A Heterogeneous Control Gain Approach to Achieve a Desired Collective Centroid by a Formation of Agents

This paper proposes a heterogeneous gains based controller design methodology to stabilize a particular type of collective motion in a multi-agent system where the heading angles of the agents are in balanced formation. Balancing refers to the situation in which the movement of agents causes the position of their centroid to become stationary. Our interest, in this paper, is to achieve balanced formation about a desired location of the centroid while allowing the agents to move either along straight line paths or around individual circular orbits. For this purpose, we derive feedback control laws that operate with heterogeneous control gains, and are more practical compared to the homogeneous gains based controls existing in the literature. We also show that if the heterogeneous control gains are zero for almost half of the agents of the group, it is possible to achieve balanced formation at an additional advantage of reduced computational complexity of the proposed control law. Simulations are given to illustrate the theoretical findings