A Game Theoretic Approach to Distributed Planning of Multi-Agent Systems under Temporal Logic Specifications

Abstract

View Video Presentation: https://doi.org/10.2514/6.2023-1657.vid Many applications of multi-agent systems require complex team objectives and constraints to be satisfied by a team of possibly heterogeneous mobile agents (e.g., aerial and ground robots). One way to express such mission specifications is to define them based on the spatio-temporal distribution of agents among the regions of interest in the mission area. For example, the mission may require periodically visiting a region by a certain number of agents from each type, visiting a certain region only after some other region is visited, or never having more than a certain number of agents inside a specified region. We study distributed planning of multi-agent systems under such complex specifications on the distribution of agents. We propose Swarm Signal Temporal Logic (SSTL), which is an extension of Signal Temporal Logic (STL) for expressing the specifications on teams of possibly heterogeneous agents. We then present a game theoretic approach for optimizing the agent trajectories. More specifically, we formulate the planning problem as a potential game and use log-linear learning, which is a noisy best-response type algorithm, to drive the agents to optimal combinations of trajectories. The performance of the proposed approach is also demonstrated numerically in a case study.