# geodex：用于黎曼流形运动规划的库

> 原文链接：https://robotics.hellobike.com/papers/2026-10-06-2610-09165
> 频道：papers | 更新日期：2026-10-06 | 标签：arxiv, cs.RO
> 核心摘要：为解决现有库不以配置相关黎曼度量驱动避障规划的问题，geodex以可互换组件实现采样式运动规划。

# geodex：用于黎曼流形运动规划的库

::: v-pre
> 原文链接：[geodex: A Library for Motion Planning on Riemannian Manifolds](https://arxiv.org/abs/2610.09165)（arXiv 2610.09165 · 发布日期：2026-10-06）

**geodex: A Library for Motion Planning on Riemannian Manifolds**

为解决现有库不以配置相关黎曼度量驱动避障规划的问题，geodex以可互换组件实现采样式运动规划。

## 核心要点

- 利用配置空间内在几何进行规划，可获得更短、低能耗且更自然的轨迹。
- geodex将流形、黎曼度量、回缩和采样器解耦为可互换组件。
- 同一规划器可在多种典型空间、矩阵Lie群、乘积空间和关节机器人配置空间上运行。
- 该库为开源C++20实现，提供Python绑定、文档、测试和可复现基准套件。

## 英文摘要 (Abstract)

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.

作者：Phone Thiha Kyaw, Wei Ben, Sepehr Samavi, Miguel Angel Rogel Garcia, Jonathan W. Kelly
:::

## 原始参考来源 (Sources)

- [arXiv 2610.09165：geodex: A Library for Motion Planning on Riemannian Manifolds](https://arxiv.org/abs/2610.09165)