用位移法将复杂优先级约束转为单目标优化，实现高效可解释的自动驾驶路径规划。
Lexicographic Minimum-Violation Motion Planning using Signal Temporal Logic
- 通过非均匀量化与位移转换，把多目标优先级问题变成交互式单目标优化
- 在不依赖二次输入代价的情况下，扩展了确定性模型预测路径积分求解器
- 提出融合时空违规的新型谓词鲁棒性度量，适合高优先级安全约束场景
自动驾驶车辆运动规划常需满足多个条件冲突的规范。当无法同时满足所有规范时，最小违规运动规划通过按优先级最小化违规来维持系统运行。信号时序逻辑（STL）提供形式化语言定义这些规范，并支持违规程度的量化评估。然而，规范的全序排列会引发字典序优化问题，传统方法求解计算成本高。本文通过非均匀量化离散化多目标字典序优化问题，并利用位移操作将其转化为单目标优化。具体地，扩展了确定性模型预测路径积分（MPPI）求解器，以高效求解无二次输入代价的优化问题。此外，提出一种结合空间与时间违规的新谓词鲁棒性度量。实验表明，该方法使用单目标求解器即可实现可解释、可扩展的字典序STL最小违规运动规划。
原文摘要 · Abstract (English)
Motion planning for autonomous vehicles often requires satisfying multiple conditionally conflicting specifications. In situations where not all specifications can be met simultaneously, minimum-violation motion planning maintains system operation by minimizing violations of specifications in accordance with their priorities. Signal temporal logic (STL) provides a formal language for rigorously defining these specifications and enables the quantitative evaluation of their violations. However, a total ordering of specifications yields a lexicographic optimization problem, which is typically computationally expensive to solve using standard methods. We address this problem by discretizing the multi-objective lexicographic optimization problem via non-uniform quantization and transforming it into a single-objective optimization problem using bit-shifting. Specifically, we extend a deterministic model predictive path integral (MPPI) solver to efficiently solve optimization problems without quadratic input cost. Additionally, a novel predicate robustness measure that combines spatial and temporal violations is introduced. Our results show that the proposed method offers an interpretable and scalable solution for lexicographic STL minimum-violation motion planning using a single-objective solver.
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