Distance-based formation control using Euclidean distance dynamics matrix: General cases

We propose a formation control law based on inter-agent distances for a general group of single-integrator modeled agents on the plane. By attempting to directly control the Euclidean distance matrix of the group, we derive the proposed control law from the time-derivative of the matrix. Accordingly, if the initial and desired formations of the group are generically rigid, then the desired formation of the group is locally asymptotically stable. The stability analysis, in which Lyapunov direct method is applied to the distance dynamics of the group, is straightforward. Simulation results demonstrates comparable effectiveness of the control law to an existing law.