Time-optimal trajectory planning of robot manipulators in point-to-point motion using an indirect method

In this study, an iterative method for computing the time-optimal point-to-point control of robot manipulators is studied, subject to limits on the actuator torques and actuator jerks. This method uses the indirect solution of an open-loop optimal control problem so that the optimal control problem is translated to a non-linear two-point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and solving the TPBVP, a simple iterative method is proposed. This method is based on solving the minimum-energy problem without the necessity of finding the switching point. So, the resultant TPBVP can be solved using the usual algorithms. In addition, since the solution of the TPBVPs is sensitive to the initial guess, a simple procedure for making proper initial guesses is introduced. Furthermore, since the inverse kinematic of redundant manipulators is an ill-posed problem, the general form for boundary conditions corresponding to the final time is considered. In addition, it is shown that the proposed method has no sensitivity for specifying the time-optimal trajectory of manipulators that may contain singular arcs.