Robust stabilization of balanced and splay formations with heterogeneous controller gains

This paper analyses collective motion of multi-vehicle systems in balanced or splay formation when the vehicles are equipped with heterogeneous controller gains. Balancing refers to a situation in which the positional centroid of the vehicles is stationary. The splay formation is a special case of balancing in which the vehicles are spatially distributed with equal angular separation between them. The paper proposes strategies to achieve such balanced and splay formations about a desired centroid location while allowing the vehicles to move either along straight line paths or on individual circular orbits. Feedback control laws that can tolerate heterogeneity in the controller gains, which may be caused by imperfect implementation, are derived and analyzed. It is shown that drastic failures leading to controller gains becoming zero for almost half of the vehicles in the group can be tolerated and balanced formation can still be achieved. On the other hand, splay formation can still be achieved if the controller gain is zero for at most one vehicle. Simulation examples are given to illustrate the theoretical findings.