Forced Multi-Agent Bipartite Consensus Control: Application to Quadrotor Formation Flying

This work investigates the multi-agent bipartite consensus problem in the presence of switching antagonistic interactions. For leaderless multi-agent systems communicating over a structurally balanced sign graph with switching antagonistic interactions, we show that, whenever the sum of the agents' initial conditions on both subsets of a bipartite graph are identical, the agents converge to the origin. For multi-agent systems communicating over balanced bipartite graphs, that have achieved or are initially in consensus, we show that bipartite consensus is not admissible. We demonstrate that switching antagonistic interactions in the multi-agent bipartite consensus problem results in a multi-agent consensus to the origin. For leader-based multi-agent systems with antagonistic interactions, the bipartite consensus problem becomes a forced bipartite consensus problem with applications in robotics, for example, Unmanned Aerial Vehicle (UAV) flight formation. An application of forced bipartite consensus with switching antagonistic interactions to a quadrotor formation is presented. The results are validated using simulations.