Connectivity preservation in a network of single integrator agents

This paper proposes a general class of distributed potential-based control laws with the connectivity preserving property for single integrator agents. Given a connected information flow graph, the potential functions are designed in such a way that when an edge in the graph is about to lose connectivity, the gradient of the potential function lies in the direction of the corresponding edge aiming to shrink it. Therefore, the corresponding control laws preserve the connectivity of the information flow graph. The potential functions are chosen to be bounded with bounded partial derivatives, resulting in bounded control inputs. The results are developed for the case of static information flow graph, but can be easily extended to the case of dynamic edge addition. Other constraints may be imposed on the potential functions to satisfy other design criteria such as consensus and formation convergence. The effectiveness of the proposed control strategy is illustrated via simulation.