New class of control laws for robotic manipulators Part 1. Non–adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has recently been recognized that the non-linear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third–order terms in the Lyapunov function derivatives, closed–loop exponential stability for both the set point and tracking control problem is demonstrated. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on–line computation of non–linear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing trade–offs between computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.