A nonlinear optimization-based scheme is developed for the motion planning of nonholonomic systems. By specifying the final states constraints and using the performance criteria involving the control energy, the motion planning of nonholonomic systems can be recast as a nonlinear optimization problem which is to find suitable control inputs for steering the system along a feasible path from an initial state to a final state. An iterative algorithm is proposed to solve for a feasible path satisfying nonholonomic constraints and necessary optimality conditions. First, multi-point shooting is used to convert the motion planning problem into the problem of finding the solution of nonlinear equations. Modified Newton's method with line search is then used to ensure the global convergence of the numerical algorithm. The proposed scheme is applied to an one-leg hopping robot and a two-wheeled mobile robot. The results of numerical simulation clearly demonstrate the effectiveness of the proposed motion planning scheme.
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