Stability of Flocking Motion

This paper investigates the aggregated stability properties of of a system of multiple mobile agents described by simple dynamical systems. The agents are steered through local coordinating control laws that arise as a combination of attractive/repulsive and alignment forces. These forces ensure collision avoidance and cohesion of the group and result to all agents attaining a common heading angle, exhibiting flocking motion. Two cases are considered: in the first, position information from all group members is available to each agent; in the second, each agent has access to position information of only the agents laying inside its neighborhood. It is then shown that regardless of any arbitrary changes in the neighbor set, the flocking motion remains stable as long as the graph that describes the neighboring relations among the agents in the group is always connected.