Touch-down angle control for spring-mass walking

Abstract

In this paper we propose the fastest converging
control policy (also known as deadbeat control) for walking with
the bipedal spring-mass model, which serves as an abstraction
of a robot on compliant legs. To fully leverage the passive
dynamics of the system, the touchdown angle of the swing-leg
is assigned as the only control input of the system. We show
that two steps (or one stride) are necessary and sufficient to
converge to target walking gaits.

We first analyze the dynamics of the system to identify the
limit cycles as well as the limitations of the control authority
within the definition of walking. Then, we present the two-step
deadbeat control policy that guarantees stability with the fastest
possible convergence rate for the system. For each equilibrium
gait, the basin of attraction in which this two-step control exists
is a measure of the robustness of the system. The simulation
results show that human-like walking gaits (double hump
ground reaction force profile) have relatively large basins of
attraction. Finally, we extend the policy to various energy levels
to accommodate walking on uneven ground that has height
changes. We show in simulation that the system indeed rejects
various disturbances and converges to the desired equilibrium
gait in two steps.