统一路径参数化规划与控制，打通传统到强化学习的路径方法
A Universal Formulation for Path-Parametric Planning and Control
- 提出无奇点、光滑可微的运动坐标系计算方法
- 实现任意曲线的笛卡尔坐标路径参数化，无需预设速度或坐标系
- 兼容经典控制到强化学习，适合机器人路径规划研究者
我们提出一种统一的路径参数化规划与控制框架。该框架具有普适性，能将从传统路径跟踪到近年流行的轮廓跟踪、进度最大化模型预测控制和强化学习等各类路径参数化方法统一纳入同一范式。其核心由两部分构成：一是提出一种紧凑高效的方法，用于计算无奇点、光滑且可微的运动坐标系；二是推导出任意曲线在笛卡尔空间中的路径参数化方法，无需预先假设曲线的速度或运动坐标系，并与前述方法完美契合。两者结合，构建了一个整合现有文献中各类路径参数化技术的统一框架。
原文摘要 · Abstract (English)
We present 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 for 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 unites existing path-parametric techniques in literature.
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