Near-optimal motion planning for nonholonomic systems using multi-point shooting method

A nonlinear optimal control scheme is developed for mechanical systems subject to nonholonomic constraints. Using the performance criteria involving the final state errors and control effort, the motion planning of nonholonomic systems can be recast as a nonlinear optimal control problem. Based on the variational principle, an optimal path and control depend on the solution of the two-point boundary value problem. A numerical algorithm such as multi-point shooting method can be used to find the solution of the two-point boundary value problem. The proposed optimal control scheme is also applied to an automated vehicle. The simulation results clearly indicate that the optimal control scheme requires smaller control energy and shorter path in comparison to the geometric phase method to steer the nonholonomic system from the initial position to the final position.