neg neg 2 Torso mass neg neg pos 3 Distance from Hip to Torso COM neg neg neg Walking rate 1 Femur/tibia length neg neg neg 2 Torso mass neg neg neg neg or pos means the value is approximately twice as large as the other values for a particular metric. neg or pos means the value is considerably more than twice as large as other values for a particular metric. 64

73 5.4 Results: same configuration different gaits In comparing the sensitivity values for the same mechanism configuration with a different gait, various trends have been recognized. The data for this aspect of the study is shown in, Table 13, and Table 14. The trends recognized are the same between the configurations; therefore, the trends will be discussed in one section as they apply to all three of the configurations. The Max GRF metric is affected as the gait is changed from having a swing leg ground clearance of m to a swing leg ground clearance of m. This general trend is consistent for all configurations, but the exact effect is not the same for each case. If design changes are to be made to the mechanism to improve the walking with respect to the Max GRF, special consideration should be shown to the three dominant parameters, which are the distance from hip to torso COM, femur/tibia length, and distance from knee to tibia COM. The sensitivity value for the stability metric is increased in magnitude as the gait is change from m clearance to m clearance. Beyond these initial trends there are some sign of other trends but the frequency of the occurrences is not consistent enough to warrant a trend. This mechanism is very complex and small changes could have unforeseen effects. This study attempts to make broad observations, but from the limited data collected limited trends can be seen. In order to identify more subtle trends more simulation should be run and analyzed in the manner presented. 65

74 Table 12: Sensitivity study: normal configuration different step height Metric Fixed Point location Max grf Stability Walking cost Same Configuration (Normal) Different gait Parameter Sign of Sensitivity Value Femur/tibia length neg neg 2 Torso mass neg neg 3 Distance from Hip to Torso COM neg pos 1 Distance from Hip to Torso COM neg neg 2 Femur/tibia length neg pos 3 Distance from knee to tibia COM neg neg 1 Torso mass neg neg 2 Distance from knee to tibia COM neg neg 1 Femur/tibia length neg neg 2 Torso mass neg neg 3 Distance from Hip to Torso COM neg neg Walking rate 1 Femur/tibia length neg neg 2 Distance from Hip to Torso COM pos pos 3 Torso mass neg neg neg or pos means the value is approximately twice as large as the other values for a particular metric. neg or pos means the value is considerably more than twice as large as other values for a particular metric. 66

75 Table 13: Sensitivity study: actuate femur configuration different step height Metric Fixed Point location Same Configuration (Actuate Femur) Different gait Sign of Sensitivity Parameter Value Femur/tibia length neg neg 2 Torso mass neg neg 3 Distance from Hip to Torso COM neg pos Max grf Stability Walking cost Walking rate 1 Femur/tibia length pos pos 2 Distance from Hip to Torso COM neg pos 3 Distance from knee to tibia COM neg neg 1 Femur mass pos pos 2 Torso mass neg neg 3 Femur/tibia length neg neg 1 Femur/tibia length neg neg 2 Torso mass neg neg 3 Distance from Hip to Torso COM neg neg 4 Distance from Hip to Femur COM neg neg 1 Femur/tibia length neg neg 2 Torso mass neg neg 3 Distance from Hip to Torso COM pos pos neg or pos means the value is approximately twice as large as the other values for a particular metric. neg or pos means the value is considerably more than twice as large as other values for a particular metric. 67

76 Table 14: Sensitivity study: direct drive configuration different step height Metric Fixed Point location Max grf Stability Walking cost Walking rate Same Configuration (Direct Drive) Different gait Sign of Sensitivity Parameter Value Femur/tibia length pos neg 2 Torso mass pos neg 3 Femur mass pos neg 1 Femur/tibia length pos pos 2 torso mass pos pos 3 Distance from hip to femur COM neg neg 1 Torso mass neg neg 2 Distance from Hip to Femur COM pos pos 3 Femur/tibia length neg neg 1 Femur/tibia length neg neg 2 Femur mass neg neg 3 Distance from Hip to Femur COM neg neg 4 Distance from Hip to torso COM neg neg 1 Femur/tibia length neg neg 2 Torso mass neg neg 3 Femur Mass pos pos 4 Distance from Hip to Femur COM pos pos neg or pos means the value is approximately twice as large as the other values for a particular metric. neg or pos means the value is considerably more than twice as large as other values for a particular metric. 68

