Rest-to-rest motion for planar multi-link flexible manipulator

In this work we consider the problem of rest-to-rest motion for planar flexi- ble multi-link manipulators. We introduce a simple idea permitting the cancellation of end-effector residual vibration when reaching a desired angular equilibrium position, in a fixed travelling time. No internal elastic damping effect is considered and the structure of the control is simply the sum of feedforward and joint feedback terms. The new approach concerns the computation of the feedforward control, which is based on backward integration of the elastic dynamics, starting from a rest position of the flexible arms. For fast rest-to-rest motion, the feedback compensator fails to drive the system states along the desired trajectories, due to the relatively large initial elastic error. To overcome this limitation, proper joint motion is planned between the desired initial and final positions through optimization techniques. This scheme is validated via numerical tests on a two-links planar manipulator.