Time-optimal path tracking for robots under dynamics constraints based on convex optimization

To fully utilize the dynamic performance of robotic manipulators and enforce minimum motion time in path tracking, the problem of minimum time path tracking for robotic manipulators under confined torque, change rate of the torque, and voltage of the DC motor is considered. The main contribution is the introduction of the concepts of virtual change rate of the torque and the virtual voltage, which are linear functions in the state and control variables and are shown to be very tight approximation to the real ones. As a result, the computationally challenging non-convex minimum time path tracking problem is reduced to a convex optimization problem which can be solved efficiently. It is also shown that introducing dynamics constraints can significantly improve the motion precision without costing much in motion time, especially in the case of high speed motion. Extensive simulations are presented to demonstrate the effectiveness of the proposed approach.