Global asymptotic stability of robot manipulators with linear PID and PI2D control

In this note we address the problem of set-point control of robot manipulators with uncertain gravity knowledge by combining several previous contributions to PID control. The main contribution is a linear PID controller which ensures global asymptotic stability of the closed loop. The key feature of the controller is that the integration is started after a short transient. In the case of unmeasurable velocities, a similar ``delayed'' PI2D controller is shown to globally asymptotically stabilize the manipulator.