Stable Gait Planning and Robustness Analysis of a Biped Robot with One Degree of Underactuation

Document Type: Original Article

Authors

Isfahan University of Technology

Abstract

In this paper, stability analysis of walking gaits and robustness analysis are developed for a five-link and four-actuator biped robot. Stability conditions are derived by studying unactuated dynamics and using the Poincaré map associated with periodic walking gaits. A stable gait is designed by an optimization process satisfying physical constraints and stability conditions. Also, considering underactuation problem, a time-invariant control law is designed to track the stable motion of biped. Validation of proposed approach is achieved by numerical simulations. Moreover, the robustness of motion on the uneven surfaces and elastic contact model are investigated.

Keywords


J. Kanniah and Z. N. Lwin, ZMP compliant gait generation strategies for seven-mass biped robots, International Journal of Humanoid Robotics, 5(4) (2008) 609-637.

S.A.A. Moosavian, M. Alghooneh, A. Takhmar, Stable trajectory planning, dynamics modeling and fuzzy regulated sliding mode control of a biped robot, IEEERAS International Conference on Humanoid Robots, Pittsburgh, USA, 2007, pp. 471-476.

M. Vukobratovic, B. Borovac, Zero-moment point – thirty five years of its life, International Journal of Humanoid Robotics, 1(1) (2004) 157–173.

T. McGeer, Passive dynamic walking, International Journal of Robotics Research, 9(2) (1990) 62–82.

E. Borzova, Y. Hurmuzlu, Passively walking five-link robot, Automatica, 40 (2004) 621-629.

A. Formal’sky, Y. Aoustin, On the stabilization of a biped vertical posture in single support using internal torques, Robotica, 23(1) (2005) 65-74.

C. Chevallereau, A. Formal’sky, D. Djoudi, Tracking of a joint path for the walking of an underactuated biped, Robotica, 22(1) (2004) 15-28.

C. Chevallereau, E. R. Westervelt, J. W. Grizzle, Asymptotically stable running for a five-link fouractuator planar bipedal robot, International Journal of Robotics Research, 24(6) (2005) 431-464.

Y. Aoustin, A. Formal’sky, Control design for a biped: Reference trajectory based on driven angles as function of the undriven angle, Journal of Computer and System Sciences International, 42(4) (2003) 159- 176.

S. K. Agrawal, A. Fattah, Motion control of a novel planar biped with nearly linear dynamics, IEEE/ASME Transactions on Mechatronics, 11(2) (2006) 162-168.

A. Chemori and A. Loria, Control of a planar underactuated biped on a complete walking cycle, IEEE Transactions on Automatic Control, 49 (2004) 838–843.

V. Sangwan, S. K. Agrawal, Differentially flat design of bipeds ensuring limit-cycles, IEEE International Conference on Robotics and Automation, (Roma, Italy, 2007), pp. 3589-3590.

T. Geng, B. Porr, F. Wörgötter, Fast biped walking with a sensor-driven neural controller and real-time online learning, International Journal of Robotics Research, 25(3) (2006) 243-259.

J. W. Grizzle, G. Abba, F. Plestan, Asymptotically stable walking for biped robots: analysis via systems with impulse effects, IEEE Transaction on Automatic Control, 46 (1) (2001) 51-64.

L. Cambrini, C. Chevallereau, C. H. Moog, R. Stojic, Stable trajectory tracking for biped robots, Proceedings of IEEE Conference Decision and Control, (Orlando Florida, 2001), pp. 4815-4820.

E. R. Westervelt, J. W. Grizzle, D. E. Koditschek, Hybrid zero dynamics of planar biped walkers, IEEE Transactions on Automatic Control, 48(1) (2003) 42- 56.

E. R. Westervelt, G. Buche, J.W. Grizzle, Experimental Validation of a Framework for the Design of Controllers that Induce Stable Walking in Planar Bipeds, International Journal of Robotics Research, 23(6) (2004) 559-582.

M. Nikkhah, H. Ashrafiuon, and F. Fahimi, Robust control of underactuated bipeds using sliding modes, Robotica, 25 (2007) 367–374.

A. D. Kuo, Stabilization of lateral motion in passive dynamic walking, International Journal of Robotics Research, 18(9) (1999) 917–930.

Y. Hurmuzlu, T. H. Chang, Rigid body collisions of a special class of planar kinematic chains, IEEE Transactions on Systems, Man, and Cybernetics, 22(5) (1992) 964-971.

A. Goswami , B. Espiau , A. Keramane , Limit cycles and their stability in a passive bipedal gait, Proceedings of the 1996 IEEE International Conference on Robotics and Automation (Minneapolis, Minnesota, 1996), pp. 246-251.

C. Canudas, H. Olsson, K. J. Astrom, P. Lischinsky, A new-model for control of systems with friction, IEEE Transactions on Automatic Control, 40(3) (1995) 419- 125.

W. D. Marhefka, D. E. Orin, A compliant contact model with nonlinear damping for simulation of robotic systems, IEEE Trans. Syst., Man and Cybernetics. part A: System and Humans, 29(6) (1999).