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The paper considers the implementation of a multiagent system that moves toward a common goal in unbounded space by swarming algorithms based on Reynolds rules. Three approaches to modeling flocking motion are presented, together implementing a final algorithm that provides collision avoidance with all available types of obstacles. To ensure avoidance of collisions with dynamically occurring obstacles, a joint application of the investigated swarming algorithm and the predator avoidance model based on reinforcement learning is proposed. Thus, it is possible to temporarily evade the target to ensure the safety of the movement of agents. The algorithm is organized on Q-learning, the result of which is an action function. We consider the behavior of the multiagent system modeled by the proposed approaches in a limited space - a polygon or range. In this case, in addition to the described interactions, the movement of a group of agents is influenced by repulsive forces from the walls. The problem of compensation of repulsive and attractive potentials with the consequent inhibition of the agent or ignoring the walls when moving toward the target is revealed. This task is proposed to be solved by applying functional-voxel models. The principle of movement of agents according to local geometric characteristics stored in the represented graphical M-images of a simulated polygon is described. The advantages of using these models and the necessity of applying to them the algorithm of escaping from a predator are emphasized.