PD control with on-line gravity compensation for robots with elastic joints: Theory and experiments

A proportional-derivative (PD) control with on-line gravity compensation is proposed for regulation tasks of robot manipulators with elastic joints. The work extends a previous PD control with constant gravity compensation at the desired configuration. The control law requires measuring only position and velocity on the motor side of the elastic joints, while the on-line gravity compensation torque uses a biased measure of the motor position. It is proved via a Lyapunov argument that the control law globally asymptotically stabilizes the desired robot configuration. A simulation study on a two-joint arm reveals the better performance that can be obtained with the new scheme as compared to the case of constant gravity compensation. Moreover, the proposed controller is experimentally tested on an eight-joint cable-driven robot manipulator, in combination with a point-to-point interpolating trajectory, showing the practical advantages of the on-line compensation.