Characterizing knee-bounce in bipedal robotic walking

Abstract

This paper studies the walking behavior of kneed bipedal robots with knee-lock and knee-bounce, formally demonstrating that if knee-locking results in stable bipedal walking, then small amounts of knee-bounce still will result in a walking gait for the robot. To achieve this result, hybrid system models of bipeds are considered wherein knee-bounce corresponds to Zeno behavior. Using results on Zeno stability, we propose a notion of generalized completion that allows solutions to be carried beyond the Zeno point, i.e., carried beyond knee-bounce. We assume that the completed hybrid system has a periodic orbit when the impacts are perfectly plastic - a plastic periodic orbit, or walking gait with knee-lock. The main result of this paper is that when the assumption of perfectly plastic impacts is relaxed, if the plastic periodic orbit is stable and the Zeno point is Zeno stable, then there exists a periodic orbit in the case of non-plastic impacts, i.e., a Zeno periodic orbit corresponding to walking with knee-bounce. This formal result is applied to a specific example of a bipedal robot with knees.