[
    {
        "id": "osp-26292",
        "type": "article-journal",
        "title": "Fast and Robust Temporal Logic Planning via ADMM-based Trajectory Optimization",
        "author": [
            {
                "family": "Pries",
                "given": "Lukas"
            },
            {
                "family": "Verhagen",
                "given": "Joris"
            },
            {
                "family": "Arrizabalaga",
                "given": "Jon"
            },
            {
                "family": "Tumova",
                "given": "Jana"
            },
            {
                "family": "Ryll",
                "given": "Markus"
            },
            {
                "family": "Manchester",
                "given": "Zachary"
            }
        ],
        "URL": "https://omanscience.com/ar/articles/fast-and-robust-temporal-logic-planning-via-admm-based-trajectory-optimization",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "We present a fast numerical method for safe continuous-time motion planning under Temporal Logic (TL) specifications. The method generates smooth continuous trajectories that remain collision-free while robustly satisfying temporal and logical task requirements. A central component of our method is the formulation of nonconvex safety and logic constraints as unions of convex sets where associated discrete decisions are encoded in a joint feasibility graph. This graph representation allows Euclidean projection onto the feasible set and proximal robustness maximization to be reformulated as shortest- and widest-path problems, respectively. Building on this structure, we develop a nonconvex splitting method based on the Alternating Direction Method of Multipliers (ADMM), which decouples smooth spatio-temporal trajectory optimization from nonsmooth discrete constraint handling within the optimization. The resulting algorithm exhibits reliable convergence across benchmarks and scales to large-scale motion-planning problems, providing a 4.7x average speedup over the state of the art on discrete and continuous-time logic problems."
    }
]