Foot placement and ankle push-off control for the orbital stabilization of bipedal robots

Abstract

The main motivation of this paper is to understand the role of foot placement and ankle push-off control in stabilizing bipedal gaits. We modify the simplest walker (heavy torso, light legs) by incorporating a hip spring, a hip actuator, and a telescopic linear actuator. We consider two stability criteria: one-step dead-beat stabilization for full correction of disturbance in a single step and exponential orbital stabilization using discrete control Lyapunov function. Our findings are as follows: (1) Both control strategies have almost similar robustness as measured by the number of steps walked on stochastic terrain before failure, but both strategies are more robust for changing terrain with step down and less robust for step up. (2) One step dead-beat stabilization is more energy-efficient than exponential stabilization. (3) Control strategy for step up is to decrease foot placement or maintain push-off and for step down is to increase foot placement or decrease the push-off. However, it is most energy-efficient to use foot placement control for step up and push-off control for step down.