77 Chapter 6 Conclusion and Future Work 6.1 Summary of Results This research has served to support all aspects of the development of a five-link biped walking robot. All of the mechanical problems and design issues confronted during this research and experimentation have been addressed. An experimental procedure has been developed from experience (see Appendix A). With the goal of advancing the knowledge of mechanism design, the sensitivity study has identified dominant trends that could lead to design changes. 6.2 Future Goals The future of this research is very promising. There are numerous possibilities to explore. Experimentation is the key to advancing this work. A constant effort to expand the scope of the understanding of biped walking will develop a solid groundwork that will eventually lead to the realization of successful running gaits. Because of the nature of experimentation, it is necessary to actively monitor the system hardware to ensure that every part of the robot is functioning as it should. Constant maintenance of the hardware will always be necessary. The foot contact is responsive to changes throughout experimentation. However, the uniqueness of the point contact feet should be maintained as it is a good approach to gait development. Rolling 69

78 contact feet are an interesting concept that could be explored by building off of the hardware developed to study the alternate shank concept presented in Section 3.4. Expansion and implementation of the sensitivity study would prove to be a very helpful tool in mechanism design. The key to the implementation of this sensitivity study is to build confidence in the results. A reliable baseline of dominant trends is identified, but more simulations would cast light on new trends. Therefore, the study should be expanded to verify the global trends identified in Section 5.2 and to expand the scope beyond the six gaits selected to increase the range of data collected. It is possible that less obvious trends were overlooked because not enough data was collected from the limited number of gaits and configurations. 6.3 Recommendations A constant focus on experimentation and the development of new experiments to study different phenomena is crucial to developing a strong understanding of how an extremely dynamic gait, such as running, will be achieved. Reliable walking has been realized. At this point, the development of gaits is largely experience based. An effort should be made to convert this qualitative knowledge of gait design to quantitative methodology of gait design. Development of new gaits and new approaches to designing these gaits should be an area of concentration. By expanding the range of reliable walking gaits, a natural progression to running gaits will be less difficult. The physical parameters of the system should be studied carefully. Using the sensitivity study presented in Chapter 5 as a starting point, the physical parameters of a 70

79 biped could be optimized based on key performance metrics. Obtaining a range of walking gaits and possible running gaits is difficult, but could be made less difficult by carefully tuning the physical parameters of the system so that stable gaits are more easily obtained. Currently the design of ERNIE constrains the femur and tibia to be the same length. It would be interesting to alter the sensitivity study to investigate the effects of the tibia length as an independent parameter. The tibia length could be redesigned and constructed more easily than the femur, because the cable length depends directly on the length of the femur. Using the sensitivity study as a platform changing the tibia length could be explored. 71

80 References 1. Aristotle, On the gaits of animals. 350 B.C. 2. T. A. McMahon, Muscles, Reflexes, and Locomotion. 1984: Princeton University Press. 3. Y. Ogura, et al. Development of a human-like walking robot having two 7- DOF legs and a 2-DOF waist. in Proceedins of the IEEE International Conference of Robotics and Automation New Orleans, LA. 4. K. Kaneko, et al. Humanoid robot HRP-2. in Proceedings of the IEEE International Conference of Robotics and Automation New Orleans, LA. 5. M. Gienger, K. Loffler, and F. Pfeiffer. Towards the design of a biped jogging robot. in Proceedings of the IEEE International Conference of Robotics and Automation Seoul, Korea. 6. Y. Sakagami, et al. The intelligent ASIMO: System overview and integration. in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems Lausanne, Switzerland. 7. K. Sabe, et al. Obstacle avoidance and path planning for humanoid robots using stereo vision. in Proceedings of the IEEE International Conference of Robotics and Automation New Orleans, LA. 8. Yachigusa-Ryu Aiki-Bugei. Yachigusa Ryu 2007 [cited 2007; Available from: 9. Honda Motor Company. ASIMO Specifications [cited; Available from: B. Landon. Honda's ASIMO Humoanoid Robot comes to CES [cited 2007; Available from: noid_robot_comes_to_ces/. 11. A. Goswami, Postural stability of biped robots and the foot-rotation indicator (FRI) point. The International Journal of Robotics Research, vol. 18(no. 6): p G. Buche. ROBEA home page [cited; Available from: 72

