Determination of minimum-time maneuvers for a robotic manipulator using numerical optimization methods

The productivity of automated production lines depends on the velocities of operating robot manipulators. Hence, time-optimal control for working cycles of robot manipulators are of decisive importance. In this paper, the minimum-time retraction of a robot arm, subject to gravity and suspended on a prismatic-rotational joint, is investigated. Iterative integration methods using a B-spline representation for the actuator force and torque, a Runge-Kutta integration method, and a sequential quadratic programming optimization algorithm are used to calculate the time-optimal control and trajectories. Results show that nonlinear gravity and centrifugal effects are exploited very effectively, to obtain minimum-time maneuvers from an initial to a final state. These states also determine the switching structures of the control. It is demonstrated that even the simple retraction of a robot arm produces unexpectedly complex time-optimal solutions.