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 cycl es of robot manipulators are of decisive importance. In this paper, the min imum-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 optimizati on algorithm are used to calculate the time-optimal control and trajectorie s. Results show that nonlinear gravity and centrifugal effects are exploite d very effectively, to obtain minimum-time maneuvers from an initial to a f inal state. These states also determine the switching structures of the con trol. It is demonstrated that even the simple retraction of a robot arm pro duces unexpectedly complex time-optimal solutions.