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 transforming the multi-objective lexicographic optimization problem into a single-objective scalar optimization problem using non-uniform quantization and 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 within a single-objective solver framework.

翻译：自主车辆的运动规划常需同时满足多个存在条件性冲突的规范。当无法同时满足所有规范时，最小违反运动规划通过按优先级最小化规范违反行为来维持系统运行。信号时序逻辑（STL）为精确定义这些规范提供了形式化语言，并可定量评估其违反程度。然而，规范的全局排序会形成词典序优化问题，采用标准方法求解通常计算代价高昂。本文通过非均匀量化和位运算，将多目标词典序优化问题转化为单目标标量优化问题。具体而言，我们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成本的优化问题。此外，本文提出了一种结合时空违反的新型谓词鲁棒性度量方法。实验结果表明，所提方法能够在单目标求解器框架内，为基于STL词典序的最小违反运动规划提供可解释且可扩展的解决方案。