Distributed region following and perimeter surveillance tasks in star-shaped sets

In this paper, a distributed control law for a kinematically modelled agent swarm is proposed, which is able to control the multi-agent system into a star-shaped set. The main idea behind the present work is to combine the traditional potential function based approach with the transformation of coordinate frames to drive a group of limited range agents into a moving region. The difficult problem of tracking a star-shaped set is transformed into a simpler problem where the star-shaped set is converted into a circular region. The control signal is designed with reference to this new circular region and then fed back to the original region of interest. The overall evolution of the agents is mainly determined by an attraction potential that directs the swarm to the region of interest and an interaction potential that controls the relationships between the agents and avoids collisions. As a further degree of freedom, the proposed control protocol can be set to move the multi-agent system to a certain perimeter around the region of interest to perform a perimeter monitoring task. In both cases, i.e. tracking the region or monitoring the perimeter, the evolution of the agents within the zone of interest can be chosen to achieve either a speed consensus or a rotational motion. The latter can be extremely useful in all those cases where a small number of agents have to explore a whole large area. Numerical simulations are carried out to illustrate the main features of the resulting control strategy.