An Investigation into Non-Smooth Locomotion

We analyze a class of mechanisms that locomote by switching between constraints. Because of the hybrid nature of such systems, most of the existing analysis tools, developed primarily for smooth systems, can not be directly applied. Our aim is to exploit the special structure provided by Lagrangian mechanics to study the controllability of this class of mechanisms. We base the analysis on a series representation of the evolution of the system. Our main result is a description of trajectories involving switches between constraints at nonzero velocity (impacts) in the presence of large inertial forces (drift). The analysis provides a basis for local motion planning. The results are applied to an example of a two-link planar mechanism that can locomote by clamping one of the links.