Flocking Coordination of Multiple Interactive Dynamical Agents with Switching Topology

In this paper, we consider a group of mobile agents moving in the space with point mass dynamics. We investigate the dynamic properties of the group for the case where the topology of the neighboring relations between agents varies with time. Under the assumption that the neighboring graph is always connected, we show that stable flocking motion can be achieved by using a set of switching control laws. The control laws are a combination of attractive/repulsive and alignment forces. Using the control laws, all agent velocities become asymptotically the same, collisions can be avoided between the agents, and the final tight formation minimizes all agent potentials. Moreover, we show that the velocity of the center of mass is invariant and is equal to the final common velocity. Subsequently, we study the motion of the group when the velocity damping is taken into account. In this case, we can appropriately modify the control laws to generate the same stable flocking motion. Finally, we provide some numerical simulations to further illustrate our theoretical results.