Coordinated Robot Navigation via Hierarchical Clustering

TL;DR

This paper presents a hierarchical clustering-based approach for coordinated robot navigation, enabling scalable, collision-free control of multiple robots in high-dimensional spaces through reactive algorithms and hybrid controllers.

Contribution

It introduces a novel hierarchical clustering framework for robot coordination, with effective algorithms and controllers that guarantee collision avoidance and convergence to desired configurations.

Findings

Successfully navigates multiple robots without collisions

Scalable algorithms with quadratic complexity in the number of robots

Proven convergence to target configurations with high probability

Abstract

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.