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：自动驾驶车辆的运动规划通常需要满足多个条件性冲突的规范。当所有规范无法同时满足时，最小违规运动规划通过依据优先级最小化规范违规来维持系统运行。信号时序逻辑（STL）提供了形式化语言以严格定义这些规范，并支持对其违规行为进行定量评估。然而，规范的完全有序化会产生词典序优化问题，使用标准方法求解通常计算成本高昂。我们通过非均匀量化与位偏移技术，将多目标词典序优化问题转化为单目标标量优化问题来解决该问题。具体而言，我们扩展了确定性模型预测路径积分（MPPI）求解器，使其能够高效求解不含二次输入成本的优化问题。此外，引入了一种结合时间与空间违规的新型谓词鲁棒性度量。结果表明，所提方法在单目标求解器框架内为词典序STL最小违规运动规划提供了可解释且可扩展的解决方案。