Trajectory optimization for the Atlas/Centaur launch vehicle

Computational techniques used to design and optimize the trajectories flown by the Atlas/Centaur launch vehicle are presented. The open-loop atmospheric guidance strategy and the closed-loop exoatmospheric pitch and yaw guidance equations are discussed breifly to indicate the control parameters available for optimization within the constraints of the current flight computer implementation. The full range of constraints that must be observed during the flight is discussed at length. The main portion of the paper is devoted to a discussion of the constrained optimization technique used, a method related to Hestenes' Method of Multipliers, (25) but using various formulas to update the multipliers. To the best of the author's Knowledge, no publications have appeared showing the applicability and advantages of multiplier methods to trajectory optimization problems. The author's experience has shown his variation of the Method of Multipliers to be almost twice as fast as competing penalty function methods. Finally, optimization of the HEAO-A direct-ascent trajectory is discussed. The HEAO-A mission demonstrates profile optimization to meet range safety, tracking, heating, structural integrity, and attitude rate constraints.