arXiv subjects

Ya-Zhong Luo

Publications and source records attributed to Ya-Zhong Luo.

3 recordsLinked to original sources

arXiv2026

Nonlinear Programming of Low-Thrust Multi-Rendezvous Trajectories Using Analytical Hessian

This study presents a fast nonlinear programming algorithm for low-thrust multi-asteroid rendezvous missions. The core contribution is the derivation of analytical formulations for both first- and second-order gradients of low-thrust rendezvous $Δv$ through an iterative Lambert-based $Δv$ estimator and their application to derive the Hessian matrix or nonlinear programming of the multi-rendezvous trajectory optimization problem. Numerical simulations demonstrate the method's accuracy, with mean relative errors of $Δv$ approximation below 0.8\% for main-belt asteroid transfers, with the analytical gradients matching those computed via the central difference method. The nonlinear programming algorithm's effectiveness is validated through a 9-asteroid rendezvous sequence under both fuel-optimal and time-optimal configurations. Additional validation on three top-ranking sequences from the 12th Global Trajectory Optimization Competition (GTOC12) shows consistent improvement over the original solutions. The proposed approach is well-suited for integration into global trajectory optimization algorithms for multi-spacecraft multi-target missions, offering high computational efficiency while maintaining precise objective function evaluation capabilities.

astro-ph.IM↗

arXiv2024

Short-Term Evolution and Risks of Debris Cloud Stemming from Collisions in Geostationary Orbit

The increasing population of objects in geostationary orbit has raised concerns about the potential risks posed by debris clouds resulting from fragmentation. The short-term evolution and associated hazards of debris generated by collisions in the geostationary region is investigated in this study. The initial distribution of two debris clouds is modeled using a single probability density function. The combined distribution of the evolved clouds is determined by solving boundary value problems. The risks associated with these debris clouds are evaluated by calculating the instantaneous impact rate and cumulative collision probability. The probability of collisions with millimeter-sized fragments may increase to 1% within 36 hours, while the probability of collisions with fragments 5 cm or larger is approximately $10^{-5}$. These findings underscore the vulnerability of the geostationary region to space traffic accidents.

astro-ph.EP↗

arXiv2024

Analytical Delta-V Approximation for Nonlinear Programming of Multi-target Rendezvous and Flyby Trajectories

This study proposes an analytical Delta-V approximation of short-time transfers based on the linear relative motion and a gradient-based nonlinear programming model of multi-target rendezvous and flyby trajectories. In previous studies, the Lambert's solution is commonly used to evaluate Delta-V of short-duration transfers. In this study, to avoid the iteration process for obtaining the Lambert's solution and its gradient, the linear relative motion equations are applied to form an analytical two-point boundary value model for the near-circular orbit rendezvous problems. Although the relative motion equations are usually applicable when the two orbits are close enough, and the position and velocity errors would become more significant as the orbital differences increase, the errors of the velocity increments were proved acceptable in our simulations. Moreover, the analytical formula facilitates the calculation of the gradients to the start epoch and flight time, which are used to establish a nonlinear programming model for sequence optimization that gradient-based algorithms can easily solve. Simulation results demonstrated that the analytical Delta-V approximation requires much less calculation than the Lambert's solution, and the proposed gradient-based nonlinear programming algorithms can obtain similar results in less time than previous methods.

astro-ph.EP↗