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 textitSTLCCP, 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 textitmellowmin function, specifically tailored to the proposed framework. Numerical experiments on motion planning benchmarks demonstrate that textitSTLCCP can efficiently handle complex scenarios over long horizons, outperforming existing methods.