发表机构
University of Toronto Institute for Aerospace Studies (UTIAS); Vector Institute for Artificial Intelligence（多伦多大学航空航天研究所; 向量人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对现有运动规划库忽略机器人构型空间内在几何的问题，提出开源库 geodex，通过统一接口支持多种流形和自定义黎曼度量，实现更短、低能耗的规划。
AI 中文摘要
规划尊重机器人构型空间内在几何（包括其曲率和与构型相关的代价概念）的运动，比在环境平坦度量下进行规划能产生更短、更低能量且更自然的轨迹。现有的流形优化库提供了丰富的几何原语，但不处理障碍物周围的规划。虽然通用运动规划库支持多种状态空间和自定义距离函数，但它们尚未将依赖于构型的黎曼度量视为驱动距离、插值和测地线的几何。我们提出 geodex，一个带有 Python 绑定的开源 C++20 库。该库通过单一的基于采样的运动规划接口，将流形、其黎曼度量、回缩和采样器作为独立、可互换的组件暴露出来。同一个规划器无需修改即可在规范空间 $\mathbb{R}^n$、$\mathbb{T}^n$、$\mathbb{S}^n$、矩阵李群如 $SO(2)$、$SE(2)$、$SO(3)$ 和 $SE(3)$、这些空间的乘积以及关节式机器人构型空间上运行，每个空间都配有用户定义的黎曼度量。我们公开提供 geodex，并附带文档、测试和可复现的基准测试套件。
英文摘要
Planning motions that respect the intrinsic geometry of a robot's configuration space, including its curvature and a configuration-dependent notion of cost, yields shorter, lower-energy, and more natural trajectories than planning under the ambient flat metric. Existing libraries for optimization on manifolds provide rich geometric primitives but do not plan around obstacles. While general-purpose motion planning libraries support many state spaces and custom distance functions, they do not yet treat a configuration-dependent Riemannian metric as the geometry that drives distance, interpolation, and geodesics. We present geodex, an open-source C++20 library with Python bindings. The library exposes the manifold, its Riemannian metric, the retraction, and the sampler as independent, interchangeable components through a single sampling-based motion planning interface. The same planner runs unchanged on canonical spaces $\mathbb{R}^n$, $\mathbb{T}^n$, $\mathbb{S}^n$, matrix Lie groups such as $SO(2)$, $SE(2)$, $SO(3)$, and $SE(3)$, products of these spaces, and articulated-robot configuration spaces, each equipped with a user-defined Riemannian metric. We make geodex publicly available with documentation, tests, and a reproducible benchmark suite.
Comments8 pages, 7 figures, 4 tables. Code, documentation, and tutorials at https://geodex.readthedocs.io
