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

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Abstract
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.
Funding Information
  • National Science Foundation (2144860)
  • UW+Amazon Science Hub Fellowship and Nakajima Foundation Fellowship

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