An Evolutionary Approach to Time-Optimal Control of Robotic Manipulators

Time-optimal control of robotic manipulators along specified paths is a well-known problem in robotics. It concerns the minimization of the trajectory-tracking time subject to a constrained path and actuator torque limits. Calculus of variations reveals that time-optimal control is of bang-bang type, meaning that at least one actuator is in saturation for every point on the path. Unfortunately, this rule is broken at singular points, where the enforcement of the maximal and/or minimal torque at the bounding actuator would cause the violation of the path constraint. At these particular points, and, sometimes, at critical ones too, the selection of the torques is cumbersome and may introduce jitters in the control references. In this paper, the time-optimal control is addressed in the phase plane with a genetic approach. Results of calculus of variations are ignored and bang-bang control is re-found for the most of the trajectory, while in the neighborhoods of singular points, torques are automatically selected in order to minimize the trajectory-tracking time. Compared to other techniques, the problem is solved directly, without intermediate steps requiring, for example, the explicit computation of the switching points and the management of torques at critical points. The algorithm is validated in simulation on a canonical 2R planar robot in order to ease the comparison with previous works.