Metastable Walking on Stochastically Rough Terrain

Simplified models of limit-cycle walking on flat terrain have provided important insights into the nature of legged locomotion. Real walking robots (and humans), however, do not exhibit true limit cycle dynamics because terrain, even in a carefully designed laboratory setting, is inevitably non-flat. Walking systems on stochastically rough terrain may not satisfy strict conditions for limit-cycle stability but can still demonstrate impressively long-living periods of continuous walking. Here, we examine the dynamics of rimless-wheel and compass-gait walking on randomly generated rough terrain and employ tools from stochastic processes to describe the ‘stochastic stability’ of these gaits. This analysis generalizes our understanding of walking stability and may provide statistical tools for experimental limit cycle analysis on real walking systems.

[1]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[2]  K. Vahala.  Handbook of stochastic methods for physics, chemistry and the natural sciences , 1986, IEEE Journal of Quantum Electronics.

[3]  P. Hänggi,et al.  Discrete dynamics and metastability: Mean first passage times and escape rates , 1987 .

[4]  Daniel E. Koditschek,et al.  Analysis of a Simplified Hopping Robot , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[5]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

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

[7]  Benoit Thuilot,et al.  Compass-Like Biped Robot Part I : Stability and Bifurcation of Passive Gaits , 1996 .

[8]  P. Talkner,et al.  RATES AND MEAN FIRST PASSAGE TIMES , 1997 .

[9]  M. Coleman,et al.  Motions of a Rimless Spoked Wheel: a Simple 3D System with Impacts , 1997 .

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

[11]  Andrew W. Moore,et al.  Barycentric Interpolators for Continuous Space and Time Reinforcement Learning , 1998, NIPS.

[12]  Mark W. Spong,et al.  Further results on control of the compass gait biped , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[13]  Russell L. Tedrake,et al.  Applied optimal control for dynamically stable legged locomotion , 2004 .

[14]  Russ Tedrake,et al.  Efficient Bipedal Robots Based on Passive-Dynamic Walkers , 2005, Science.

[15]  Katie Byl,et al.  Approximate optimal control of the compass gait on rough terrain , 2008, 2008 IEEE International Conference on Robotics and Automation.