Legged Robots on Rough Terrain: Experiments in Adjusting Step Length Jessica Kate Hodgins November 1989 CMU-CS-89-151 Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science at Carnegie Mellon University Copyright Q1989 Jessica Kate Hodgins This research was sponsored by contract MDA903-85-K-0179 from the Defense Advanced Research Projects Agency, Information Sciences Technology Office, and by a grant from the System Development Foundation. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any of the sponsoring agencies. Abstract To travel on rough terrain, a legged system must use the available footholds, even when they are isolated or hidden by obstacles. This thesis addresses the task of adjusting the length of each step to place the feet on available footholds, in the context of a dynamic biped robot that actively balances itself as it runs. In order for the biped to use specific footholds, the control system must simultaneously satisfy the constraints for stability and the constraints dictated by the geometry of the terrain. I explored three methods for controlling step length each of which adjusted a different parameter of the running cycle. The parameters were forward running speed, running height, and duration of ground contact. All three control methods were successful in manipulating step length, but the forward speed method provided accurate control of step length (average absolute error 0.07 m) and the widest range of step lengths (from 0.1 m to 1.1 m). In laboratory demonstrations the biped used step length adjustment to place its feet on targets, leap over obstacles, and run up and Clown a short flight of stairs. Acknowledgments I would like to thank the members of the Leg Laboratory for their support and encourage- ment. I am grateful to Marc Raibert for helping me over many rough spots and tbr his unflagging enthusiasm and remarkable intuitions. Jeff Koechling, Ben Brown, Mike Chep- ponis, and Dave Barrett patiently answered my many questions. Thanks to Matt Mason for stepping in as my advisor when the need arose. The CMU Computer Science Department was most generous in allowing me to complete the latter part of my research at MIT. Sharon Burks, of course, was the one who made all the administrative tangles disappear. Thanks also to my friends in Pittsburgh and in Boston who were always willing to go out for ice cream when work in the lab demanded it. And finally, many thanks to my parents for getting me started on the right foot. iii Contents Abstract i Acknowledgments iii Contents iii Chapter 1. Introduction 1 1.1 Statement of Problem: Control of Step Length .............. 7 1.2 Overview of the Thesis ........................ 12 Chapter 2. Background 13 2.1 Machine Locomotion ......................... 13 2.2 Animal Locomotion ......................... 19 Chapter 3. Experimental Methods 23 3.1 Experimental Apparatus: Planar Biped ................ 26 3.2 Control Algorithms .......................... 32 3.3 Experiments with the Planar Biped ................... 35 Chapter 4. Forward Speed 43 4.1 What Determines Forward Speed? ................... 44 4.2 Controlling Forward Speed ...................... 46 4.2.1 Oscillations in Forward Speed ........... ..... 48 4.2.2 Modeling Error ...................... 54 4.3 How Well Is Forward Speed Controlled? ................. 57 4.4 Using Forward Speed to Control Step Length .............. 60 Chapter 5. Flight Duration 65 5.1 What Determines Flight Duration? .................. 66 5.2 Controlling Flight Duration ...................... 68 v vi CONTENTS 5.2.1 Desired System Energy ................... 68 5.2.2 Actual System Energy ................... 69 5.2.3 Controlling the Energy ................... 71 5.3 How Well Is Flight Duration Controlled? ................ 74 5.4 Using Flight Duration to Control Step Length .............. 76 Chapter 6. Stance Duration 81 6.1 What Determines Stance Duration? .................. 82 6.2 Controlling Stance Duration ...................... 86 6.3 How Well Is Stance Duration Controlled? ................ 88 6.4 Using Stance Duration to Control Step Length .............. 94 Chapter 7. Direct Placement 101 7.1 A Fourth Method for Controlling Step Length? ............. 102 7.2 In Combination with Other Methods .................. 104 Chapter 8. Control of Step Length 107 8.1 Comparison of the Three Methods ................... 107 8.1.1 Range of Step Lengths ................... 109 8.1.2 Accuracy ......................... 113 8.1.3 Other Criteria for Evaluation ................ 114 8.2 Demonstrations ........................... 115 8.2.1 One-dimensional Rough Terrain ............... 116 8.2.2 Two-dimensional Rough Terrain ............... 122 Chapter 9. Summary 127 9.1 Control of Step Length ........................ 128 9.2 Results ............................. 132 9.3 Demonstrations ........................... 135 9.4 Future Research ........................... 