Stabilization of a Modified Slotine-Li Adaptive Robot Controller by Robust Fixed Point Transformations

The “Adaptive Slotine-Li Robot Controller (ASLRC)” of the nineties of the past century was designed by a sophisticated process based on the use of Lyapunov’s 2nd method. In the possession of the exact analytical form of the system model it generally can achieve global asymptotic stability by learning the system’s exact dynamic parameters. However, it is not robust to friction effects and unknown external disturbances. In contrast to that the adaptive controllers designed by the use of “Robust Fixed Point Transformations (RFPT)” are only locally stable, work on the mathematical basis of Banach’s Fixed Point Theorem, cannot learn the system’s analytical model parameters but they are very robust to modeling deficiencies (e.g. abandoned friction effects) and unknown external forces. In this paper it is shown that by evading the use of Lyapunov function in the adaptive control design an appropriate modification of the ASLRC can be elaborated that is able to properly learn the exact model parameters if external disturbances are missing. It can be combined with the RFPT-based controller that makes it robust to formal modeling inconsistencies and external forces, though in this case it cannot learn the appropriate system parameters. It is also shown that the symbiosis with the RFPT-based method does not disturb the parameter identification process if modeling inconsistencies and disturbances are absent. Key–Words: Adaptive control; Lyapunov function, Lyapunov’s direct method, Slotine-Li Adaptive Robot Controller; Robust Fixed Point Transformation; Global stability; Asymptotic Stability; Robustness.