Regulation with on-line gravity compensation for robots with elastic joints

In this paper a PD control with on-line gravity compensation is proposed for robot manipulators with elastic joints. The work extends the existing PD control with constant gravity compensation, where only the gravity torque needed at the desired configuration is used throughout motion. The control law requires measuring only position and velocity on the motor side of the elastic joints, and the on-line compensation scheme estimates the actual gravity torque using a biased measure of the motor position. It is proved via a Lyapunov argument that the control law globally stabilizes the desired robot configuration. Experimental results on an 8-d.o.f. robot manipulator with elastic joints show that this control scheme improves the transient behavior with respect to a PD controller with constant gravity compensation. In addition, it can be usefully applied in combination with a point-to-point interpolating trajectory leading to a reduction of final steady-state errors due to static friction and/or uncertainty in the gravity compensation.