NONLINEAR OPTIMIZATION-BASED MOTION PLANNING OF NONHOLONOMIC SYSTEMS USING AN ITERATIVE ALGORITHM

A nonlinear optimization-based scheme is developed for the motion plan ning of nonholonomic systems. By specifying the final states constrain ts and using the performance criteria involving the control energy, th e motion planning of nonholonomic systems can be recast as a nonlinear optimization problem which is to find suitable control inputs for ste ering the system along a feasible path from an initial state to a fina l stare. An iterative algorithm is proposed to solve for a feasible pa th satisfying nonholonomic constraints and necessary optimality condit ions. First, multi-point shooting is used to convert the motion planni ng problem into the problem of finding the solution of nonlinear equat ions. Modified Newton's method with line search is then used to ensure the global convergence of the numerical algorithm. The proposed schem e is applied to an one-leg hopping robot and a two-wheeled mobile robo t. The results of numerical simulation clearly demonstrate the effecti veness of the proposed motion planning scheme.