136 9.4.1 Combining Methods .................... 136 9.4.2 Other Demonstrations ................... 137 9.4.3 Three-dimensional Rough Terrain .............. 137 9.4.4 Reflexes .......................... 138 9.5 Conclusion ............................. 139 Bibliography 141 Chapter 1 Introduction Legged vehicles may someday travel on terrain that is too rough for wheeled and tracked vehicles of comparable size. To travel on rough terrain, legged vehicles will have to use the best footholds they can reach, even those which are isolated or hidden by obstacles. The problem of traveling over rough terrain includes many sub-problems, including terrain sensing, path planning, selections of foothold, and adjustment of step length. This thesis concentrates on the last of these problems, the need to adjust the length of each step so the feet are placed on chosen footholds. The ability to adjust step length permits a legged system to use the best foothold within reach or to approach an obstacle in a way that allows the system to step or leap over it. When a legged system runs on a smooth surface, all the terrain is available as footholds and the length of its steps can vary freely. When a legged system runs on rough terrain, however, the nature of the terrain may dictate where it can place its feet and the length of its steps. The ability to adjust step length allows a legged system to run across rough terrain by using the regions of the terrain that provide good footholds while avoiding the others. Figure 1-1 illustrates the need for positioning the foot and controlling step length in order to negotiate obstacles. The foot must be in the correct position on takeoff to clear the blocks. If the position of the foot is too close to the blocks, the machine kicks the blocks at the beginning of the jump. If the position of the foot at takeoff is too far away, the machine lands on top of the blocks. The top photograph shows a good placement that allowed the 2 INTRODUCTION Figure 1-1. Planar one-legged hopping machine leaping. In order to leap over an obstacle success- fully, a legged system must choose a foothold that is properly positioned with respect to the obstacle, and it must place its foot on that foothold. The correct foot placement in the top photograph was a matter of good luck. In the middle photograph, the foot was too close to the stack of blocks when the leap began; in the bottom photograph, it was too far away. In each photograph action is from right to left, with lines indicating the paths of foot and hip (Raibert 1986). foot to clear the blocks and the machine to continue running. If this legged system had the ability to adjust step length, it could adjust the steps preceding the blocks so that the position of the foot at takeoff was correct every time and each leap was successful. I have studied the control of step length for a restricted class of legged systems-- dynamically stable legged systems running with a single-foot gait. For the legged systems I have considered, a running step contains a ballistic flight phase during which no feet touch the ground and a stance phase when a single foot is in contact with the ground. At the end of the flight phase, one foot touches the ground and a spring in the leg compresses. Halfway through stance, the spring expands and the body accelerates upward. The next flight phase begins when the foot is pulled off the ground. The control of step length is an interesting problem for a dynamically stable legged system. The act of positioning tile feet with respect to available footholds interacts with the stability and general behavior of the system. Each placement of a foot on the ground causes the body to accelerate, influencing the system's forward speed and direction of travel. A system that controls placement of the feet must simultaneously satisfy the geometric constraints dictated by the locations of good footholds and the dynamic constraints of stability. On each step there is a location on the ground where the foot should be placed if balanced steady-state running is to continue, the balance foothold. If the terrain limits the choice of footholds, the foot will not necessarily be able to be placed on the balance foothold. The legged system can either take action before the touchdown to make the desired foothold coincide with the balance foothold or it can take corrective action after the touchdown to restore the nominal running pattern. Once the problem of placing feet on chosen footholds is solved, a dynamic legged system should be able to traverse more difficult terrain than a static system of comparable size and reach. A dynamic system need not maintain support continuously in time, nor must there be a continuous path of closely spaced footholds to allow a gradual transfer of support from one support tripod to another. A dynamic system can use its flight phase to leap over regions that do not offer any good footholds.