geodex: A Library for Motion Planning on Riemannian Manifolds

Key points

• Existing libraries for optimization on manifolds provide rich geometric primitives but do not plan around obstacles.1
• 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.1
• We present geodex, an open-source C++20 library with Python bindings.1
• 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.1

Sources (1)

• [1]geodex: A Library for Motion Planning on Riemannian Manifolds
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 10:08 PM

  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.

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