Reduced-Order Entry Trajectory Planning for Acceleration Guidance

The acceleration guidance concept is to plan an aerodynamic acceleration proe le that integrates to the desired e nal position and velocity and satise es all vehicleconstraints and to track theacceleration proe le. The longitudinal entryguidanceforthespaceshuttleisaccelerationguidance;adragdecelerationproe lethatintegratestothedesired downrange and satise es the vehicle constraints is planned and tracked primarily by bank-angle adjustments. The kinematics relating the drag proe le to the downrange assume that the entry trajectory is a great circle arc. In this paper we consider lateral as well as longitudinal motion in acceleration planning. Three differential equations that are the kinematic relations between the aerodynamic accelerations and the position and velocity variables with energy as the independent variable are used as the basis for two methods of planning the drag and lateral acceleration proe les. The e rst is simpler and produces a feasible trajectory for a given angle-of-attack proe le. The second requires more computation, but produces an optimal trajectory using both angle-of-attack and angleof-bank variations to control the entry trajectory and has greater capability to shape the entry trajectory. Both methods are demonstrated using an X-33 vehicle model. The optimal method is capable of achieving a specie ed e nal heading angle and adjusting the number of bank reversals.