Dynamic Coupling as an Indicator of Gait Robustness for Underactuated Biped Robots

Abstract

This paper employs velocity decomposition of underactuated mechanical systems to determine the degree of dynamic coupling in the gaits of a two-link biped model. The degree of coupling between controlled and uncontrolled directions quantifies the control authority the system has over its unactuated degree of freedom. This paper shows that the amount of coupling is directly correlated to gait robustness, as seen through the size of the gait's region of attraction. The analytical measure of coupling is applied in the context of trajectory optimization to generate two-link gaits that maximize or minimize coupling. Simulation studies show that gaits maximizing coupling exhibit significantly superior robustness, as measured by 1) stochastic performance on uneven terrain, 2) ability to maintain desired walking speed under non-vanishing disturbances, 3) size of the region of attraction, and 4) robustness to model uncertainties.