A Global Asymptotic Stable Output Feedback PID Regulator for Robot Manipulators

In this paper, we provide an answer to the long-standing question of designing global asymptotically stable proportional-integral-derivative (PID) regulators with only position feedback for uncertain robots. Our main contribution is to establish the global asymptotic stability of the controlled system by using Lyapunov direct method and LaSalle´s invariance principle. We provide explicit conditions on the regulator gains to ensure global asymptotic stability. The proposed controller does not utilize the modeling information in the control formulation, and thus permits easy implementation. Simulations performed on a planar two degrees-of-freedom robot manipulator demonstrate the effectiveness of the proposed approach.