Thrust Magnitude Constraint Handling for Low-Thrust Trajectory Optimization

A detailed analysis of six control constraint methods for thrust magnitude limitations is presented. The inequality augmented Lagrangian and penalty inequality augmented Lagrangian methods are widely used, whereas the box, Heaviside augmented Lagrangian, and penalty Heaviside augmented Lagrangian methods are less common. The newly coined implicit method uses a simple cosine function to bound relevant decision variables. Cartesian and spherical control frames with normalization schemes are also examined, along with techniques for avoiding singularities. The resulting 27 submethods are applied to 10 diverse spacecraft trajectory optimization problems with up to 10 revolutions, including both bang-bang and smooth thrusting profiles. The results confirm that proper scaling is paramount for consistent performance across widely varying test cases. The implicit method is the simplest to implement, does not require tuning, and demonstrates the best median performance of all the nonapproximate solution methods.