An Optimization-Based Consensus Approach for Distributed Density Regulation of Swarms

Dear Editor, This letter addresses the distributed density regulation problem for large-scale robotic swarms. To accommodate swarm size, system dynamics are formulated within an Eulerian framework, modeling the swarm's actual density distribution (ADD) as a probability distribution, with state transition probabilities governed by a Markov matrix. We then propose a consensus protocol to specify the Markov matrix without relying on the detailed balance condition of the Markov chain. Within this framework, an optimization-based consensus approach is developed to achieve fast and distributed density regulation. Next, we show that the swarm converges to the target density distribution in probability. Finally, the efficacy of the proposed method is verified by numerical examples.