*Article* **Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm**

**Askhat Diveev 1, Elena Sofronova 1,\* and Ivan Zelinka 2,3**


Received: 29 October 2020; Accepted: 20 November 2020; Published: 25 November 2020

**Abstract:** A numerical method based on the Pontryagin maximum principle for solving an optimal control problem with static and dynamic phase constraints for a group of objects is considered. Dynamic phase constraints are introduced to avoid collisions between objects. Phase constraints are included in the functional in the form of smooth penalty functions. Additional parameters for special control modes and the terminal time of the control process were introduced. The search for additional parameters and the initial conditions for the conjugate variables was performed by the modified self-organizing migrating algorithm. An example of using this approach to solve the optimal control problem for the oncoming movement of two mobile robots is given. Simulation and comparison with direct approach showed that the problem is multimodal, and it approves application of the evolutionary algorithm for its solution.

**Keywords:** optimal control problem; evolutionary computation; robotics applications
