An SVD based modification of the Adaptive Inverse Dynamics Controller

The most popular classical adaptive robot control methods as the Adaptive Inverse Dynamics Control or the Slotine-Li Adaptive Robot Controller are constructed on the basis of exact knowledge on the form of the equations of motion, and on the application of Lyapunov's 2^nd 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 set in the commencement of the controller's operation. In the here presented approach the Adaptive Inverse Dynamics control is simplified by evading the use of the Lyapunov function and the inversion of the actual estimated inertia matrix by utilizing the information encoded in the equations of motion in a quite different manner. The advantage is the limitation in the number of the fixed control parameters, and possibility for faster parameter tuning due to the evasion of the most critical step of the original method, i.e. the inversion of the actual estimation of the inertia matrix the singularity of which can interrupt and stop the whole control process. The modified control is also illustrated by numerical examples calculated via simulation for a simple Classical Mechanical System as a paradigm.