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We present and analyze the Motion Grammar: a novel unified representation for task decomposition, perception, planning, and control that provides both fast online control of robots in uncertain environments and the ability to guarantee completeness and correctness. The grammar represents a policy for the task which is parsed in real-time based on perceptual input. Branches of the syntax tree form the levels of a hierarchical decomposition, and the individual robot sensor readings are given by tokens. We implement this approach in the interactive game of Yamakuzushi on a physical robot resulting in a system that repeatably competes with a human opponent in sustained gameplay for the roughly six minute duration of each match.