Optimal Gait Design for Nonlinear Soft Robotic Crawlers

Soft robots offer a frontier in robotics with enormous potential for safe human-robot interaction and agility in uncertain environments. A stepping stone towards unlocking their potential is a control theory tailored to soft robotics, including a principled framework for gait design. We analyze the problem of optimal gait design for a soft crawling body - the crawler. The crawler is an elastic body with the control signal defined as actuation forces between segments of the body. We consider the simplest such crawler: a two-segmented body with a passive mechanical connection modeling the viscoelastic body dynamics and a symmetric control force modeling actuation between the two body segments. The model accounts for the nonlinear asymmetric friction with the ground, which together with the symmetric actuation forces enable the crawler's locomotion. Using a describing-function analysis, we show that when the body is forced sinusoidally, the optimal actuator contraction frequency corresponds to the body's natural frequency when operating with only passive dynamics. We then use the framework of Optimal Periodic Control (OPC) to design optimal force cycles of arbitrary waveform and the corresponding crawling gaits. We provide a hill-climbing algorithm to solve the OPC problem numerically. Our proposed methods and results inform the design of optimal forcing and gaits for more complex and multi-segmented crawling soft bodies.