geodex: A Library for Motion Planning on Riemannian Manifolds

2026-10-06

AI Summary

This work addresses the lack of Riemannian metric-driven obstacle avoidance in existing motion planning libraries by proposing an open-source C++20 framework that, for the first time, employs configuration-dependent Riemannian metrics as core geometric drivers for distance computation and interpolation. By decoupling components such as manifolds and metrics, the library provides a unified sampling-based planning interface that enables seamless transitions across multiple spaces, while integrating Lie group geometric primitives and Python bindings. Experimental evaluations demonstrate that the proposed approach generates shorter, more energy-efficient trajectories across diverse manifolds. The project is accompanied by comprehensive documentation, extensive testing, and a fully 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.

Problem

• Motion Planning
• Riemannian Manifolds
• Configuration Space
• Obstacle Avoidance
• Geodesics

Innovation

• Riemannian Manifolds
• Motion Planning
• Geodesics
• Sampling-based Planning
• Matrix Lie Groups