Robotic locomotion of three generations of a family tree of dynamical systems. Part II: Impulsive control of gait patterns

Abstract

The objective of this paper is to develop a simple active control scheme for the systems presented in a companion paper (Part I). These are the single mass, the baton, and the three-mass (one revolute joint, two links) systems. The three systems can generate a rich set of passive gaits such as hopping, tapping, and walking each including various gait modes. Yet, we have shown that none of these gait patterns are asymptotically stable except the passive walking. Our control objective is to generate asymptotically stable gait patterns by emulating contact based conditions of passive gaits via impulsive control for the three generations of the family. We consider an impulsive actuator located at all the point masses to actively emulate the contact based rules of passive gait patterns that we introduced in Part I. Consequently, a nonlinear impulsive controller is designed for the hybrid dynamics of our systems that can actively generate the passive gaits on arbitrary ground slope angles. Furthermore, the role of continuous control in the closed loop dynamics of the three-mass system is investigated. We show a combination of continuous and impulsive control can maintain a nonscuffing bipedal walking on arbitrary ground slope angles. Our results show that the controlled systems successfully generate active gaits without significant degradation in the energetic efficiencies of the equivalent passive systems.