Leader-follower and leaderless bipartite formation-consensus over undirected coopetition networks and under proximity and collision-avoidance constraints

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We propose a method to control networks involving both cooperative and competitive interactions simultaneously under proximity and collision-avoidance constraints. The control design is of gradient type, using a barrier-Lyapunov function. Then, under the assumption that the network is structurally balanced, we establish asymptotic stability of the leaderless and leader-follower bipartite formation-consensus manifold. We assume that the agents are modelled by second-order integrators, but we also demonstrate the utility of our theoretical findings via numerical simulations on a problem of formation-consensus control of nonholonomic vehicles.