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arXiv · 2602.00325

Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes

Andrew F. Thompson·Joshua A. Robbins·Jonah J. Glunt·Sean B. Brennan·Herschel C. Pangborn
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Abstract

Metric temporal logic (MTL) provides a formal framework for defining time-dependent mission requirements on autonomous vehicles. However, optimizing control decisions subject to these constraints is often computationally expensive. This article presents a method that uses reachability analysis to implicitly express the set of states satisfying an MTL specification and then optimizes to find a motion plan. The hybrid zonotope set representation is used to efficiently and conveniently encode MTL specifications into reachable sets. A numerical benchmark highlights the proposed method's computational advantages as compared to existing methods in the literature. Further numerical examples and an experimental application demonstrate the ability to address time-varying environments, region-dependent disturbances, and multi-agent coordination.

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Andrew F. Thompson, Joshua A. Robbins, Jonah J. Glunt, Sean B. Brennan, Herschel C. Pangborn. 2026-01-30. Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes. https://arxiv.org/abs/2602.00325

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