Coordinated Robot Navigation via Hierarchical Clustering


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

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