STLCCP: Efficient Convex Optimization-based Framework for Signal Temporal Logic Specifications
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916686742945792 |
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| author | Takayama, Yoshinari Hashimoto, Kazumune Ohtsuka, Toshiyuki |
| author_facet | Takayama, Yoshinari Hashimoto, Kazumune Ohtsuka, Toshiyuki |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_09441 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | STLCCP: Efficient Convex Optimization-based Framework for Signal Temporal Logic Specifications Takayama, Yoshinari Hashimoto, Kazumune Ohtsuka, Toshiyuki Systems and Control Formal Languages and Automata Theory Robotics 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. |
| title | STLCCP: Efficient Convex Optimization-based Framework for Signal Temporal Logic Specifications |
| topic | Systems and Control Formal Languages and Automata Theory Robotics |
| url | https://arxiv.org/abs/2305.09441 |