  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.
