Shape-based approximation of constrained low-thrust space trajectories using Fourier series

Document Type


Publication Date



Space mission trajectory design using low-thrust capabilities is becoming increasingly popular. However, trajectory optimization is a very challenging and time-consuming task. In this paper, we build upon existing shapebased techniques to present an alternative Fourier series approximation for rapid low-thrust-rendezvous/orbitraising trajectory construction with thrust-acceleration constraint-handling capability. The new flexible representation, along with the constraint-handling capability, makes this method a suitable candidate for feasibility assessment of a whole range of trajectories within the given system propulsive budget. In addition, the solutions present opportunities for direct optimization techniques. A key point in the proposed method is its ability to solve problems with a greater number of free parameters than in shape-based methods. Several case studies are presented: simple Earth-Mars rendezvous, rendezvous/orbit raising for low Earth orbit to geostationary orbit, and two phasing problems. Results clearly depict the advantage of the proposed method in handling thrust constraints and its applicability to a wide range of problems. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc.

Publication Title

Journal of Spacecraft and Rockets