Probabilistic and Distributed Control of a Large-Scale Swarm of Autonomous Agents

We present a distributed control algorithm simultaneously solving both the stochastic target assignment and optimal motion control for large-scale swarms to achieve complex formation shapes. Our probabilistic swarm guidance using inhomogeneous Markov chains (PSG-IMC) algorithm adopts a Eulerian density-control framework, under which the physical space is partitioned into multiple bins and the swarm's density distribution over each bin is controlled in a probabilistic fashion to efficiently handle loss or the addition of agents. We assume that the number of agents is much larger than the number of bins and that each agent knows in which bin it is located, the desired formation shape, and the objective function and motion constraints. PSG-IMC determines the bin-to-bin transition probabilities of each agent using a time IMC. These time-varying Markov matrices are computed by each agent in real time using the feedback from the current swarm distribution, which is estimated in a distributed manner. The PSG-IMC algorithm minimizes the expected cost of transitions per time instant that are required to achieve and maintain the desired formation shape, even if agents are added to or removed from the swarm. PSG-IMC scales well with a large number of agents and complex formation shapes and can also be adapted for area exploration applications. We demonstrate the effectiveness of this proposed swarm guidance algorithm by using numerical simulations and hardware experiments with multiple quadrotors.