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In this paper, we propose a novel gradient-type iterative algorithm for solving the optimal trajectory planning problems with multiple constraints. Since it is too difficult to generate trajectories considering all constraints at the same time, we introduce the concept of the order of priority into the trajectory generation procedure. In the proposed algorithm, a nominal trajectory is iteratively improved considering the order of priority of the constraints. The procedure is executed based on the gradient function which is synthesized in a hierarchical manner so that the convergence rate of the constraint with lower priority does not change the one with higher priority. The convergence properties of the proposed algorithm are examined. A method to improve the convergence properties when we apply the algorithm to the problem of nonholonomic systems is also proposed. The simulation results of planning trajectories for a 3-DOF planar free-joint manipulator show the effectiveness of the proposed algorithm.

A Numerical Algorithm for Optimal Trajectory Planning Problems with Multiple Constraints and Its Application to Nonholonomic Systems.