Selection of different abstract groups for developing uniform structures to be used in adaptive control of robots

This paper is a brief summary on a particular approach aiming at the creation of a new branch of soft computing (SC) for the special problem class of mechanical systems' control. To evade the development of intricate system models it is based on the idea of "situation dependent partial system identification" and uses simple uniform structures obtained from various Lie groups used in different fields of physics. These structures are far more lucid and more concentrated than that of "traditional" SC based on either Kolmogorov's approximation theorem or typical membership functions in fuzzy controllers. The "obscure" process of learning or parameter tuning seems to be replaceable by simple explicit algebraic procedures. Simulation examples are considered for a 3 DOF robot arm under unmodelled environmental interaction.