This paper considers the problem of computing an optimal trajectory for an autonomous system that is subject to a set of potentially conflicting rules. First, we introduce the concept of prioritized safety specifications, where each rule is expressed as a temporal logic formula with its associated weight and priority. The optimality is defined based on the violation of such prioritized safety specifications. We then introduce a class of temporal logic formulas called $\textrm{si-FLTL}_{\mathsf{G_X}}$ and develop an efficient, incremental sampling-based approach to solve this minimum-violation planning problem with guarantees on asymptotic optimality. We illustrate the application of the proposed approach in autonomous vehicles, showing that $\textrm{si-FLTL}_{\mathsf{G_X}}$ formulas are sufficiently expressive to describe many traffic rules. Finally, we discuss practical considerations and present simulation results for a vehicle overtaking scenario.

中文翻译：

---

自治系统的最小违规规划：理论和实践考虑

本文考虑了为受一组潜在冲突规则约束的自治系统计算最佳轨迹的问题。首先，我们引入了优先安全规范的概念，其中每个规则都表示为具有相关权重和优先级的时间逻辑公式。最优性是基于违反此类优先安全规范而定义的。然后，我们引入了一类称为 $\textrm{si-FLTL}_{\mathsf{G_X}}$ 的时间逻辑公式，并开发了一种有效的、基于增量采样的方法来解决这个最小违反规划问题，并保证渐近最优性. 我们说明了所提出的方法在自动驾驶汽车中的应用，表明 $\textrm{si-FLTL}_{\mathsf{G_X}}$ 公式具有足够的表现力来描述许多交通规则。