A connectivity preserving containment control strategy for unicycles with static leaders

This paper proposes a connectivity preserving containment control strategy for a team of unicycles with static leaders. Existing results on connectivity preservation of unicycles are first extended to the problems involving static leaders. These extensions are then used to design connectivity preserving controllers for containment of the followers by static leaders for unicycle agents, as the main contribution of this work. The results are first obtained for a static information flow graph, and are then shown to be valid for the case of dynamic edge addition as well. A Lyapunov functional and an important property of positive limit sets of nonlinear systems are used to show the convergence of followers to the convex hull of the leaders. The proposed control strategy is also verified by simulations.