Coordinated Robot Navigation via Hierarchical Clustering
This addresses the challenge of centralized coordination for multiple robots in arbitrary dimensions, offering a deterministic and provably safe solution, though it is incremental as it builds on existing hierarchical clustering methods.
The paper tackles the problem of coordinating multiple robots by using hierarchical clustering to develop reactive navigation algorithms, resulting in a hybrid controller that guarantees collision-free movement to a desired configuration for almost all initial states with computational complexity quadratic in the number of robots and algebraic in the dimension.
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.