Collision avoidance is very important problem in the domain of multi-robot interaction. In this paper we propose a new approach of collision avoidance in the context of the optimal control system synthesis problem definition with minimal information available. It is assumed that robots have a certain scope within which they can interact with static and dynamic phase constraints. A group of robots is considered to be homogeneous, and control system unit for reaching terminal states already available to robots. The control system which is responsible for collision avoidance is only activated when the nearest neighbor is located in the scope of the considered robot. The first important feature of this work is the fact that the collision avoidance between two robots is reciprocal with joint control system, without assigning priorities. Another key feature of this work is the complete absence of information about the environment and the current state of other robots at given time. Robots only share information with nearest neighbors if they locate in the scope of each other. We also present a computational experiment with mobile robots as control objects. A multilayer perceptron was used to approximate the control function. Weights of the perceptron were optimized in unsupervised paradigm by an algorithm belonging to the evolutionary strategies class. At the beginning of each epoch we generate a sample of collision scenarios for optimization, while the quality criterion of the achieved weights at the end of epoch is evaluated on a fixed test sample. Experimental results demonstrate strong ability of the optimized multilayer perceptron to map the relative state of two mobile robots to controls in order to avoid collisions. © 2020 New Technologies Publishing House. All right reserved.