Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915764553908224 |
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| author | Thompson, Andrew F. Robbins, Joshua A. Glunt, Jonah J. Brennan, Sean B. Pangborn, Herschel C. |
| author_facet | Thompson, Andrew F. Robbins, Joshua A. Glunt, Jonah J. Brennan, Sean B. Pangborn, Herschel C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00325 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes Thompson, Andrew F. Robbins, Joshua A. Glunt, Jonah J. Brennan, Sean B. Pangborn, Herschel C. Systems and Control Robotics 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. |
| title | Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2602.00325 |