Deform flexible beams by two manipulators through neural network learning

In a previous paper (1993), the authors proposed an optimal trajectory for two manipulators to bend a flexible beam. The criterion was to minimize the interaction forces and moments between the beam and the end-effectors. It turned out that computation for specifying such a trajectory was complicated since an elliptic integral was involved in the computation. In this study, a circular arc is used as the motion trajectory of the two end-effectors. Since a circular arc is easy to specify, the computation time is greatly reduced. However, the interaction forces and moments become non-minimal. To overcome this problem, a neural network mechanism is proposed to adjust the trajectory in real-time such that the interaction forces and moments are reduced. The residual forces and moments are further minimized by a force feedback control mechanism. Simulation results are presented to verify the proposed method