Motion planning for flexible manipulators

Control algorithms for flexible manipulators are usually designed to calculate the torques which are required to move the manipulator along a specified joint trajectory. In this paper, we describe a method for generating a trajectory between two manipulator configurations which optimizes some objective function measured over the complete motion. In particular, we attempt to determine point-to-point motions of a flexible manipulator which minimize undesirable elastic vibrations. Accordingly, the trajectory planning problem is formulated and solved as a two-point boundary value problem with the objective function chosen to minimize the elastic deformations during the motion. The proposed methodology should therefore ease the requirements on the controller and the control algorithm in their tasks of eliminating trajectory-tracking errors and residual vibrations