analiza aiqbench
This article introduces geodex, an open-source library designed specifically for motion planning on Riemannian manifolds, addressing a gap in existing tools that handle intrinsic geometry and obstacles simultaneously. By treating configuration-dependent metrics as the core driver for distance and geodesics, it enables more energy-efficient and natural trajectories across various robotic state spaces, from Lie groups to articulated systems.
geodex: A Library for Motion Planning on Riemannian Manifolds
arXiv:2610.09165v1 Announce Type: new 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.
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.
8 pages, 7 figures, 4 tables. Code, documentation, and tutorials at this https URL
Robotics (cs.RO)
arXiv:2610.09165 [cs.RO]
(or arXiv:2610.09165v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2610.09165 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 272 cuvinte
Subiecte conexe
Geometry-Aware Sampling-Based Motion Planning on Riemannian Manifolds
arXiv · 6 aug. 2026
Riemannian Splat Regression Models for Learning Time Fields on Arbitrary Riemannian Manifolds
arXiv · 30 sept. 2026
RMRRT: Riemannian Barrier Metric RRT for Inequality-Aware Steering on Equality Manifolds
arXiv · 7 oct. 2026
The Open Motion Planning Library 2.0
arXiv · 3 aug. 2026