Numerical Computation of Optimal Atmospheric Trajectories

Abstract

A second-order direct trajectory optimization method in which the state time history is described by Chebychev polynomials and the dynamical equations are satisfied by penalty functions is described. The convergence and fidelity of the method are demonstrated with solutions to the following problems: brachistochrone, subsonic transport minimum-time climb, supersonic interceptor minimum-time climb, Goddard rocket problem with a singular arc, subsonic transport minimum-fuel for a fixed-range mission including climb, cruise and descent, and optimal evasive maneuvers for an airplane pursued by a missile with proportional guidance. The results demonstrate that the method provides an efficient and reliable procedure for solving a wide variety of realistic trajectory optimization problems.