81 13. B. Morris, et al., Achieving bipedal running with RABBIT: six steps toward infinity. Fast Motions in Biomechanics and Robotics: Optimization and Feedback Control, E. R. Westervelt, G. Buche, and J. W. Grizzle. Inducing dynamically stable walking in an underactuated prototype planar biped. in Proceedings of the IEEE International Conference of Robotics and Automation New Orleans, LA. 15. A.R. Dunki-Jacobs, Design of a planar walking machine that integrates mechanical and control design approaches, in Mechanical Engineering. 2005, The Ohio State University. 16. R. Bockbrader, Design of a five-link planar bipedal running mechanism, in Mechanical Engineering. 2006, The Ohio State University. 17. E. O. Doebelin, Measurement Systems, Application and Design. 2004, New York, New York: Mcgraw-Hill. 18. E. R. Westervelt, J. W. Grizzle, and D. E. Kodedischek, Hybrid Zero Dynamics of Planar Biped Walkers, in IEEE Transactions on Automatic Control. January p Harmonic Drive LLC. SHF and SHG Component Sets Housed Units [cited; Available from: A.R. Dunki-Jacobs, Sensitivity study of a 5-link biped walking machine. 2006, Unpublished project report, The Ohio State University. 73

82 Appendix A (Write ups) Disassembly of Ernie to access motors and gear heads. 1.) Loosen/Remove all the Hex head cap screws so that the leg will move freely relative to the right leg and the torso (24 on torso + 14 attaching torque tube to torso) ** Be certain to support the leg at all times, an additional person will be necessary to support the leg and help slide the leg to the extended position in step 2** a.) Remove the 14 Hex head cap screws on the torque tube (be careful when removing the torque tube because the hip potentiometers are fragile) b.) Remove the 8 screws from the electronic mount support (back of Ernie) to gain easier access to the motor mount screws c.) Remove all 8 screws on the front support (front of Ernie) to gain easier access to the motor mount screws d.) Remove the 4 screws from the top support. The entire left leg is now free to move (this includes the left hip and knee motors, left hip pulley, left knee idler pulley, thigh and shank with cabling. 2.) Slide the left leg to the fully extended position and attach to the torso. Not all the cap screws are necessary to hold the left leg in place because Ernie will not be walking and will only be in this position temporarily. 3.) With Ernie s torso in the fully extended position, remove the motors. a.) Release the drive cable tension by loosening the nuts that tension the cables with a 7/16 combo wrench. b.) Remove the 4 stainless steel hex head cap screws that mount the motor/gearhead to the torso using a 3mm allen key. This may require the use of the shortened 3 mm allen key because of tight spaces. (Shortened 3mm allen key should be in the lab tool box.) c.) Begin to slide the motor/gearhead out of the bearings. Because the fit between the output shaft of the motor and the inner race of the bearings is a tight fit there will be resistance. **Slide firmly but be extremely careful not to damage the motors, gearhead or encoder.** d.) While sliding the motor/gearhead out, the keys must be removed from the gearhead output shafts. The pulleys on the output shaft may need to be moved out of the way. 74

83 Gearbox Motor Encoder Aluminum Collar 4.) With all of the motor removed from the torso the gearbox can be removed. a.) Holding the motor and the gearbox and motor together is an aluminum collar with only two threads and a set screw. b.) Remove the small set screw. c.) The Aluminum collar is very easily damaged as it is aluminum threaded into steel. The collar is left handed thread. With a rubber mallet and a small flat headed screw driver carefully tap the collar loose. Another person will be necessary to secure the motor/gearbox as the collar is loosened. d.) Remove the snap ring on the output shaft of the gearbox. The three stage planetary gear reducer can be remove from the sun gear. 5.) Repeat instructions in reverse to reassemble the torso. a.) Remember to take great care in threading the aluminum collar on the motor gearbox assembly. The collar only has 1 or 2 threads total to tighten the gearbox to the motor. b.) Take care when tightening all of the screws onto the torso. The torso is primarily made of aluminum and the screws are steel. Therefore the threads on the torso could easily be damaged. c.) Because the tight fit between the bearings on the torso and the output shaft of the gearbox/motor, it will be necessary to temporarily assembly Ernie in an extended torso configuration. d.) Insert and hand tighten the 4 stainless steel screws on each of the motors. Do not tighten the 4 stainless steel screws that mount each of the motors to the torso until the cables are tensioned. 75