This article presents MAPS$^2$ : a distributed algorithm that allows multi-robot systems to deliver coupled tasks expressed as Signal Temporal Logic (STL) constraints. Classical control theoretical tools addressing STL constraints either adopt a limited fragment of the STL formula or require approximations of min/max operators, whereas works maximising robustness through optimisation-based methods often suffer from local minima, relaxing any completeness arguments due to the NP-hard nature of the problem. Endowed with probabilistic guarantees, MAPS$^2$ provides an anytime algorithm that iteratively improves the robots' trajectories. The algorithm selectively imposes spatial constraints by taking advantage of the temporal properties of the STL. The algorithm is distributed, in the sense that each robot calculates its trajectory by communicating only with its immediate neighbours as defined via a communication graph. We illustrate the efficiency of MAPS$^2$ by conducting extensive simulation and experimental studies, verifying the generation of STL satisfying trajectories.

翻译：本文提出MAPS$^2$：一种分布式算法，能使多机器人系统完成以信号时序逻辑（STL）约束表达的耦合任务。针对STL约束的经典控制理论工具或采用STL公式的有限片段，或需要最小/最大算子的近似；而通过基于优化的方法最大化鲁棒性的工作常受困于局部极小值，因问题的NP难性质而弱化了任何完备性论证。借助概率保证，MAPS$^2$提供了一种即时算法，能迭代优化机器人的轨迹。该算法利用STL的时间特性有选择地施加空间约束；其具备分布式特性，即每台机器人仅通过与通信图定义的直接邻居通信来计算自身轨迹。我们通过大量仿真与实验研究验证了MAPS$^2$的效率，证实其能生成满足STL规范的轨迹。