Family of Bounded Regulators with Variable Gains and Lyapunov Asymptotic Stability for Robot Manipulators

In this paper, the regulation problem for robot manipulators in joint space through the proposal of a new family of bounded regulators with variable gains is presented. The proposed regulators have bounded functions that replace the classical position error and the velocity; moreover, the variable gains are formed by a family of Lipchitz functions with the position error and the velocity as their arguments. This structure avoids exceeding the physical limits of the servomotors. A strict Lyapunov function is proposed to demonstrate the global and asymptotic stability. Finally, the functionality and performance of the proposal are examined by experimental results on a direct-drive-robot of 3-degrees-of-freedom against the PD regulator