Control input histories are determined for flying precision three-dimensional acrobatic maneuvers using inverse- control and optimization methods. A point-mass model is used with three controls, angle of attack, bank angle, and thrust. Bounds are placed on normal load factor, thrust, and angle of attack. By choosing cylindrical coordinates for the position vector and spherical coordinates for the velocity vector, simple inverse solutions are found for precision acrobatic maneuvers. Requiring constant radius and constant helix angle produces nonlinear feedback laws for angle of attack and bank angle. Numerical results are presented for an F4H aircraft performing barrel rolls. EROBATIC maneuvers are the ultimate art of flying. They re- quire keen reflexes in the pilot and close coordination of the various controls. The acrobatic aircraft must be structurally sound, have a large wind area, and have an engine that is powerful rel- ative to its weight. The American Pitts special, with a composite structure and a modified engine, achieves a thrust/weight ratio well above 1. Most fighters can also perform such maneuvers because of their powerful engines (e.g., the maximum thrust/weight ratio of an F-16 ranges between 1.0 and 1.4). Acrobatic maneuvers are an integral part of a fighter pilot's tactics in aerial combat and help him to recover from unexpected flight conditions such as spins.1 For example, a high-g barrel roll is often effective against an attacker closing from astern. Immelman or split-S maneuvers are standard methods of disengaging from combat.2 In conventional flight control design, the aircraft dynamics are assumed linear and time invariant about some nominal equilibrium flight trajectory. These assumptions are not valid in aerobatic maneu- vers because they generally involve large changes in aircraft altitude and attitude. This study develops a systematic approach to determine the control inputs for specified aerobatic maneuvers. The approach uses inverse and optimal control methods to generate feedforward control histories. A unified approach for analyzing precision aero- batic maneuvers is presented by specifying the flight path as either a horizontal or a vertical helix. These specifications are then used in inverse analysis to generate the controls. If the resulting controls are not feasible or if terminal conditions are not met, optimal control methods are used to satisfy the constraints while minimizing the deviations from the ideal aerobatic maneuver. Uehara et al.3 considered minimum time loop maneuvers using a point-mass model. They showed that the controls are mainly on the control boundaries (i.e., bang-bang). A similar study by Shinar et al.4 used an energy state model. They showed that by using this reduced-order model, the solution can be expressed in a feedback form. In recent years, inverse control methods have been used to analyze large-amplitude aircraft motions. Kato and Sugiura5 pre- sented an aileron roll maneuver as an example of inverse analysis of aircraft motion. In their example, however, the inverse control magnitudes are not feasible. Hess et al.6 found the inverse controls for the same maneuver using an inverse simulation technique. A rigid-body model was used in both cases. In another paper by Kato7