Globally asymptotically stable 'PD+' controller for robot manipulators

We describe a globally stable tracking controller for robot manipulators. The controller is an extension of Takegaki and Arimoto's position controller to the tracking case where a theorem of Matrosov is used to prove its stability. An attractive feature of this controller is its resemblance to the computed torque controller with the inertia matrix outside the position and velocity feedback loops. Thus, our controller is decomposed into an inner PD loop and an outer dynamic compensation loop. This structure allows the simple PD computations to be run at a higher speed than the dynamic compensation loop in digital implementations.