Constrained Impulsive Trajectory Optimization for Orbit-to-Orbit Transfer

Abstract

A method for rapidly generating preliminary estimates of performance for orbit-to-orbit transfer vehicles subject to complex operational constraints is presented. Given the characteristics of a particular multistage design and the position and time of the thrusting arcs, the performance index and constraints are evaluated by solving Lambert's problem. An intrinsic equality constraint is imposed on each thrusting arc to insure that the velocity increment provided by each stage is equal to the impulsive velocity increment required by the solution to Lambert's problem. A problem solution is sought by solving a nonlinear programming problem where the independent variables may be chosen from a set of vehicle design parameters and the positions and times of the various thrusting arcs. A Lambert's problem formulation is shown to be preferable to a Kepler's problem formulation for complex missions. Pitfalls in the solution to Lambert's problem are highlighted. A variation of the Method of Multipliers is used for reliably solving the nonlinear programming problem generated by the problem formulation. Finally, several highly constrained orbit-to-orbit transfer problems are presented as examples.