Optimal power-limited rendezvous with thrust saturation

Abstract

Very general arguments show that thrust saturation is not helpful in terms of performance in optimal spacecraft trajectories, but these arguments do not provide quantitative information. For optimal power-limited rendezvous problems with thrust saturation and linearized equations of motion, two simple mathematical conditions that are relatively easy to check are presented that may be of value to mission planners. These conditions relate respectively to the problem of reaching a terminal point in a specified time in the presence of thrust saturation and in doing so in a fuel-efficient way. They can be useful in indicating whether or not the flight interval should be lengthened or whether or not additional thrusters should be implemented if possible, and if so how many. For the case of optimal power-limited rendezvous with a satellite in circular orbit, quantitative information is presented for certain boundary conditions. For certain low-thrust saturation levels and boundary conditions, significant improvements in performance and computation can be attained by lengthening the flight time or implementing an additional thruster, if possible. In one example, the use of two thrusters instead of one reduced the mission fuel requirements by nearly 50%.