STLCG++: A Masking Approach for Differentiable Signal Temporal Logic Specification

Signal Temporal Logic (STL) offers a concise yet expressive framework for specifying and reasoning about spatio-temporal behaviors of robotic systems. Attractively, STL admits the notion of robustness , the degree to which an input signal satisfies or violates an STL specification, thus providing a...

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Bibliographic Details
Published in:IEEE robotics and automation letters Vol. 10; no. 9; pp. 9240 - 9247
Main Authors: Kapoor, Parv, Mizuta, Kazuki, Kang, Eunsuk, Leung, Karen
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.09.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Back propagation
Deep learning
deep learning methods
Formal methods in robotics and automation
Graphics processing units
Libraries
Logic
Masking
Optimization
Performance evaluation
Python
Robotics
Robots
Robustness
Semantics
software tools for robot programming
Specifications
Temporal logic
Trajectory optimization
Transformers
ISSN:2377-3766, 2377-3766
Online Access:Get full text
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Summary:Signal Temporal Logic (STL) offers a concise yet expressive framework for specifying and reasoning about spatio-temporal behaviors of robotic systems. Attractively, STL admits the notion of robustness , the degree to which an input signal satisfies or violates an STL specification, thus providing a nuanced evaluation of system performance. In particular, the differentiability of STL robustness enables direct integration to robotic workflows that rely on gradient-based optimization, such as trajectory optimization and deep learning. However, existing approaches to evaluating and differentiating STL robustness rely on recurrent computations, which become inefficient with longer sequences, limiting their use in time-sensitive applications. In this letter, we present STLCG++ , a masking-based approach that parallelizes STL robustness evaluation and backpropagation across timesteps, achieving significant speed-ups compared to a recurrent approach. We also introduce a smoothing technique to enable the differentiation of time interval bounds , thereby expanding STL's applicability in gradient-based optimization tasks involving spatial and temporal variables. Finally, we demonstrate STLCG++ 's benefits through three robotics use cases and provide JAX and PyTorch libraries for seamless integration into modern robotics workflows.
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ISSN:2377-3766
2377-3766
DOI:10.1109/LRA.2025.3588389