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.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Kyaw, P. T., Wei, B., Samavi, S., Garcia, M. A. R., & Kelly, J. (2026). geodex: A Library for Motion Planning on Riemannian Manifolds. https://omanscience.com/en/articles/geodex-a-library-for-motion-planning-on-riemannian-manifolds
MLA 9
Kyaw, Phone Thiha, et al. "geodex: A Library for Motion Planning on Riemannian Manifolds." https://omanscience.com/en/articles/geodex-a-library-for-motion-planning-on-riemannian-manifolds.
Chicago (author–date)
Kyaw, Phone Thiha, Ben Wei, Sepehr Samavi, Miguel Angel Rogel Garcia, and Jonathan Kelly. 2026. "geodex: A Library for Motion Planning on Riemannian Manifolds." https://omanscience.com/en/articles/geodex-a-library-for-motion-planning-on-riemannian-manifolds.
Harvard
Kyaw, P. T., Wei, B., Samavi, S., Garcia, M. A. R. and Kelly, J. (2026) 'geodex: A Library for Motion Planning on Riemannian Manifolds', Available at: https://omanscience.com/en/articles/geodex-a-library-for-motion-planning-on-riemannian-manifolds.
Vancouver
Kyaw PT, Wei B, Samavi S, Garcia MAR, Kelly J. geodex: A Library for Motion Planning on Riemannian Manifolds. https://omanscience.com/en/articles/geodex-a-library-for-motion-planning-on-riemannian-manifolds
IEEE
P. T. Kyaw, B. Wei, S. Samavi, M. A. R. Garcia, and J. Kelly, "geodex: A Library for Motion Planning on Riemannian Manifolds," https://omanscience.com/en/articles/geodex-a-library-for-motion-planning-on-riemannian-manifolds.