Coordination of Multiple Dynamic Agents with Asymmetric Interactions

This paper considers multiple mobile agents moving in Euclidean space with point mass dynamics and with asymmetric coupling weights. Using a coordination control scheme, we can make the group generate stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces, and the control law acting on each agent relies on the position information of all agents in the group and the velocity information of its neighbors. By using the control laws, all agent velocities become asymptotically the same, collisions are avoided between the agents, and the group final formation minimizes all agent global potentials. Moreover, we show that the velocity of the center of mass (CoM) is invariant and is equal to the final common velocity. Finally, we study the motion of the group when the velocity damping is taken into account, and prove that the common velocity asymptotically approaches zero. In this case, we can properly modify the control scheme to generate the same stable flocking. Numerical simulations are worked out to illustrate our theoretical results