A fuel-optimal trajectory for a constrained hypersonic vehicle using a direct transcription method

It is well-known that the takeoff weight of a space operation vehicle is composed mainly of fuel. Payload and vehicle hardware make up only a small percentage of the total weight. As a consequence, an important component of mission design for a space operation vehicle is trajectory planning since mission designers can increase the amount of payload or time-in-orbit by reducing the fuel required to accomplish the mission. In this paper, a method to calculate a fuel-optimal cruise trajectory for a hypersonic space vehicle is presented. The method of direct transcription is used to discretize the state and control variables along the vehicle´s flight path to transform the optimization problem into a nonlinear programming problem to find the most fuel-efficient trajectory. Structural constraint in terms of normal loading on the vehicle is imposed along the trajectory. Comparisons are made between the fuel-optimal trajectory and static cruise trajectory.