Insects are among the most agile natural flyers. Hypotheses on their flight control cannot always be validated by experiments with animals or tethered robots. To this end, we developed a programmable and agile autonomous free-flying robot controlled through bio-inspired motion changes of its flapping wings. Despite being 55 times the size of a fruit fly, the robot can accurately mimic the rapid escape maneuvers of flies, including a correcting yaw rotation toward the escape heading. Because the robot's yaw control was turned off, we showed that these yaw rotations result from passive, translation-induced aerodynamic coupling between the yaw torque and the roll and pitch torques produced throughout the maneuver. The robot enables new methods for studying animal flight, and its flight characteristics allow for real-world flight missions.