Large-Scale Lunar Transportation Trajectory Optimal Programming Method Based on the Bilevel Convexification Model

Abstract

In order to solve the trajectory planning problem of the launch vehicle during the large-scale lunar transportation, which involves vertical takeoff and landing, multiple maneuvers, and high landing accuracy requirements. Firstly, the equations of motion of the vehicle's center of mass are established, and a large-scale trajectory optimization model is constructed considering initial position, terminal position, velocity constraints, and thrust constraints. The nonlinear optimization problem is linearized and discretized using convex optimization methods; Secondly, the large-scale optimal trajectory planning problem is converted into a bilevel convex optimization problem. The optimization problems in the dynamic ascent phase, the large-scale dynamic flight phase, and the vertical descent phase are treated as the inner layer convex optimization problems, and solved using the interior point method. At the same time, combined with the fuel optimization purpose, the objective function is designed as the outer layer convex optimization problem, and iterative calculations are performed using the gradient descent method, obtain the optimal fuel trajectory for a wide range of vertical takeoff and landing. Simulation experiments show that the algorithm proposed in this paper ensure the vertical landing of the vehicle which meets the requirements of high-precision landing. Monte Carlo simulation is conducted considering position errors, and the results show that the algorithm has good robustness.

Keywords

lunar vehicle / large-scale transportation / bilevel convexification / trajectory programming / optimal control

References

[1] 于萍，张洪华，李骥，等. 嫦娥五号着陆上升组合体GNC系统设计与实现[J]. 中国科学（技术科学），2021，51（7）：763-777.YU P，ZHANG H H，LI J，et al. Design and implementation of GNC system of lander and ascender module of Chang’e-5 spacecraft[J]. SCIENTIA SINICA Technologica，2021，51（7）：763-777.
[2] 王平，于晓强，郭继峰. 月球大范围探测巡视器及GNC技术发展综述[J]. 宇航学报，2022，43（5）：548-562.WANG P，YU X Q，GUO J F. A survey of lunar wide-range exploration rover and GNC technology[J]. Journal of Astronautics，2022，43（5）：548-562.
[3] 张熇，杜宇，李飞，等. 月球南极探测着陆工程选址建议[J]. 深空探测学报（中英文），2020，7（3）：232-240.ZHANG H，DU Y，LI F，et al. Proposals for lunar south polar region soft landing sites selection[J]. Journal of Deep Space Exploration，2020，7（3）：232-240.
[4] 李扬，张烽，汪小卫，等. 重复使用单级月面着陆与上升器方案设计与制导[J]. 深空探测学报（中英文），2022，9（5）：512-520.LI Y，ZHANG F，WANG X W，et al. Reusable single-stage lunar landing and ascent spacecraft scheme design and guidance[J]. Journal of Deep Space Exploration，2022，9（5）：512-520.
[5] 邱文杰，孟秀云. 基于hp自适应伪谱法的飞行器多阶段轨迹优化[J]. 北京理工大学学报，2017，37（4）：412-417.QIU W J，MENG X Y. Multi-phase trajectory optimization of vehicle based on hp-adaptive pseudospectral method[J]. Transactions of Beijing Institute of Technology，2017，37（4）：412-417.
[6] REYNOLDS T，MALYUTA D，MESBAHI M, et al. A real-time algorithm for non-convex powered descent guidance[C]// Proceedings of AIAA Scitech 2020 Forum （p.0844），[S. l.]：AIAA，2020.
[7] MALYUTA D，REYNOLDS T P，SZMUK M，et al. Discretization performance and accuracy analysis for the rocket powered descent guidance problem[C]//Proceedingss of the AIAA Scitech 2019 Forum，California，USA：AIAA，2019.
[8] MAO Y Q，SZMUK M，AÇIKMEŞE B. Successive convexification of non-convex optimal control problems and its convergence properties[C]//Proceedingss of 2016 IEEE 55th Conference on Decision and Control （CDC）. Las Vegas，NV，USA：AIAA，2016.
[9] AMINI K，SHIKER M A，KIMIAEI M. A line search trust-region algorithm with nonmonotone adaptive radius for a system of nonlinear equations[J]. 4OR-Q J Oper Res 14，2016，14：133-152.
[10] SZMUK M，REYNOLDS T，ACIKMESE B，et al. Successive convexification for 6-dof powered descent guidance with compound state-triggered constraints[C]//Proceedings of AIAA Scitech 2019 Forum. San Diego，California，USA：AIAA，2019.
[11] LI W B，LI W T，LIN C，et al. Trajectory optimization with complex obstacle avoidance constraints via homotopy network sequential convex programming[J]. Aerospace，2022，9（11）：720.
[12] CHEN H B，MA Z W，WANG J B，et al. Online trajectory optimization method for large attitude flip vertical landing of the starship-like vehicle[J]. Mathematics，2023，11（2）：288.
[13] HE X J，ZUO X Y，LI Q L，et al. Surrogate-based entire trajectory optimization for full space mission from launch to reentry[J]. Acta Astronautica，2022，190：83-97.
[14] 王浩帆，张洪华，王泽国，等. 一种月球表面飞跃转移轨迹设计方法[J]. 中国空间科学技术，2021，41（2）：112-124.WANG H F，ZHANG H H，WANG Z G，et al. An optimal trajectory design for lunar surface hop[J]. Chinese Space Science and Technology，2021，41（2）：112-124.
[15] 柳钮滔，施贤正，徐丰，等. 月球永久阴影区着陆点选取要求的高分辨率极化SAR数据分析[J]. 深空探测学报（中英文），2022，9（1）：42-52.LIU N T，SHI X Z，XU F，et al. Analysis of high resolution SAR data and selection of landing sites in the permanently shadowed region on the Moon[J]. Journal of Deep Space Exploration，2022，9（1）：42-52.
[16] JENIE Y I，ASYARY A C，PEOTRO R E. Preliminary design of a liquid propellant engine for a reusable sounding rocket[C]//Proceedings of the 6th International Seminar of Aerospace Science and Technology. Jakarta，Indonesia：AIAA，2018.
[17] ACIKMESE B，PLOEN S R. Convex programming approach to powered descent guidance for Mars landing[J]. Journal of Guidance，Control，and Dynamics，2007，30（5）：1353-1366.