Distributed Self-Organization Of Swarms To Find Globally $ε$-Optimal Routes To Locally Sensed Targets

The problem of near-optimal distributed path planning to locally sensed targets is investigated in the context of large swarms. The proposed algorithm uses only 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 excess of $10^4$ agents.