This work presents a unified framework for path-parametric planning and control. This formulation is universal as it standardizes the entire spectrum of path-parametric techniques -- from traditional path following to more recent contouring or progress-maximizing Model Predictive Control and Reinforcement Learning -- under a single framework. The ingredients underlying this universality are twofold: First, we present a compact and efficient technique capable of computing singularity-free, smooth and differentiable moving frames. Second, we derive a spatial path parameterization of the Cartesian coordinates applicable to any arbitrary curve without prior assumptions on its parametric speed or moving frame, and that perfectly interplays with the aforementioned path parameterization method. The combination of these two ingredients leads to a planning and control framework that brings togehter existing path-parametric techniques in literature. Aiming to unify all these approaches, we open source PACOR, a software library that implements the presented content, thereby providing a self-contained toolkit for the formulation of path-parametric planning and control methods.

翻译：本文提出了一种路径参数化规划与控制的统一框架。该框架具有普适性，它将从传统路径跟踪到近年发展的轮廓跟踪或进度最大化模型预测控制及强化学习等所有路径参数化技术，统一标准化于单一框架之下。实现这种普适性的基础包含两个关键要素：首先，我们提出了一种紧凑高效的技术，能够计算无奇异性、光滑且可微的动标架。其次，我们推导了笛卡尔坐标的空间路径参数化方法，该方法适用于任意曲线，无需预先假设其参数化速度或动标架，并能与前述路径参数化方法完美协同。这两项要素的结合产生了一个规划与控制框架，将文献中现有的路径参数化技术整合在一起。为了统一所有这些方法，我们开源了PACOR软件库，该库实现了本文所述内容，从而为路径参数化规划与控制方法的构建提供了一个自包含的工具包。