Trajectory optimization for the Atlas/Centaur launch vehicle

A method for finding solutions to complex trajectory optimization problems with detailed hardware and launch vehicle constraints is presented. The trajectory optimization problem is formulated as a constrained function minimization problem by modeling the control by a function of a finite number of parameters. Although any parametric control model may be selected, the natural choice of parameters is the actual parameters of the parametric guidance equations flown on the flight digital computer. A variation of the method of multipliers is presented for performing the constrained function minimization. A functional is proposed that allows incorporation of state variable inequality constraints. 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.