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  • A nonlinear programming approach to space shuttle trajectory optimization

    Paper ID



    • Richard G. Brusch


    Convair Aerospace division of General Dynamics






    The solution of constrained optimal control problems has received considerable attention in recent years, motivated primarily by the need for solutions to practical problems in the aeronautical sciences. In particular, trajectory design for the reusable space shuttle vehicle will require optimization of highly constrained trajectories. Structural integrity and human factors necessitate the consideration of state variable inequality constraints on the instantaneous normal and axial accelerations, on the instantaneous heat flux, and on the total heating during both launch and entry. Thrust, roll, and pitch controls must obey complex inequality constraints during periods of high dynamic pressure for reasons of stability. The practical considerations of range safety, tracking, and weather also constrain the flight path. This paper considers the solution to such problems using the nonlinear programming method of Fiacco-McCormick [1], Several authors [2-8] have successfully applied the technique to constrained optimal control problems of a limited scope. Reference [9] surveys many of the recent applications of mathematical programming to optimal control problems. The present study expands the theory to encompass a general mathematical model for trajectory optimization capable of directly handling six types of equality and inequality constraints. Results of the numerical solution of a highly constrained space shuttle trajectory optimization problem are presented.