Optimal Control Using Nonholonomic Integrators

This paper addresses the optimal control of nonholonomic systems through provably correct discretization of the system dynamics. The essence of the approach lies in the discretization of the Lagrange-d´Alembert principle which results in a set of forced discrete Euler-Lagrange equations and discrete nonholonomic constraints that serve as equality constraints for the optimization of a given cost functional. The method is used to investigate optimal trajectories of wheeled robots.