Low-Thrust Minimum-Fuel Trajectory Optimization Using Multiple Shooting Augmented by Analytical Derivatives

What is it about?

Optimizing the fuel consumption under a given thrust in designing space flight trajectories is a very important topic. The optimal thrust is always in a sequence of “on-off-on-off...”. Due to this so-called “bang-bang structure”, it is always a difficult task to find such optimal trajectories. In this article, we developed a technique to tackle this problem in two major steps. In the first step, a special trajectory with a smaller thrust is obtained. The trajectory is special in such way that the thrust is always “on”; and thus it is relatively easier to calculate. People called this trajectory ‘’fully-propelled’’. Then, we increase the thrust bit by bit all the way to our given value. This step is called numerical continuation. The logic behind this approach is that we believe that the optimal trajectories of two successive thrusts are very similar. However, this technique is usually computationally slow. Therefore, we have developed special techniques to boost the computation speed. To show the effectiveness, our method has been successfully used to solve a GTO-GEO trajectory with more than 100 spirals.

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