Distributed Policy Synthesis of Multi-Agent Systems With Graph Temporal Logic Specifications
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We study the distributed synthesis of policies for multi-agent systems to perform spatial-temporal tasks. We formalize the synthesis problem as a factored Markov decision process subject to graph temporal logic specifications. The transition function and task of each agent is a function of the agent itself and its neighboring agents. By leveraging the structure in the model, and the specifications, we develop a distributed algorithm that decomposes the problem into a set of smaller problems, one for each agent. We show that the running time of the algorithm is linear in the number of agents. The size of the problem for each agent is exponential only in the number of neighboring agents, which is typically much smaller than the number of agents. If the transition function of each agent does not depend on its neighboring agents, we show that we can simplify the algorithm, which improves the runtime by multiple orders of magnitude. We demonstrate the algorithms in case studies on disease control, urban security, and ground robot surveillance. The numerical examples show that the algorithms can scale to hundreds of agents with hundreds of states per agent.
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