  In this paper, we present a geometric variational algorithm for optimizing
the gaits of kinematic locomoting systems. The dynamics of this algorithm are
analogous to the physics of a soap bubble, with the system's Lie bracket
supplying an "inflation pressure" that is balanced by a "surface tension" term
derived from a Riemannian metric on the system's shape space. 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.
