Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods
This work addresses the challenge of infusing human-domain knowledge into robotics problems for researchers and practitioners, though it is incremental as it builds on existing STL and gradient-based methods.
The authors tackled the problem of integrating logical specifications into gradient-based robotics methods by developing STLCG, a technique that translates Signal Temporal Logic (STL) robustness formulas into computation graphs, enabling efficient backpropagation and demonstrating versatility and computational efficiency across various robotics applications.
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.