Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions

This paper considers the collective dynamics of a group of mobile autonomous agents moving in Euclidean space with a virtual leader. We introduce a set of coordination control laws that enable the group to generate the desired 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 state information of its flockmates and the external reference signal (or “virtual leader”). Using the control laws, all agent velocities asymptotically approach the desired velocity, collisions can be avoided between the agents, and the final tight formation minimizes all agent global potentials. Moreover, we show that the velocity of the center of mass either is equal to the desired velocity or exponentially converges to it. Furthermore, when the velocity damping is taken into account, we can appropriately modify the control laws to generate the same stable flocking motion. Subsequently, for the case where not all agents know the desired common velocity, we show that the desired flocking motion can still be guaranteed. Numerical simulations are worked out to illustrate our theoretical results. Additionally, we consider the effect of white noise on the collective dynamics of the group, and demonstrate numerically that the desired flocking motion can be kept for weak noise and, as the noise intensity increases, the flocking motion can be destroyed.