Heading consensus with collision avoidance for linearized Vicsek model with a connected initial graph

The consensus problem with collision avoidance is considered for linearized Vicsek model composed of many particles with possibly different initial absolute velocities. The updating laws of absolute velocities and directions are adopted as the linear protocols. It is revealed that, if the initial graph is connected and the maximum value of the initial absolute velocities is sufficiently small, then the consensus problem with collision avoidance can be solved. Simulation results are presented to demonstrate the obtained result.