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

TL;DR

This paper introduces STLCG, a method to compute and differentiate Signal Temporal Logic (STL) robustness metrics using computation graphs, facilitating the integration of logical specifications into gradient-based robotics solutions.

Contribution

The paper presents a systematic approach to translate STL robustness formulas into computation graphs, enabling efficient backpropagation and integration with gradient-based methods in robotics.

Findings

STLCG efficiently computes STL robustness using computation graphs.

The method enables gradient-based optimization with STL specifications.

Applications demonstrate versatility and efficiency in robotics tasks.

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.