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This paper introduces a new method for designing low-level controllers for nonlinear robotic platforms based on a discrete-state high-level controller encoding the behaviors of a reactive task specification. We build our method upon a new type of trajectory constraint which we introduce in this paper, reactive composition, to provide the guarantee that any high-level reactive behavior may be fulfilled at any moment during the continuous execution. We generate pre-computed motion controllers in a piecewise manner by adopting a sample-based synthesis method that associates a certificate of invariance with each controller in the sample set. 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