Cartesian controller's evaluation in joint space

This paper addresses the problem of position control for robot manipulators. A new family of controllers for robot manipulators on cartesian coordinates with gravity compensation is presented. The simple PD-type cartesian controller can be found among this family of controllers. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear robot dynamics and the new family is asymptotically stable in local sense in agreement with Lyapunov's direct method and La Salle's invariance principle. To illustrate the performance of new controllers family, time-real experimental results on a two degrees of freedom direct-dirve arm are also presented.