We present the Motion Grammar: an approach to represent and verify robot control policies based on context-free grammars. The production rules of the grammar represent a top-down task decomposition of robot behavior. The terminal symbols of this language represent sensor readings that are parsed in real time. Efficient algorithms for context-free parsing guarantee that online parsing is computationally tractable. We analyze verification properties and language constraints of this linguistic modeling approach, show a linguistic basis that unifies several existing methods, and demonstrate effectiveness through experiments on a 14-degree-of-freedom (DOF) manipulator interacting with 32 objects (chess pieces) and an unpredictable human adversary. We provide many of the algorithms discussed as Open Source, permissively licensed software.