Abstract
Minimum time paths for a two-link robot arm are determined so that the tip moves a specified distance, starting from rest and ending at rest. Two torquers are used, one at the shoulder and one at the elbow, each having bounded torque. The optimal locations of the two end points in the robot coordinate system are determined as part of the solution. The paths are found to be “bang-bang” in both controls. For distances that are small compared to the reach of the arm, the minimum time paths are asymmetric, changing to symmetric paths when the distance is just slightly less than the maximum reach of the arm. A new gradient algorithm for systems with multiple bounded controls was developed to solve the problem.
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