Using Energy Shaping and Regulation for Limit Cycle Stabilization, Generation, and Transition in Simple Locomotive Systems

Abstract

This paper explores new ways to use energy shaping and regulation methods in walking systems to generate new passive-like gaits and dynamically transition between them. We recapitulate a control framework for Lagrangian hybrid systems, and show that regulating a state varying energy function is equivalent to applying energy shaping and regulating the system to a constant energy value. We then consider a simple one-dimensional hopping robot and show how energy shaping and regulation control can be used to generate and transition between nearly globally stable hopping limit cycles. The principles from this example are then applied on two canonical walking models, the spring loaded inverted pendulum (SLIP) and compass gait biped, to generate and transition between locomotive gaits. These examples show that piecewise jumps in control parameters can be used to achieve stable changes in desired gait characteristics dynamically/online.