nanoflann: A Header-Only KD-Tree Library for Exact Nearest-Neighbor Search on Compile-Time Product Manifolds

Key points

• Nearest-neighbor (NN) search underlies countless robotics algorithms, but many state spaces are not Euclidean: orientations live on $SO(2)$ or $SO(3)$ and poses on $SE(2)$ or $SE(3)$, and a Euclidean KD-tree on their raw coordinates returns wrong neighbors.1
• Experiments confirm exactness (recall $1.0$ vs an exhaustive scan under the same product metric), where the Euclidean-on-raw shortcut collapses to recall $\approx 0.5^{m}$ for $m$ rotation blocks, with up to three orders of magnitude speedup over brute force.1
• We further contribute an incremental, self-balancing single-tree index for points under heavy churn (e.g. sliding-window LiDAR maps) or $SE(3)$ trajectories: bounded memory and faster updates than prior work, with an optional asynchronous tail-latency-bounding mode.1

Sources (1)

• [1]nanoflann: A Header-Only KD-Tree Library for Exact Nearest-Neighbor Search on Compile-Time Product Manifolds
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 10, 11:10 PM

  We present a header-only, dependency-free C++ KD-tree library for exact NN search on user-defined product manifolds declared at compile time: the space is composed from base manifolds ($\mathbb{R}^n$, $SO(2)$, $SO(3)$, $S^n$; products $SE(2)$, $SE(3)$, tori) with a single type alias, and the library synthesizes a metric whose pruning is provably admissible, wrap-aware for circular coordinates and

  Nearest-neighbor (NN) search underlies countless robotics algorithms, but many state spaces are not Euclidean: orientations live on $SO(2)$ or $SO(3)$ and poses on $SE(2)$ or $SE(3)$, and a Euclidean KD-tree on their raw coordinates returns wrong neighbors.

Extractive summary: sentences quoted from the sources.