Design and evaluation of a three-dimensional optimal ascent guidance algorithm

The problem of optimal three-dimensional guidance of a launch vehicle through the atmosphere, while satisfying a set of operational constraints and satisfying a set of tangency conditions at main engine cutoff, is considered. A hybrid analytic/numerical approach is applied to the solution of this problem. The resulting guidance algorithm makes maximum utilization of the analytically tractable portions of the solution to construct a set of interpolating functions. These functions are then used in a numerical treatment of the total problem based on the method of collocation. A numerical study is performed using a single-stage vehicle model. The results indicate that the guidance algorithm converges reliably and accurately and that the execution time required for a single guidance update is well within the realm of real-time implementation.