Machines That Walk
This paper explores the notion that the control of dynamically stable legged systems that locomote in 3-space can be decomposed into a planar part and an extra-planar part. The planar part generates the large leg and body motions that raise and lower the legs to achieve stepping, that propel the system forward, and that maintain balance. The planar part of the control system deals only with 2D dynamics. The extra-planar part of the locomotion control system suppresses motion in those degrees of freedom that would cause deviation from the plane of motion. These degrees of freedom include roll of the body, yaw of the body, and translation perpendicular to the intended direction of travel.
Study of 2D one-legged hopping systems shows that the planar part of the control system may be quite simple, incorporating separate controllers for hopping height, running velocity, and body attitude. We review data from such planar systems, both simulated and physical, that illustrate the ability to hop in place, to run at a specified rate, to travel from place to place, and to leap over obstacles. Simulations of a 3D one-legged system show that the extra-planar part suppresses roll and yaw with good precision, while the planar part behaves as it did in 2D. Using the planar and extra-planar controls, the simulated 3D system traversed paths composed of straight segments.
KeywordsInverted Pendulum Lateral Translation Forward Velocity Planar Part Servo Valve
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- 2.Beletskii, V.V., Kirsanova, T.S. “Plane linear models of biped locomotion.” Izv. AN SSSR. Mekhanika Tverdogo Tela 11, 4 (1976), 51–62.Google Scholar
- 7.Higdon, D.T., Cannon, R.H., Jr. On the control of unstable multiple-output mechanical systems. Proc. of Winter Annual Meeting, ASME Winter Annual Meeting, 1963.Google Scholar
- 8.Juricic, D., Vukobratovic, M. “Mathematical modelling of bipedal walking system.” ASME Publication 72-WA BHE-13 (1972).Google Scholar
- 9.Kato, T., Takanishi, A., Jishikawa, H., Kato, I. The realization of the quasi-dynamic walking by the biped walking machine. 4th Symposium on Theory and Practice of Robots and Manipulators, IFTMOM, 1981.Google Scholar
- 10.Matsuoka, K. A model of repetitive hopping movements in man. Proc. of Fifth World Congress on Theory of Machines and Mechanisms, IFIP, 1979.Google Scholar
- 11.Matsuoka, K. “A mechanical model of repetitive hopping movements.” Biomechanisms 5 (1980), 251–258. In JapaneseGoogle Scholar
- 13.Miura, H., Shimayama, I. “Computer control of an unstable mechanism.” J. Eac. Eng., 17 (1980), 12–13. In JapaneseGoogle Scholar
- 14.Murthy, S.S., Raibert, M.H. 3D Balance in Legged Locomotion: Modeling and Simulation for the One-Legged Case. Inter-Disciplinary Workshop on Motion: Representation and Perception, ACM, 1983.Google Scholar
- 15.Raibert, M.H., Brown, H.B., Jr., Chepponis, M., Hastings, E., Murthy, S.S., Wimberly, F.C. Dynamically Stable Legged Locomotion — Second Report to DARPA. Tech. Rept. CMU-RI-TR-83–1, Robotics Institute, Carnegie-Mellon University, 1983.Google Scholar