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

Abstract

The \u201cAdaptive Slotine-Li Robot Controller (ASLRC)\u201d of the nineties of the past century was designed by a sophisticated process based on the use of Lyapunov\u2019s 2 nd method. In the possession of the exact analytical form of the system model it generally can achieve global asymptotic stability by learning the system\u2019s 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 \u201cRobust Fixed Point Transformations (RFPT)\u201d are only locally stable, work on the mathematical basis of Banach\u2019s Fixed Point Theorem, cannot learn the system\u2019s 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