Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods

• URL: http://arxiv.org/abs/2008.00097v3
• Date: Mon, 27 Dec 2021 17:15:34 GMT
• Title: Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods
• Authors: Karen Leung, Nikos Ar\'echiga, Marco Pavone
• Abstract summary: This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems.
• Score: 28.72161643908351
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, i.e., how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.

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