Correct-by-Construction Behavior Tree Synthesis from Signal Temporal Logic Specifications with Application to Robotic Missions

Abstract:Behavior Trees (BTs) are widely adopted for complex task execution in robotics, providing modular, reactive control but lacking formal guarantees. However, existing correct-by-construction synthesis from Linear Temporal Logic (LTL) cannot express quantitative timing constraints. This letter synthesizes correct-by-construction BTs from Signal Temporal Logic (STL) specifications. The workspace is modeled as a timed transition system and abstracted into a zone graph, and an augmented state space tracking both logical progress and timing constraints is introduced. A hierarchical fixed-point algorithm computes winning sets for an STL fragment encompassing safety, reachability, response, recurrence, and persistence, yielding BT subtrees with a runtime constraint function. Correctness guarantees are proven and complexity bounds are derived. Simulations demonstrate specification satisfaction with strictly positive robustness, and a physical quadrotor experiment with six STL specifications validates practical deployability.

8 pages, 9 figures. This work has been submitted to the IEEE for possible publication

Robotics (cs.RO)

arXiv:2607.18731 [cs.RO]

(or arXiv:2607.18731v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2607.18731 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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