中国空间科学技术

中国空间科学技术 ›› 2026, Vol. 46 ›› Issue (3): 143-156.doi: 10.16708/j.cnki.1000-758X.2026.0043

• 《中国空间科学技术（中英文）》创刊45周年专刊 • 上一篇    下一篇

Multi-phase trajectory programming with divert capability for lunar lander powered descent

ZHANG Xiaowen1,2，WANG Dayi3,*，HUANG Xiangyu1，LI Ji1，WANG Tianshu2   

  1. 1.Beijing Institute of Control Engineering, Beijing 100094, China
    2.School of Aerospace Engineering, Tsinghua University，Beijing 100084，China
    3.Beijing Institute of Spacecraft System Engineering, Beijing 100094，China
  • 收稿日期:2026-01-20 修回日期:2026-02-15 录用日期:2026-03-22 发布日期:2026-05-21 出版日期:2026-05-31

Multi-phase trajectory programming with divert capability for lunar lander powered descent

ZHANG Xiaowen1,2，WANG Dayi3,*，HUANG Xiangyu1，LI Ji1，WANG Tianshu2   

  1. 1.Beijing Institute of Control Engineering, Beijing 100094, China
    2.School of Aerospace Engineering, Tsinghua University，Beijing 100084，China
    3.Beijing Institute of Spacecraft System Engineering, Beijing 100094，China
  • Received:2026-01-20 Revision received:2026-02-15 Accepted:2026-03-22 Online:2026-05-21 Published:2026-05-31

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摘要： It is important for a lunar lander to possess a large divert capability during the final landing phase, as this can enhance the tolerance for flight deviations in the early phase or improve the obstacle avoidance performance. Therefore, when designing the powered descent trajectory, sufficient final phase divert capability should be reserved at the minimum propellant cost. To this end, a multi-phase trajectory programming (MPTP) method for powered descent with approaching phase divert capability is proposed. First, the entire powered descent trajectory is divided into the main braking phase and the approaching phase. The main braking phase is responsible for dissipating the majority of the initial velocity. The approaching phase is responsible for safely and precisely flying toward the landing site. It is nominally a vertical descent trajectory and possesses equal divert capability in all horizontal directions. Then, a constant-thrust linear tangent guidance (LTG) accounting for the lunar curvature is designed for the main braking phase. For the approaching phase, a variable-thrust lossless convex programming (LCP) guidance considering the constraints of tilt angle and glide-slope angle is developed. Subsequently, to connect the two phases and further optimize the propellant consumption throughout the entire trajectory, a method for determining the phase switching condition is proposed. The originally difficult-to-solve two-parameter optimization problem is decomposed into two more easily solvable subproblems, which are solved iteratively via a bilevel optimization framework. Finally, the divert capability of the proposed method is verified through numerical simulation. The programmed trajectory is basically consistent with the results of the pseudospectral method, with the difference in propellant consumption being only 0.006%. This method is suitable for the rapid iterative design of nominal trajectories for lunar lander powered descent in engineering applications.

关键词: lunar landing, powered descent, trajectory programming, multi-phase, divert capability

Abstract: It is important for a lunar lander to possess a large divert capability during the final landing phase, as this can enhance the tolerance for flight deviations in the early phase or improve the obstacle avoidance performance. Therefore, when designing the powered descent trajectory, sufficient final phase divert capability should be reserved at the minimum propellant cost. To this end, a multi-phase trajectory programming (MPTP) method for powered descent with approaching phase divert capability is proposed. First, the entire powered descent trajectory is divided into the main braking phase and the approaching phase. The main braking phase is responsible for dissipating the majority of the initial velocity. The approaching phase is responsible for safely and precisely flying toward the landing site. It is nominally a vertical descent trajectory and possesses equal divert capability in all horizontal directions. Then, a constant-thrust linear tangent guidance (LTG) accounting for the lunar curvature is designed for the main braking phase. For the approaching phase, a variable-thrust lossless convex programming (LCP) guidance considering the constraints of tilt angle and glide-slope angle is developed. Subsequently, to connect the two phases and further optimize the propellant consumption throughout the entire trajectory, a method for determining the phase switching condition is proposed. The originally difficult-to-solve two-parameter optimization problem is decomposed into two more easily solvable subproblems, which are solved iteratively via a bilevel optimization framework. Finally, the divert capability of the proposed method is verified through numerical simulation. The programmed trajectory is basically consistent with the results of the pseudospectral method, with the difference in propellant consumption being only 0.006%. This method is suitable for the rapid iterative design of nominal trajectories for lunar lander powered descent in engineering applications.

Key words: lunar landing, powered descent, trajectory programming, multi-phase, divert capability