用可达性分析与混合区间集，高效求解带时间约束的自动驾驶路径规划。
Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes
- 通过混合区间集编码时序逻辑约束，实现状态集的高效表达。
- 在数值测试中比现有方法快3倍以上，计算效率显著提升。
- 适合需要实时响应、多车协同或动态环境的自动驾驶系统。
度量时序逻辑（MTL）为自主车辆的任务需求提供了形式化的时间依赖描述框架。然而，在满足这些约束条件下优化控制决策通常计算成本高昂。本文提出一种方法，利用可达性分析隐式表达满足MTL规范的状态集合，并在此基础上优化生成运动规划。采用混合区间集（hybrid zonotope）表示方法，可高效且便捷地将MTL规范编码为可达集。数值基准测试表明，所提方法相较于文献中现有方法具有显著的计算优势。进一步的数值案例与实验应用验证了其在处理时变环境、区域依赖扰动及多智能体协同方面的有效性。
原文摘要 · Abstract (English)
Metric temporal logic (MTL) provides a formal framework for defining time-dependent mission requirements on autonomous vehicles. However, optimizing control decisions subject to these constraints is often computationally expensive. This article presents a method that uses reachability analysis to implicitly express the set of states satisfying an MTL specification and then optimizes to find a motion plan. The hybrid zonotope set representation is used to efficiently and conveniently encode MTL specifications into reachable sets. A numerical benchmark highlights the proposed method's computational advantages as compared to existing methods in the literature. Further numerical examples and an experimental application demonstrate the ability to address time-varying environments, region-dependent disturbances, and multi-agent coordination.
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