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Metastable Walking Machines

Harvard Engineering and Applied Science, 60 Oxford Street, Cambridge, MA 02138, USA, katiebyl{at}alum.mit.edu, Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Russ Tedrake

Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA russt{at}csail.mit.edu

Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Owing to limited energy budgets and limited control authority, these "disturbances" cannot always be canceled out with high-gain feedback. Minimally actuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limit-cycle stability; however, they can still demonstrate impressively long-living periods of continuous walking. Here, we employ tools from stochastic processes to examine the "stochastic stability" of idealized rimless-wheel and compass-gait walking on randomly generated uneven terrain. Furthermore, we employ tools from numerical stochastic optimal control to design a controller for an actuated compass gait model which maximizes a measure of stochastic stability—the mean first-passage time—and compare its performance with a deterministic counterpart. Our results demonstrate that walking is well characterized as a metastable process, and that the stochastic dynamics of walking should be accounted for during control design in order to improve the stability of our machines.

Key Words: legged locomotion • rough terrain • passive dynamic walking • metastability • mean first-passage time1 stability metrics • compass gait • rimless wheel

This version was published on August 1, 2009

The International Journal of Robotics Research, Vol. 28, No. 8, 1040-1064 (2009)
DOI: 10.1177/0278364909340446


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