STLCCP: Efficient Convex Optimization-based Framework for Signal Temporal Logic Specifications

TL;DR

This paper presents STLCCP, a convex optimization framework for signal temporal logic control problems, leveraging structural properties of STL to improve efficiency and scalability over existing methods.

Contribution

The paper introduces STLCCP, a novel convex optimization-based approach that transforms STL control problems into difference of convex programs and solves them efficiently.

Findings

Outperforms existing methods on motion planning benchmarks.

Handles complex, long-horizon STL specifications efficiently.

Utilizes a structure-aware decomposition and a smooth robustness approximation.

Abstract

Signal temporal logic (STL) is a powerful formalism for specifying various temporal properties in dynamical systems. However, existing methods, such as mixed-integer programming and nonlinear programming, often struggle to efficiently solve control problems with complex, long-horizon STL specifications. This study introduces \textit{STLCCP}, a novel convex optimization-based framework that leverages key structural properties of STL: monotonicity of the robustness function, its hierarchical tree structure, and correspondence between convexity/concavity in optimizations and conjunctiveness/disjunctiveness in specifications. The framework begins with a structure-aware decomposition of STL formulas, transforming the problem into an equivalent difference of convex (DC) programs. This is then solved sequentially as a convex quadratic program using an improved version of the convex-concave procedure (CCP). To further enhance efficiency, we develop a smooth approximation of the robustness function using a function termed the \textit{mellowmin} function, specifically tailored to the proposed framework. Numerical experiments on motion planning benchmarks demonstrate that \textit{STLCCP} can efficiently handle complex scenarios over long horizons, outperforming existing methods.