Interaction Between Area Boundary and Formation of Agents Interacting by the Thermal Motion Equivalent Method

A significant part of scientific works is devoted to methods of group control of swarm agents and to the problem of creation of spatial geometrical structures - formations - by swarm agents. Formation of agents is useful in solving transport problems, navigation problems and others. One of the methods of swarm control, which also solves the problem of formation, is the thermal motion equivalent method. The essence of the method lies in the behavioural repetition by agents of the thermal motion of atoms interacting in a topologically closed region. The method solves the formation problem with swarm and formation stability preservation, but the interaction of the formation with the boundaries of the agent's functioning domain is not considered. In this paper we propose a finite state machine for the interaction of agent formation with the boundary of the domain, which ensures the stability of swarm and formation. The workability of the proposed solution is demonstrated by numerical simulation using a simplified linear model of the agent - a quadrocopter.