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We apply a hierarchical control framework to a realistic arm model. With 7 degrees of freedom and 14 muscles, this arm model has complex nonlinear dynamics operating on 28-dimensional state space and 14-dimensional control space. A high-level controller is designed to capture the main features of the complex high-dimensional plant dynamics but with reduced dimensionality. This allows us to solve the original optimal control problem without running into the curse of dimensionality. We also provide a method to design a low-level controller to generate arm configurations that are consistent with high-level controls and at the same time satisfy biological constraints. To the best of our knowledge, this is the first feedback controller for a detailed 3-D model of a human arm.