Distributed controller for collective motion of agents based on bounded potential functions

In this paper, we develop a distributed controller for a group of local interaction agents, which consists of four elements: a bounded repulsive potential field, a bounded attractive potential field, a velocity matching term, and a desired moving mode. We prove that under some initial conditions, the control law not only can drive a group of agents to synchronization with a desired moving mode, but also can avoid the collision as well as preserve the connectivity among agents for all time. Simulation results are presented to demonstrate the theoretical results.