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Optimal Trajectory Planning for Minimum Vibration of Flexible Redundant Cooperative Manipulators

The optimal path planning for two flexible cooperating manipulators carrying a solid object on a prescribed tip trajectory has been studied using kinematic resolution. The formulation has been derived using the Pontryagin minimum principle that results in a two-point boundary value problem. Also, a numerical technique based on converting the abstract optimization to parametric optimization problem has been proposed. The problem has been solved and compared for globally minimized elastic deformation of flexible links and joints as well as minimization of joints velocities while the end-effector moves along the specified path.