Flocking of Multi-Vehicle Systems With A Leader

We study the coordinated motion of a group of vehicles with a leader based on nearest neighbor rules. The leader may be a special vehicle in the group or an external signal (virtual leader) to steer the vehicle group. The control law consists of two parts: a potential field force that makes the vehicles attract to each other and at the same time avoid collision in the group, and an alignment force that makes all vehicles´ headings and speeds to converge respectively to common values. We assume that the interaction patterns are either fixed or switching based on the information topologies of the leader and member vehicles. Our approach is based on the Lyapunov theory and basic graph theory. We also consider the effect of noise on the collective dynamics of the group. Numerical simulations are worked out to illustrate the analytical results