Approximation-free Control for Signal Temporal Logic Specifications using Spatiotemporal Tubes

Abstract: This paper presents a spatiotemporal tube (STT)-based control framework for satisfying Signal Temporal Logic (STL) specifications in unknown control-affine systems. We formulate STL constraints as a robust optimization problem (ROP) and recast it as a scenario optimization program (SOP) to construct STTs with formal correctness guarantees. We also propose a closed-form control law that operates independently of the system dynamics, and ensures the system trajectory evolves within the STTs, thereby satisfying the STL specifications. The proposed approach is validated through case studies and comparisons with state-of-the-art methods, demonstrating superior computational efficiency, trajectory quality, and applicability to complex STL tasks.