Improvements of the adaptive Slotine & Li controller: comparative analysis with solutions using local robust fixed point transformations

Abstract

One of the most sophisticated classical robot controller, the Slotine-Li Adaptive Controller is constructed on the basis of exact knowledge on the form of the equations of motion of the system under control, and on the application of Lyapunov's 2nd Method. This generic technique makes it possible to guarantee the stability of the controlled system using only simple estimations without having any detailed knowledge on its motion that is a great advantage. However, in the application of this elegant technique the main problem is the proper construction of the Lyapunov function. Formal elegance usually has the price of limitations in the applicable trajectory tracking policy and in the presence of a huge number of the constant control parameters to be determined in the commencement of the controller's operation. In the here presented approach the controller invented by Slotine and Li is modified in two steps: the first step modifies the original Lyapunov function, the second one -as an addition-modifies the parameter tuning by utilizing the information encoded in the equations of motion for which no any Lyapunov function is needed. The advantage is the limitation in the number of the fixed control parameters, and possibility for faster parameter tuning. The modified controller's operation is compared with that of a simple adaptive technique using locally convergent Cauchy sequences in iterative learning via simulation for a simple Classical Mechanical System as a paradigm.