ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Adaptive initial value Newton-Raphson algorithm for free return orbit design in lunar exploration
Received date: 2023-03-29
Revised date: 2023-04-26
Accepted date: 2023-05-15
Online published: 2023-05-26
Supported by
National Natural Science Foundation of China(12072365);Technology Innovation Team of Manned Space Engineering
Free return orbit design is one of the indispensable parts in the orbit scheme design of manned lunar exploration missions. Existing methods for designing free return orbit are relatively complicated， and heavily dependent on initial values， which hinders direct high-precision design and the adaption to large-scale fast search requirements， and thus limits the efficiency of solving problems such as window design and reachable domain analysis. To solve these problems， a model of nonlinear equations with perilune pseudo-parameters as independent variables was first established in this paper. Then， a Newton-Raphson algorithm based on adaptive initial values for fast solution of the equations was proposed. Furthermore， two indexes were defined to evaluate the quality of the initial values and the capability of the algorithm. Compared with the simulation results of Sequential Quadratic Programming algorithm， the calculation speed of the proposed method was significantly improved， and the simulation results of high-precision calculation showed a significant enhancement in large-scale search capability.
Zeyue LI , Haiyang LI , Zhen YANG , Qibo PENG . Adaptive initial value Newton-Raphson algorithm for free return orbit design in lunar exploration[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023 , 44(15) : 528753 -528753 . DOI: 10.7527/S1000-6893.2023.28753
| 1 | ZEA L， PIPER S S， GAIKANI H， et al. Experiment verification test of the Artemis I ‘Deep Space Radiation Genomics’ experiment［J］. Acta Astronautica， 2022， 198： 702-706. |
| 2 | 贺波勇， 沈红新， 李海阳. 地月转移轨道设计的改进微分校正方法［J］. 国防科技大学学报， 2014， 36（6）： 60-64. |
| HE B Y， SHEN H X， LI H Y. An improved differential correction method for trans-lunar orbit design［J］. Journal of National University of Defense Technology， 2014， 36（6）： 60-64 （in Chinese）. | |
| 3 | 张磊， 谢剑锋， 唐歌实. 绕月自由返回飞行任务的轨道设计方法［J］. 宇航学报， 2014， 35（12）： 1388-1395. |
| ZHANG L， XIE J F， TANG G S. Method of mission trajectory design for circumlunar free return flight［J］．Journal of Astronautics， 2014， 35（12）： 1388-1395 （in Chinese）. | |
| 4 | 曹鹏飞， 贺波勇， 彭祺擘， 等. 载人登月绕月自由返回轨道混合-分层优化设计［J］. 宇航学报， 2017， 38（4）： 331-337. |
| CAO P F， HE B Y， PENG Q B， et al. Hybrid and two-level optimization design of circumlunar free-return trajectory for manned lunar landing mission［J］. Journal of Astronautics， 2017， 38（4）： 331-337 （in Chinese）. | |
| 5 | 彭祺擘， 和星吉， 陈天冀， 等. 星历模型下地月自由返回全飞行过程轨道设计［J］. 宇航学报， 2023， 44（1）： 43-51. |
| PENG Q B， HE X J， CHEN T J， et al. Design of Earth-Moon free return transfer trajectory under ephemeris model during the entire flight process［J］. Journal of Astronautics， 2023， 44 （1）： 43-51 （in Chinese）. | |
| 6 | PHO， HUNG K. Improvements of the Newton–Raphson method［J］. Journal of Computational and Applied Mathematics， 2022， 408： 114106. |
| 7 | MORADIAN H， KIA S. A distributed continuous-time modified Newton–Raphson algorithm［J］. Automatica， 2022， 136： 109886. |
| 8 | SANAM S M， RAJIV A， CHAND A M， et al. The study of Newton–Raphson basins of convergence in the three-dipole problem［J］. Nonlinear Dynamics， 2022， 107（1）： 829-854. |
| 9 | YANG X， CHENG G， WANG Z. Newton method for computing the adaptation coefficient in the CIE system of mesopic photometry［J］. Color Research & Application， 2022， 47（1）： 49-54. |
| 10 | LYU W， CAI L， HUANG D. Compressed Newton-Raphson method for power flow analysis in DC traction network［J］. IEEE Transactions on Power Systems， 2023， 38（2）： 1783-1786. |
| 11 | 夏存言， 张刚， 耿云海. 共面单脉冲拦截多目标问题［J］. 航空学报， 2022， 43（3）： 325093. |
| XIA C Y， ZHANG G， GENG Y H. Coplanar multi-target interception with a single impulse ［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（3）： 325093 （in Chinese）. | |
| 12 | FORMICA G， MILICCHIO F， LACARBONARA W. A Krylov accelerated Newton–Raphson scheme for efficient pseudo-arclength pathfollowing［J］. International Journal of Non-Linear Mechanics， 2022， 145： 104-116. |
| 13 | LIU Y， LI Z， FAN M. A Newton-Raphson-Based sequential power flow algorithm for hybrid AC/DC microgrids［J］. IEEE Transactions on Industry Applications， 2022， 58（1）： 843-854. |
| 14 | ANDREIS E， FRANZESE V， TOPPUTO F. Onboard orbit determination for Deep-Space CubeSats［J］. Journal of Guidance， Control， and Dynamics， 2022， 45（8）： 1466-1480. |
| 15 | CHOI H， KIM S D， SHIN B. Choice of an initial guess for Newton’s method to solve nonlinear differential equations［J］. Computers & Mathematics with Applications， 2022， 117（C）： 69-73. |
| 16 | CHERIF R， TANG Z， GUYOMARCH F， et al. An improved Newton method based on choosing initial guess applied to scalar formulation in nonlinear magnetostatics［J］. IEEE Transactions on Magnetics， 2019， 55（6）： 1-4. |
| 17 | CASELLA F， BACHMANN B. On the choice of initial guesses for the Newton-Raphson algorithm［J］. Applied Mathematics & Computation， 2021， 398（0）： 125991. |
| 18 | 周晚萌. 载人探月序列任务有限推力轨道逆动力学设计方法研究［D］. 长沙：国防科技大学， 2019： 61-62. |
| ZHOU W M. Finite thrust orbit design for manned lunar prospecting series mission using inverse dynamics method［D］. Changsha： National University of Defense Technology， 2019： 61-62 （in Chinese）. | |
| 19 | 贺波勇， 李海阳， 周建平. 载人登月绕月自由返回轨道与窗口精确快速设计［J］. 宇航学报， 2016， 37（5）： 512-518. |
| HE B Y， LI H Y， ZHOU J P. Rapid design of circumlunar free-return high accuracy trajectory and trans-lunar window for manned lunar landing mission［J］．Journal of Astronautics， 2016， 37（5）： 512-518 （in Chinese）. | |
| 20 | PENG Q B， SHEN H X， LI H Y. Free return orbit design and characteristics analysis for manned lunar mission［J］. Science China Technological Sciences， 2011， 54（12）： 3243-3250. |
/
| 〈 |
|
〉 |
CJA