Achieving a desired collective centroid by a formation of agents moving in a controllable force field

In this paper, we study the problem of a formation of agents trying to achieve a desired stationary or moving collective centroid. The agents are assumed to be moving in a force field which is controlled externally. The stabilization of the collective centroid to a fixed desired location results in a balanced formation of the agents about that point. Similarly, the centroid of the system of agents may be required to move along a certain given trajectory. For this, the centroid of the formation must converge to the desired trajectory. To solve this problem, we propose an all-to-all coupled planar motion model that explicitly incorporates an additional control pertaining to the external force field. Simulation results are presented to support the theoretical findings.