On the Time-optimal Trajectory Planning and Control of Robotic Manipulators Along Predefined Paths

In this paper we study the problem of time-optimal trajectory planning and control of robotic manipulators along predefined paths. An algorithm that generates dynamically feasible time-optimal trajectories and controls is presented, which considers the complete dynamic model with both Coulomb and viscous friction. Even though the effects of viscous friction for fast motions become more significant than Coulomb friction, in previous formulations viscous friction was ignored. We propose a formulation that naturally leads to a convex relaxation which solves exactly the original non-convex formulation. In order to numerically solve the proposed formulation, a discretization scheme is also developed. Through simulation and experimental studies on the resulting tracking errors, applied torques, and accelerometer readings for a 6-axis manipulator, we emphasize the significance of penalizing a measure of total jerk. The importance of imposing acceleration constraints at the initial and final transitions of the trajectory is also studied.