The landing-phase guidance of launch vehicle is a typical nonlinear optimal control problem. With the convex optimization method, the landing-phase guidance can be effectively realized by being converted into a convex programming problem, while satisfying constraints. However, due to the nonlinearity of the landing-phase guidance, the optimal solution by convex optimization would oscillate and could not converge if only successive linearization is used. On the other hand, if variable substitution and relaxation convexification techniques are employed, the optimal solution can be clearly improved. However, different convexification techniques should be used for different convex optimization problems, lacking versatility. To address this issue, the bias proportional guidance and convex optimization are integrated to solve the landing-phase guidance of launch vehicle with the terminal track angle, velocity and thrust constraints. With the proposed method, normal guidance and tangential guidance are separated. The former adopts bias proportional guidance to satisfy the constraints on the terminal track angle and the landing point. For the latter, convex optimization and receding horizon control are employed to satisfy the constraints on the terminal velocity and the thrust constraint, and the method to estimate time-to-go and approximate trajectory parameters based on cubic curves, which could provide the necessary approximate state, is presented. The simulation results indicate that the convex optimization guidance method combined with the proposed guidance can effectively satisfy the constraints, and compared with the existing guidance method that directly adopts convex optimization and receding horizon control, the proposed method clearly improves the solution efficiency and smoothness of the control quantity. Therefore, it is more applicable to practical engineering.
AN Ze
,
XIONG Fenfen
,
LIANG Zhuonan
. Landing-phase guidance of rocket using bias proportional guidance and convex optimization[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020
, 41(5)
: 323606
-323606
.
DOI: 10.7527/S1000-6893.2019.23606
[1] DENEU F, MALASSIGNE M, LE-COULS O, et al. Promising solutions for fully reusable two-stage-to-orbit configurations[J]. Acta Astronautica, 2005, 56(8):729-736.
[2] 高朝辉, 张普卓, 刘宇, 等. 垂直返回重复使用运载火箭技术分析[J]. 宇航学报, 2016, 37(2):145-152. GAO Z H, ZHANG P Z, LIU Y, et al. Analysis of vertical landing technique in reusable launch vehicle[J]. Journal of Astronautics, 2016, 37(2):145-152(in Chinese).
[3] ALEXANDER N, VLADIMIR N. Reusable space planes challenges and control problems[J]. IFAC-Paperonrime, 2016, 49(17):480-485.
[4] MEDITCH J S. On the problem of optimal thrust programming for a lunar soft landing[J]. IEEE Transactions on Automatic Control, 1964, 9(4):477-484.
[5] MIELE A. The Calculus of variations in applied aerodynamics and flight mechanics[J]. Mathematics in Science & Engineering, 1962, 5:99-170.
[6] KLUMPP A R. Apollo lunar descent guidance[J]. Automatica, 1974, 10(2):133-146.
[7] SOSTARIC R, REA J. Powered descent guidance methods for the moon and mars[C]//AIAA Guidance, Navigation, and Control Conference and Exhibit. Reston:AIAA, 2005.
[8] 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.
[9] BLACKMORE L, ACIKMESE B, SCHARF D P. Minimum-landing-error powered-descent guidance for mars landing using convex optimization[J]. Journal of Guidance, Control, and Dynamics, 2010, 33(4):1161-1171.
[10] NESTEROV Y E, TODD M J. Self-scaled barriers and interior-point methods for convex programming[J]. Mathematics of Operations Research, 1997, 22(1):1-42.
[11] LIU X F, LU P. Solving nonconvex optimal control problems by convex optimization[J]. Journal of Guidance, Control, and Dynamics, 2014, 37(3):750-765.
[12] 路钊. 高超声速飞行器再入末段轨迹在线优化[D]. 哈尔滨:哈尔滨工业大学, 2014:39-74. LU Z. Online trajectory optimization for the terminal stage of retry hypersonic vehicles[D]. Harbin:Harbin Institute of Technology, 2014:39-74(in Chinese).
[13] 张志国, 马英, 耿光有, 等. 火箭垂直回收着陆段在线制导凸优化方法[J]. 弹道学报, 2017, 29(1):9-16. ZHANG Z G, MA Y, GENG G Y, et al. Convex optimization method used in the landing-phase online guidance of rocket vertical recovery[J]. Journal of Ballistics, 2017, 29(1):9-16(in Chinese).
[14] LIU X F, SHEN Z, LU P. Entry trajectory optimization by second-order cone programming[J]. Journal of Guidance Control & Dynamics, 2015, 39(2):1-15.
[15] LIU X F. Fuel-optimal rocket landing with aerodynamic controls[J]. Journal of Guidance, Control, and Dynamics, 2019, 42(1):65-77.
[16] 宋建梅, 张天桥. 带末端落角约束的变结构导引律[J]. 弹道学报, 2001, 13(1):16-20. SONG J M, ZHANG T Q. The passive homing missiles variable structure proportional navigation with terminal impact angular constraint[J]. Journal of Ballistics, 2001, 13(1):16-20(in Chinese).
[17] TOH K C, TODD M J. SDPT3-a MATLAB software package for semidefinite programming[J]. Optimization Methods & Software, 1999, 11(1-4):545-581.
[18] 马爽, 杨军, 袁博. 基于多项式函数求解的落角约束制导律[J]. 导航定位与授时, 2018, 5(5):43-47. MA S, YANG J, YUAN B. Impact angle constraint guidance law proposed by polynomial function[J]. Navigation Positioning & Timing, 2018, 5(5):43-47(in Chinese).
[19] DINH Q T, SAVORGNAN C, DIEHL M. Real-time sequential convex programming for nonlonear model predictive control and applications to a hydro-power plant[C]//2012 Decision & Control & European Control Conference. Piscataway:IEEE Press, 2012.
[20] JIANG H, AN Z, YU Y N, et al. Cooperative guidance with multiple constraints using convex optimization[J]. Aerospace Science and Technology, 2018, 79:426-440.
[21] LU P, LIU X. Autonomous trajectory planning for rendezvous and proximity operations by conic optimization[J]. Journal of Guidance, Control, and Dynamics, 2013, 36(2):375-389.
CJA