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

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 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 programs. This is then solved sequentially as a convex quadratic program using an improved version of the convex-concave procedure. To further enhance efficiency, we develop a smooth approximation of the robustness function using a function termed the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mellowmin</i> function, specifically tailored to the proposed framework. Numerical experiments on motion planning benchmarks demonstrate that STLCCP can efficiently handle complex scenarios over long horizons, outperforming existing methods.