Journal
INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
Volume 42, Issue 6, Pages 356-370Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/02783649221082115
Keywords
Signal Temporal Logic; backpropagation; computation graphs; gradient-based methods
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This paper presents a technique called STLCG that computes the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform for integrating logical specifications into robotics problems that benefit from gradient-based solutions. It translates STL robustness formulas into computation graphs and leverages off-the-shelf automatic differentiation tools to efficiently backpropagate through the formulas. Through examples, it is shown that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.
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, that is, 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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