A key challenge in autonomous driving is that Autonomous Vehicles (AVs) must contend with multiple, often conflicting, planning requirements. These requirements naturally form in a hierarchy -- e.g., avoiding a collision is more important than maintaining lane. While the exact structure of this hierarchy remains unknown, to progress towards ensuring that AVs satisfy pre-determined behavior specifications, it is crucial to develop approaches that systematically account for it. Motivated by lexicographic behavior specification in AVs, this work addresses a lexicographic multi-objective motion planning problem, where each objective is incomparably more important than the next -- consider that avoiding a collision is incomparably more important than a lane change violation. This work ties together two elements. Firstly, a multi-objective candidate function that asymptotically represents lexicographic orders is introduced. Unlike existing multi-objective cost function formulations, this approach assures that returned solutions asymptotically align with the lexicographic behavior specification. Secondly, inspired by continuation methods, we propose two algorithms that asymptotically approach minimum rank decisions -- i.e., decisions that satisfy the highest number of important rules possible. Through a couple practical examples, we showcase that the proposed candidate function asymptotically represents the lexicographic hierarchy, and that both proposed algorithms return minimum rank decisions, even when other approaches do not.

翻译：自动驾驶领域的一个关键挑战在于，自动驾驶汽车（AVs）必须应对多个常相互冲突的规划要求。这些要求自然地形成一个层次结构——例如，避免碰撞比保持车道更为重要。尽管该层次结构的确切构成尚不明确，但为了确保自动驾驶汽车满足预设行为规范，开发能系统性地考虑该层次结构的方法至关重要。受自动驾驶汽车中词典序行为规范的启发，本研究探讨了一个词典序多目标运动规划问题，其中每个目标的重要性均无可比拟地高于下一个目标——例如，避免碰撞的重要性无可比拟地高于违反变道规则。本研究整合了两个核心要素。首先，引入了一种能渐近表示词典序的多目标候选函数。与现有的多目标成本函数构建方法不同，该方法能确保返回的解渐近符合词典序行为规范。其次，受延拓方法的启发，我们提出了两种渐近逼近最小秩决策的算法——即满足尽可能多重要规则的决策。通过若干实际案例，我们展示了所提出的候选函数能渐近表示词典序层次结构，且两种算法均能返回最小秩决策，而其他方法在此情况下可能无法做到。