Discrete maximum principle in Hamel’s formalism for nonholonomic optimal control

In this work, a discrete maximum principle in Hamel’s formalism for optimal nonholonomic motion planning is proposed, which is a discrete analogue of the usual necessary conditions for optimality obtained from the Pontryagin maximum principle. The exact Hamel integrator associated with discrete Lagrangian mechanics is adopted to derive the forced and nonholonomic integrator. A universal discrete nonholonomic optimal control framework based on moving frames is established. The optimal nonholonomic trajectory optimization for a wall-crawling mobile robot moving on a spherical tank is considered for the established framework, where the configuration space is a non-Euclidean space. The simulated results by the proposed framework accurately capture some interesting nonholonomic behaviors and geometric structures for the given mechanical model, and the feasibility and computing efficiency are verified by comparison with the open-loop control and direct parameter optimization methods.