Study of Numerical Methods for Solving Optimal Control Problem for a Group of Robots

The problem of numerical solution of the optimal control problem for a group of robots is considered. The main complexity of the problem is the presence of dynamic phase constraints that describe the condition to prevent collisions between robots. Since there are several possibilities to avoid collision, and each of these possibilities corresponds to a local minimum, therefore the objective function has many local minima, thus the problem belongs to the class of global optimization. Precise methods for solving global optimization problems in this case cannot be applied due to the large dimension of the search space. It is proposed to use evolutionary algorithms to solve the optimal control problem of a group of robots. In computational experiment a complex optimal control problem for four quadcopters moving in space with four obstacles was solved by genetic and hybrid algorithms.