Joint trajectory tracking for planar multi-link flexible manipulator: Simulation and experiment for a two-link flexible manipulator

In this work we consider the problem of joint trajectory control with oscillations cancelling for planar multi-link flexible manipulators. We extend a method introduced initially in [2] for the rest to rest motion problem. The scheme based on backward integration of the elastic dynamics, starting from a rest position of the flexible arms, is used here to solve the joint trajectory tracking problem. For slow joint motion, the obtained nominal elastic trajectory is used to compute a causal nominal feedforward torque permitting, together with a simple joint feedback term, to track the desired motion and damp out any residual tip-vibrations. For fast joint motion, the causal controller fails to solve the tracking problem: a noncausal feedforward torque is then designed to preset the elastic coordinates of the system, so that the causal control is able to drive the arm along the desired trajectory. The final position is then reached without end-effector residual oscillations. These results hold without considering any internal elastic damping effect. The scheme is validated through numerical and experimental results obtained on a two-links flexible planar arm.