Enhanced Low-Thrust Rendezvous with Augmented Q-laws Using Advance Phasing and Proportional-Derivative Control

A modified Q-law is developed to perform continuous-thrust orbital rendezvous using feedback guidance. This work builds on the EQ-law and RQ-law, adding the use of advance phasing and a novel target element augmentation scheme based on proportional-derivative control to achieve shorter times of flight for rendezvous trajectories. Advance phasing is based on an idea introduced with the EQ-law of matching phase (true anomaly) while orbit matching is still underway to achieve simultaneous convergence in all six orbital elements. Examples of rendezvous-enabled Q-laws from literature are compiled together into a taxonomy and compared against each other through a parameter optimization study to assess performance, namely in terms of time of flight. Replacing the phasing controller of the RQ-law (state of the art) with the proportional-derivative controller reduces time of flight by 11 percent, while including the advance phasing technique brings the reduction to 14 percent. The modified Q-law introduced in this work is suitable for designing low Earth orbit multiple-target rendezvous missions where a reduction in time spent on phasing with each target yields significant gains. The various combinations of guidance laws are all tested with J2 perturbations in the dynamics, demonstrating the usability of these guidance laws in perturbed orbits.