Dominant sources of variability in passive walking

Abstract

This paper investigates possible sources of variability in the dynamics of legged locomotion, even in its most idealized form. The rimless wheel model is a seemingly deterministic legged dynamic system, popular within the legged locomotion community for understanding basic collision dynamics and energetics during passive phases of walking. Despite the simplicity of this legged model, however, experimental motion capture data recording the passive step-to-step dynamics of a rimless wheel down a constant-slope terrain actually demonstrate significant variability, providing strong evidence that stochasticity is an intrinsic-and thus unavoidable-property of legged locomotion that should be modeled with care when designing reliable walking machines. We present numerical comparisons of several hypotheses as to the dominant source(s) of this variability: 1) the initial distribution of the angular velocity, 2) the uneven profile of the leg lengths and 3) the distribution of the coefficients of friction and restitution across collisions. Our analysis shows that the 3rd hypothesis most accurately predicts the noise characteristics observed in our experimental data while the 1st hypothesis is also valid for certain contexts of terrain friction. These findings suggest that variability due to ground contact dynamics, and not simply due to geometric variations more typically modeled in terrain, is important in determining the stochasticity and resulting stability of walking robots. Although such ground contact variability might be an expected result in field robotics on significantly rough terrain, we again note our experimental data applies seemingly deterministic-looking terrains: our results suggest that stochastic ground collision models should play an important role in the analysis and optimization of dynamic performance and stability in robot walking.