发表机构
TU Munich; KTH Royal Institute of Technology; MIT（慕尼黑工业大学; 瑞典皇家理工学院; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于ADMM的非凸分裂方法，将时序逻辑规划中的安全与逻辑约束转化为凸集并集，通过图表示实现快速投影与鲁棒性最大化，实现连续时间运动规划，平均加速4.7倍。
AI 中文摘要
我们提出了一种快速数值方法，用于在时序逻辑（TL）规范下进行安全的连续时间运动规划。该方法生成平滑的连续轨迹，这些轨迹在保持无碰撞的同时，稳健地满足时间和逻辑任务要求。我们方法的核心组成部分是将非凸的安全和逻辑约束表述为凸集的并集，其中相关的离散决策被编码在一个联合可行性图中。这种图表示允许将欧几里得投影到可行集和近端鲁棒性最大化分别重新表述为最短路径和最宽路径问题。基于这一结构，我们开发了一种基于交替方向乘子法（ADMM）的非凸分裂方法，该方法在优化过程中将平滑的时空轨迹优化与非光滑的离散约束处理解耦。所得到的算法在基准测试中表现出可靠的收敛性，并可扩展到大规模运动规划问题，在离散和连续时间逻辑问题上，平均速度比现有技术快4.7倍。
英文摘要
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.
