Geometric Mechanics of Contact-Switching Systems

Discrete and periodic contact switching is a key characteristic of steady-state legged locomotion. This paper introduces a framework for modeling and analyzing this contact-switching behavior through the framework of geometric mechanics on a toy robot model that can make continuous limb swings and discrete contact switches. The kinematics of this model form a hybrid shape-space and by extending the generalized Stokes' theorem to compute discrete curvature functions called \textit{stratified panels}, we determine average locomotion generated by gaits spanning multiple contact modes. Using this tool, we also demonstrate the ability to optimize gaits based on the system's locomotion constraints and perform gait reduction on a complex gait spanning multiple contact modes to highlight the method's scalability to multilegged systems.