STABLE PERIODIC GAITS OF N-LINK BIPED ROBOT IN THREE DIMENSIONAL SPACE

Abstract In passive walking, dissipation due to impacts or damping is offset by the use of potential energy supplied by walking down a slope. In this paper, we develop an analytical procedure to prove the existence and find active limit cycles of a rigid biped in 3-dimensional space. From an existing passive limit cycle, we use the theoretical framework of dynamic geometry and energy shaping, to develop a nonlinear feedback control law wich allows the robot to reach stable gaits corresponding to various velocities. Finally, an example that treat a biped robot with knees is presented to illustrate the theoretical results.

[1]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[2]  Arthur D. Kuo,et al.  Stabilization of Lateral Motion in Passive Dynamic Walking , 1999, Int. J. Robotics Res..

[3]  Tad McGeer,et al.  Passive walking with knees , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[4]  Carlos Canudas de Wit,et al.  Switching and PI control of walking motions of planar biped walkers , 2003, IEEE Trans. Autom. Control..

[5]  Mark W. Spong,et al.  Passivity based control of the compass gait biped , 1999 .

[6]  Katsuhisa Furuta,et al.  Passive velocity field control of biped walking robot , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[7]  Bernard Espiau,et al.  A Study of the Passive Gait of a Compass-Like Biped Robot , 1998, Int. J. Robotics Res..

[8]  Fumihiko Asano,et al.  Extended passive velocity field control with variable velocity fields for a kneed biped , 2001, Adv. Robotics.

[9]  Bernard Espiau,et al.  Limit Cycles in a Passive Compass Gait Biped and Passivity-Mimicking Control Laws , 1997, Auton. Robots.

[10]  Fumihiko Asano,et al.  Virtual gravity and coupling control for robotic gait synthesis , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[11]  M. Coleman,et al.  The simplest walking model: stability, complexity, and scaling. , 1998, Journal of biomechanical engineering.

[12]  Franck Plestan,et al.  Asymptotically stable walking for biped robots: analysis via systems with impulse effects , 2001, IEEE Trans. Autom. Control..

[13]  Francesco Bullo,et al.  Controlled symmetries and passive walking , 2005, IEEE Transactions on Automatic Control.

[14]  Martijn Wisse,et al.  A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees , 2001, Int. J. Robotics Res..

[15]  G. W. Howell,et al.  Simple controllable walking mechanisms which exhibit bifurcations , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[16]  Frédéric Boyer,et al.  An Efficient Calculation of Flexible Manipulator Inverse Dynamics , 1998, Int. J. Robotics Res..

[17]  Tad McGeer,et al.  Passive Dynamic Walking , 1990, Int. J. Robotics Res..