Formal non-exact analytical modeling of mechanical systems and environmental interactions in an adaptive control

On the basis of Lagrangian mechanics uniform structures made of simple and standardized procedures and closed form analytical formulas were previously used to develop an adaptive control for SCARA robots in dynamic interaction with an unmodeled environment. This standardized form contains well defined free parameters by tuning of which the complex effect of the behavior of the controlled system as well as that of the external interactions can be `imperfectly´ modeled and learned. These structures, free parameters and procedures play exactly the same role as that of the traditional artificial neural networks (ANNs) or fuzzy controllers: the structures and the procedures are fit for a wide class of problems more or less similar to each other, while parameter tuning corresponds to learning the concrete properties of a particular element of this wider set. While in the case of the standard soft computing methods there is no reliable a priori information on the number of the concrete elements in the uniform structures, the proposed method has definite indication for this by using the Lie parameters of the orthogonal group. In the initial stage of learning the proposed methods also use a standardized ancillary procedure, a very simple form of regression analysis based controller compensating the remnant errors whenever appropriate. In this paper certain details of the uniform control and parameter-tuning are discussed on the basis of simulation results. It can be concluded that the approach is promising therefore experimental investigations are under preparation