Bipartite Formation over Undirected Signed Networks with Collision Avoidance

We address the problem of bipartite formation control, with collision avoidance, for double integrators with limited sensing ranges. We assume that the systems are interconnected over an undirected, signed, and structurally balanced network. Then, to ensure that the proximity constraints are satisfied, we design a barrier-Lyapunov-function-based control law that guarantees connectivity maintenance for cooperative agents, and inter-agent collision avoidance for all agents. Relying on the edge-based agreement, we establish asymptotic stability of the bipartite formation control for signed networks. Finally, we illustrate our theoretical results via numerical simulations.