# Coordinated Robot Navigation via Hierarchical Clustering

arXiv: https://arxiv.org/abs/1507.01637 · HTML: https://mlsanity.com/paper/1507.01637/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2015.

## Built on by (most cited first, 4 of 4)

- [ActiveSplat: High-Fidelity Scene Reconstruction through Active Gaussian Splatting](https://mlsanity.com/paper/2410.21955/) (2024)
- [Detecting danger in gridworlds using Gromov's Link Condition](https://mlsanity.com/paper/2201.06274/) (2022)
- [Fault-Tolerant Multi-Robot Coordination with Limited Sensing within Confined Environments](https://mlsanity.com/paper/2505.15036/) (2025)
- [Visual Place Cell Encoding: A Computational Model for Spatial Representation and Cognitive Mapping](https://mlsanity.com/paper/2504.15953/) (2025)

## Abstract (arXiv)

We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of n perfectly sensed and actuated Euclidean spheres in a d-dimensional ambient space (for arbitrary n and d). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in n and algebraic in d and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way.