Flocking shape analysis of multi-agent systems

In this paper,we consider the shape control in flocking behavior of a multi-agent system with a virtual leader.Besides the traditional flocking control terms,which include a gradient-based term,a velocity consensus term and a navigational feed-back in general,a new piecewise smooth neighbor-based local controller is added to regulate the configuration to the desired flocking shape.All agent velocities approach the desired velocity asymptotically,while collisions among agents can be avoided.Furthermore,based on the proved stability,we obtain three kinds of flocking shapes,such as those in a single line,vee shape or corner shape.Some numerical simulation results are provided to demonstrate theoretical issues.