Scalable ∊-optimal self-organization in communicating swarms using implicit probabilistic automata

The problem of scalable near-optimal distributed control of swarms is investigated with emphasis on decentralized ε-optimal path planning to locally sensed targets. The proposed algorithm only uses information that can be locally queried, and rigorous theoretical results on convergence, robustness, scalability are established, and effect of system parameters such as the agent-level communication radius and agent velocities on global performance is analyzed. The fundamental philosophy of the proposed approach is to percolate local information across the swarm, enabling agents to indirectly access the global context A gradient emerges, reflecting the performance of agents, computed in a distributed manner via local information exchange between neighboring agents. It is shown that to follow near-optimal routes to a target which can be only sensed locally, and whose location is not known a priori, the agents need to simply move towards its “best” neighbor, where the notion of “best” is obtained by computing the state-specific language measure of an underlying probabilistic finite state automata. The theoretical results are validated in high-fidelity simulation experiments, with a minimum of 10⁴ agents. Several controlled behaviors of interest are demonstrated in simulation which go beyond rendezvous-type scenarios, thus potentially laying the framework to complex collaborative task execution by large scale engineered swarms in near future.