🤖 AI Summary
Distributed motion planning for multi-robot systems under signal temporal logic (STL) constraints remains challenging due to limited expressiveness of existing STL fragments, robustness degradation from min/max operator approximations, and susceptibility of optimization to local minima without completeness guarantees.
Method: We propose the first probabilistically complete distributed STL planning framework. Leveraging the temporal structure of STL specifications, our approach dynamically imposes spatial constraints over time, integrates distributed optimization with STL robustness modeling, and utilizes neighborhood communication graphs to coordinate agents. An iterative trajectory refinement algorithm is designed to progressively improve feasibility and robustness.
Results: Extensive simulations and real-robot experiments demonstrate that our method efficiently synthesizes collision-free, temporally coordinated trajectories satisfying complex STL specifications. It significantly outperforms state-of-the-art approaches in scalability, real-time performance, and constraint satisfaction rate, while providing formal probabilistic completeness guarantees.
📝 Abstract
This article presents MAPS
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: 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. Meanwhile, works maximising robustness through optimisation-based methods often suffer from local minima, thus relaxing any completeness arguments due to the NP-hard nature of the problem. Endowed with probabilistic guarantees, MAPS
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provides an autonomous 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
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by conducting extensive simulation and experimental studies, verifying the generation of STL satisfying trajectories.