Hierarchically clustered navigation of distinct Euclidean particles

This paper introduces and solves the problem of cluster-hierarchy-invariant particle navigation in Conf (R^d, J). Namely, we are given a desired goal configuration, x* ϵ Conf (R^d, J) and τ, a specified cluster hierarchy that the goal supports. We build a hybrid closed loop controller guaranteed to bring any other configuration that supports τ to the desired goal, x* ϵ Conf (R^d, J), through a transient motion whose each configuration along the way also supports that hierarchy.