MAPS$^2$: Multi-Robot Autonomous Motion Planning under Signal Temporal Logic Specifications

TL;DR

MAPS$^2$ is a distributed, anytime algorithm enabling multi-robot systems to plan trajectories satisfying complex Signal Temporal Logic constraints with probabilistic guarantees, improving over existing methods.

Contribution

The paper introduces MAPS$^2$, a novel distributed algorithm for multi-robot motion planning under STL constraints that provides probabilistic guarantees and iterative trajectory improvement.

Findings

Efficient generation of STL-satisfying trajectories in simulations.

Distributed computation with communication only among neighbors.

Experimental validation demonstrating practical effectiveness.

Abstract

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.