geodex

geodex is a general-purpose software framework for motion planning on Riemannian manifolds.

We ship ready-to-use manifolds (\(\mathbb{R}^n\), \(S^n\), \(T^n\), and \(\mathrm{SE}(2)\)), all built from swappable metric, retraction, and sampler policies, along with efficient algorithms for geodesic distance and interpolation.

The core engine of geodex is written purely in C++20 for performance, with first-class Python support (pip install geodex). We are also actively working on integrating popular motion planning frameworks (OMPL, VAMP) and ROS 2 stacks (Nav2, MoveIt 2) into geodex.

cmake -B build \
  -DBUILD_TESTING=ON
cmake --build build
ctest --test-dir build

Getting started

Build the library, run the tests, and wire up the OMPL and Nav2 integrations.

Core concepts

Riemannian geometry, design principles, and algorithms.

SE(2) planning

Plan paths for holonomic and non-holonomic robots on a real costmap with OMPL.

Two-link planar arm sweeping along a minimum-energy geodesic

Minimum-energy planning

Compute minimum-energy motions for a two-link planar manipulator under kinetic energy and Jacobi Riemannian metrics.

Roadmap

Integration	Description	Status
OMPL and VAMP integrations	Planning on Riemannian manifolds with state-of-the-art sampling-based planners	In progress
Nav2 and MoveIt 2 plugins	Geometry-aware planning for ROS 2 mobile robots and manipulators	Planned

Citation

geodex accompanies the paper Geometry-Aware Sampling-Based Motion Planning on Riemannian Manifolds, accepted to WAFR 2026.

If you use geodex in your research, consider citing:

@inproceedings{kyaw2026geometry,
  address = {Oulu, Finland},
  author = {Phone Thiha Kyaw and Jonathan Kelly},
  booktitle = {Proceedings of the 17th World Symposium on the Algorithmic Foundations of Robotics {(WAFR)}},
  date = {2026-06-15/2026-06-17},
  month = {Jun. 15--17},
  title = {Geometry-Aware Sampling-Based Motion Planning on {Riemannian} Manifolds},
  url = {https://arxiv.org/abs/2602.00992},
  year = {2026}
}