Nonlinear PID global regulators with selftuned PD gains for robot manipulators: theory and experimentation

It is known that the Proportional Integral and Derivative (PID) regulator with constant and symmetric positive definite gain matrices (Kp, Kv and Ki), in closed loop with robotic manipulators, guarantees semiglobal asymptotic stability of the equilibrium point. In this paper, a fresh approach for control of robots manipulators based on a class of PID regulators with variable gain matrices Kp and Kv, which guarantee global asymptotic stability, is proposed. This PID control scheme, proposed with PD variable gains and fixed integral gains, improves the performance of the transient response and the handling of constraints, such as the limits of the actuator torques. Based on the authors experience, our proposal is the first scheme of a nonlinear PID regulator for robot manipulators whose PD gains are variable and its stability proof is global asymptotic in the sense of Lyapunov. The PD variable gains are directly dependent on the joint position errors and are fine tuned by fuzzy logic methodology. Good results were obtained on an experimental direct-drive robot arm of two degrees of freedom, when it was tested in order to verify the effectiveness of the new controller.