Nonlinear Programming of Low-Thrust Multi-Rendezvous Trajectories Using Analytical Hessian
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915947549294592 |
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| author | Huang, An-Yi Luo, Ya-Zhong |
| author_facet | Huang, An-Yi Luo, Ya-Zhong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19573 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear Programming of Low-Thrust Multi-Rendezvous Trajectories Using Analytical Hessian Huang, An-Yi Luo, Ya-Zhong Instrumentation and Methods for Astrophysics Earth and Planetary Astrophysics 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. |
| title | Nonlinear Programming of Low-Thrust Multi-Rendezvous Trajectories Using Analytical Hessian |
| topic | Instrumentation and Methods for Astrophysics Earth and Planetary Astrophysics |
| url | https://arxiv.org/abs/2604.19573 |