Sources of Stochasticity in Passive Walking

This paper investigates the possible sources of stochasticity and their relative role in metastability of legged locomotion in its simplest form. Passive locomotion of a rimless wheel suggests that stochasticity is an intrinsic–and thus unavoidable– property of legged locomotion. Numerical test results of several hypotheses have been presented on the source of stochasticity of walking: the stochasticity of the angular velocities at the points of collision between the leg and the ground predominantly depends on 1) the initial distribution of the angular velocity, 2) the distribution of the coefficient of energy loss at each step, and 3) the uneven profile of the leg lengths. We found that the 2nd hypothesis holds more validity than the others to closely explain the experimental observations. We go on to present several methods to estimate the expected arrival time to a failed state in passive dynamic walking. These findings provide a compelling theoretical background to the design of legged robots interacting with uncertain environments.