Abstract :
This paper presents a solution to the problem of minimizing the cost of moving a robotic manipulator along a specified geometric path subject to input torque/force constraints, taking the coupled, nonlinear dynamics of the manipulator into account. The proposed method uses dynamic programming (DP) to find the positions, velocities, accelerations, and torques that minimize cost. Since the use of parametric functions reduces the dimension of the state space from 2n for an n-jointed manipulator to two, the DP method does not suffer from the "curse of dimensionality". While maintaining the elegance of the path planning methods in [1], [11], the DP method offers the advantages that it can be used in the general case where (i) the actuator torque limits are dependent on one another, (ii) the cost functions can have an arbitrary form, and (iii) there are constraints on the jerk, or derivative of the acceleration. As a numerical example, the path planning method is simulated for a two-jointed robotic manipulator. The example considers first the minimum-time problem, comparing the solution with that of the phase plane plot method in [11]. Secondly, the sensitivity of the path solutions to the grid size is examined. Finally, the DP method is applied to cases with interactions between joint torque bounds and with cost functions other than minimum-time, demonstrating its power and flexibility.
