Trajectory planning for two manipulators to deform flexible beams

The coordination of two manipulators to deform flexible beams is studied. Two coordination methods are identified. The first method allows the relative position of the two manipulators to be altered, but no relative orientation changes. The second method allows both the position and the orientation to be altered. By studying the mechanics of elastic deformations the performance of the methods, in terms of the interaction forces and moments between the object and the manipulators, is analyzed. The analysis shows that the second mechanism may result in less interaction forces and moments than the first. Optimal motion trajectories of the end-effectors to generate zero interaction moments in the second mechanism are then derived