Optimizing coordinate choice for locomoting systems

Gait evaluation techniques that use Stokes´s theorem to integrate a system´s equations of motion have traditionally been limited to finding only the net rotations or small translations produced by gaits. Recently, we have observed that certain choices of generalized coordinates allow these techniques to be extended to gaits that produce large translations. In this paper, we present a method for finding the optimal coordinate choice for this purpose, based on a Hodge-Helmholtz decomposition of the system constraints, and demonstrate the efficacy of the Stokes´s theorem approach over a wide variety of gaits when using the optimized coordinate choice.