Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes
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.
Cite
@article{arxiv.2602.00325,
title = {Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes},
author = {Andrew F. Thompson and Joshua A. Robbins and Jonah J. Glunt and Sean B. Brennan and Herschel C. Pangborn},
journal= {arXiv preprint arXiv:2602.00325},
year = {2026}
}