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In this paper, we propose a methodology for implementing multirobot navigation-function-based controllers to mixed teams of holonomic and nonholonomic agents. A new nonsmooth backstepping controller is introduced for translating kinematic controllers to equivalent dynamic ones, while maintaining bounded velocity specifications. The derived backstepping controller is applied to a dynamic model of the mobile robots, yielding a globally asymptotically stable dynamic controller. The effectiveness of the methodology is verified through nontrivial computer simulations.