Stable swarming by mutual interactions of Attraction/Alignment/Repulsion

In this paper we present a general decentralized controller for a swarm of agents with a dynamic topology to move in a given environment. The controller utilizes the hypothesis of attraction/alignment/repulsion (A/A/R) interactions which is widely used to model fish schools in mathematical biology community.We assume that during the swarm¿s motion, each agent can sense and interact with its neighbors via mutual A/A/R interactions, while following the gradient force of the environment. The environment is assumed to have identical effects on all agents. With the assumption of connected graph, we show that the controller makes the velocities of all swarm members asymptotically converge to a common value. The contributions of this paper are two folds. First, the controller is general and works for any specific function of the A/A/R interactions. In other words, this paper analytically proves the common A/A/R model of fish schools in the literature. Second, all the information needed by the controller can be locally sensed, therefore, communication modules and associated problems (such as communication noise and time delay) are avoided. Simulation results are presented to verify the controller.