Fast Estimation of Perturbed Impulsive Rendezvous via Semi-Analytical Equality-Constrained Optimization

Fast optimization of impulsive perturbed orbit rendezvous using simplified parametric model

“…Therefore, we provide an efficient method to obtain the optimal rendezvous trajectory starting with the estimated impulses in Ref. [18] as an acceptable initial guess.…”

“…Ref. [18] designed a fast estimation model for perturbed LEO rendezvous. In this section, the ten parameters obtained by the estimation method are used to calculate the initial values of the impulses.…”

“…Based on Ref. [18], we first convert the osculating orbit elements into mean elements and calculate the difference between the orbit elements of the chaser and target without maneuvers. The difference can be expressed using a nonsingular orbit element:…”

“…However, the optimal parameters of the drift orbit, such as the semi-major axis and inclination, were determined using a traversal search. To obtain the optimal parameters of the drift orbit analytically, Huang et al established an equal constraint optimization model that could be quickly solved to obtain the approximated near-optimal velocity increment [18]. However, as the analytical equation of the J 2 perturbation was used in the calculation, the solution was approximate and could not be directly applied as a precise solution of full perturbations.…”

“…Specifically, the optimal four impulses and transfer trajectory are expressed by only ten parameters based on an existing estimation method from Ref. [18]. A method for predicting the orbital deviations between the chaser and target with high-precision dynamics is proposed.…”