Geometric Gait Optimization

Locomotion for many robots and animals is achieved through cyclic changes in shape called gaits. Gait optimization algorithms for locomoting systems must contend with many nonlinear effects, including shape-dependent system dynamics and history-dependent input-output mappings. In this work, we present a variational algorithm for generating optimal gaits for drag-dominated kinematic locomoting systems that encodes recent insights from the geometric mechanics community. For kinematic systems with two shape variables this process is analogous to the process by which internal pressure and surface tension combine to produce the shape and size of a soap bubble. The internal pressure in the case of our algorithm is provided by the flux of the curvature passing through the surface, and surface tension by the cost associated with the gait. We then extend this optimizer to work on systems with 3 and then more than 3 shape variables. We demonstrate this optimizer on a variety of system geometries (including Purcell's swimmer) and for optimization criteria that include maximizing displacement and efficiency of motion for both translation and turning motions.