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，使多机器人系统能够完成以信号时序逻辑（STL）约束表示的耦合任务。经典的STL约束控制理论方法要么采用STL公式的有限片段，要么需要最小/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，且由于问题的NP-hard性质，任何完备性论证均被削弱。MAPS$^2$具备概率性保证，提供了一种可随时终止的算法，能迭代优化机器人的轨迹。该算法利用STL的时间属性，有选择性地施加空间约束。算法具有分布式特性，即每个机器人仅通过与通信图中定义的直接邻居进行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，证实了其能生成满足STL的轨迹。