Mixed-Integer Programming for Signal Temporal Logic with Fewer Binary Variables

Abstract: Signal Temporal Logic (STL) provides a convenient way of encoding complex control objectives for robotic and cyber-physical systems. The state-of-the-art in trajectory synthesis for STL is based on Mixed-Integer Convex Programming (MICP). The MICP approach is sound and complete, but has limited scalability due to exponential complexity in the number of binary variables. In this letter, we propose a more efficient MICP encoding for STL. Our new encoding is based on the insight that disjunction can be encoded using a logarithmic number of binary variables and conjunction can be encoded without binary variables. We demonstrate in simulation examples that our proposed approach significantly outperforms the state-of-the-art for long and complex specifications. Open-source software is available at https://stlpy.readthedocs.io.