Distance-based formation control using euclidean distance dynamics matrix: Three-agent case

In this paper, we propose a triangular formation control law based on inter-agent distance information for a group of three single-integrator modeled agents on the plane. Although most of existing distance-based formation control laws have been designed by using the gradient of artificial potential functions, the proposed control law is derived from the time derivative of the Euclidean distance matrix associated with the realization of the agent group. Consequently, if the initial and desired formations are not collinear and the information graph of the group is complete, then the desired formation of the group is globally asymptotically stable with all squared inter-agent distance errors exponentially converging to zero. Furthermore, the proposed control law has a coordination property in the sense that the dynamics of all inter-agent distances are fully decoupled. Simulation results support the effectiveness of the proposed control law, demonstrating the coordination property.