Collision-free vehicle formation control using graph Laplacian and edge-tension function

This paper is concerned with collision-free vehicle formation control (FC) when the communication between vehicles is model by a graph. Unlike previous FC works (dealing with either non-trivial vehicle dynamics with no consideration of collision avoidance (CA) or trivial first-order vehicle dynamics with consideration of CA), this paper discusses non-trivial (second-order) vehicle FC with consideration of CA. This collision-free vehicle FC is done by manipulating entries of the graph Laplacian and by constructing a proper edge-tension function. Theoretical and numerical evidences are provided to show that the proposed control law effectively address both CA and FC.