A New Class of Energy Based Control Laws for Revolute Robot Arms: Tracking Control, Robustness Enhancement and Adaptive Control

A new class of joint level control laws for all-revolute robot arms is introduced in this paper. The analysis is similar to the recently proposed energy Lyapunov function approach [1, 2], except that the closed loop potential function is shaped in accordance with the underlying joint space topology. By using energy Lyapunov functions with the modified potential energy, a much simpler analysis can be employed to show closed loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction, and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the non-adaptive control laws by their estimates.