Subriemannian geodesics for coupled nonholonomic integrators

We introduce in this paper a one-parameter family of optimal control problems for a pair of nonholonomic integrators, coupled through a mismatch term in the cost functional. The coupling constant parametrizes associated geodesic equations and a novel model problem in subriemannian geometry. A typical slice of the corresponding 5-dimensional geodesic sphere can be visualized by methods used to compute the 2-dimensional subriemannian geodesic sphere for a single nonholonomic integrator.