This paper addresses the Motion Execution Gap, the disconnect between high-level symbolic task descriptions using semantic constraints and executable robot motions. \textbf{Motion Statecharts} are introduced as an executable symbolic representation for complex motions. They allow the arbitrary arrangement of motion constraints, monitors or nested statecharts in parallel and sequence. World-centric motion specification and generalization across embodiments are enabled through the use of a unified differentiable kinematic world model of both, robots and environments. Motion execution is realized through a \ac{lmpc}-based implementation of the task-function approach, in which smooth transitions during task switches are ensured using jerk bounds. Cross-platform transferability was demonstrated by deploying the method on eight robot platforms, operating in diverse environments. The proposed framework is called Giskard and is available open source (https://github.com/cram2/cognitive_robot_abstract_machine).