This paper describes a computationally very efficient method of finding the time-optimal solution to the control of robotic manipulators along specified paths. Specifically speaking, this can be done through a novel way of approximating the dynamic equation for robotic manipulators. Most importantly, the time-optimal control problem corresponding to the approximated dynamic equation can be solved with O(m) elementary operations, where m is the number of grids used in the approximation process. Furthermore, the authors show that as the approximation is finer, the suboptimal solution converges to the true time-optimal solution at least as fast as O(1/m). Finally, some simulation results using a six degree of freedom robotic manipulator are presented to demonstrate the generality and practical use of the proposed algorithm. In simulation, actuator constraints and the nondiagonal components of the inertia matrix as well as the centrifugal and Coriolis forces are taken into full account.
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