ADMMベースの軌道最適化による高速でロバストな時相論理プランニング
Fast and Robust Temporal Logic Planning via ADMM-based Trajectory Optimization
時相論理仕様を満たす連続時間動作計画を、凸集合の和として安全・論理制約を表現し、ADMMで滑らかな軌道最適化と離散制約処理を分離して高速化する手法を提案。
著者: Lukas Pries, Joris Verhagen, Jon Arrizabalaga, Jana Tumova, Markus Ryll, Zachary Manchester
分類: cs.RO, cs.FL
原文アブストラクト
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.