Collision-Free Formation Control of Multi-agent Systems with Switching Topology under Aggregation Game

This paper investigates the formation control and collision avoidance problem for high-dimensional multi-agent systems under dynamically switching communication topologies via an aggregative game framework. A distributed control algorithm is proposed, integrating second-order agent dynamics, artificial repulsion potentials, and topology-dependent neighbor coupling to achieve convergence to a desired formation while ensuring collision-free operations. The quadratic cost function, combining target tracking, inter-agent/obstacle repulsion, and topological consistency, is rigorously proven to admit a unique Nash equilibrium equivalent to the desired formation configuration. Through Lyapunov-based stability analysis, exponential convergence of the system states is guaranteed under switching topologies with persistent connectivity, and minimum interagent/obstacle distance constraints are analytically ensured. The proposed framework bridges game-theoretic optimization with multi-agent coordination, offering scalability in high-dimensional spaces and robustness against topology variations. Potential applications include agent swarms and robotic networks.