Abstract
A control problem for a group of robots is considered. The robots have to move from given initial conditions to terminal ones without collisions between themselves and stationary obstacles. To solve the problem, the optimal synthesized control method is used. According to this method firstly the control system synthesis problem for each robot is solved. As a result, the control system stabilizes the robot relative to some point in the state space. After that positions of these stable equilibrium points in the state space for each robot are found so that all robots can move from point to point till the terminal positions without collisions. For synthesis problem on the first stage the Cartesian genetic programming is used. This method of symbolic regression allows to find a mathematical expression for control function in the form of special code by a special genetic algorithm. It's shown, that using the symbolic regression methods directly doesn't allow to find a synthesized control function in a code space, because this search space does not have numerical measure for distance between two elements of the space. So the Cartesian genetic programming was modified and the principle of small variations of the basic solution was included in it. A computational example of controlling eight robots on the plane with phase constraints is presented.
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