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The problem of escorting a moving target with a team of mobile robots was solved in this article by resorting to a formation control algorithm that can be cast in the framework of the NSB control approach. The overall mission, therefore, is decomposed into properly defined elementary tasks that are hierarchically arranged, so that the higher-priority tasks are not influenced by the lower-priority ones. The validity of the proposed approach has been proved by both simulation case studies and experimental results with a team of six Khepera II mobile robots. Stability analysis concerning effective conditions needed to verify that the behaviors of specific missions are properly defined and merged is under investigation. Future improvements might regard decentralization of the algorithm, consideration of the vehicles' nonholonomicity in the definition of the task functions, and the introduction of a piecewise-constant constraint for the linear velocity to allow application of the method to teams of cruise vehicles (e.g., a fleet of vessels or a flight of planes).