Machine Learning Control for Mobile Robot by Approximation Extremals by Symbolic Regression

Abstract

AbstractThe control system synthesis problem is considered for mobile robot. It is necessary to find a control as function of state space vector that supplies achievement of terminal position from some compact set of initial conditions with optimal value of quality criterion. For solution of this problem symbolic regression is used. This allows to find a structure of control function mathematical expression. General properties of symbolic regression are presented. Search of mathematical expression structure for control system is performed on the space of codes, therefore here a specific forms of genetic algorithms are used. They are differed crossover and mutation operations in depend on form of mathematical expression codding. At the searching optimal mathematical expression for control system by symbolic regression methods two approaches can be applied two approaches, as in artificial neural network technology, with teacher and without one. For obtaining a training set it is necessary to solve the optimal control problem some times for set of initial conditions. It is shown, that for decreasing the search space the principle of small variations of basic solution can be used and a basic solution should be set as closed to optimal one intuitively. In this case crossover and mutation operations will be performed the same on sets of variation vectors independently on symbolic regression method. In a computational experiment the control system synthesis problem for mobile robot is considered, that must be move from an area of initial conditions to the set terminal position on the plane with phase constraints.KeywordsControl synthesisMachine learning controlOptimal controlExtremalsEvolutionary algorithmSymbolic regression