嫦娥三号软着陆预测及优化模型

Prediction and Optimization Model of Chang'e 3 Soft Landing

本文是对2014年全国大学生数学建模竞赛A题的解答.本文利用动力学模型,基于变推力发动机结合螺旋搜索等算法解决了嫦娥三号软着陆预测及优化问题.在问题一中,首先建立物理学模型,解出嫦娥三号着陆准备轨道近、远月点速度大小;然后在主减速阶段,建立了主减速变推力动力学模型,对主减速阶段嫦娥三号所经过的极角θ进行求解,加以考虑月球自转带来的影响,确定着陆准备轨道近月点和远月点的位置以及嫦娥三号在近、远月点的速度方向.在问题二中,建立变推力发动机燃耗优化模型对于问题一中的主减速阶段进行优化;以安全半径与速度增量为指标建立综合评价模型,求出粗避障式安全的降落范围;精避障阶段以保证安全为前提,建立评价指标为不平坦程度与平均坡度的综合评价模型确定精确降落区域.最后根据对每个阶段建立的力学模型,进行求解.最后综合起来确定嫦娥三号的着陆轨道和在6个阶段的最优控制策略.在问题三中,建立误差模型对设计的着陆轨道和控制策略做相应的误差分析,并且利用单因素敏感性分析对主减速阶段与剩余4阶段进行自变量与因变量敏感度计算.

In this paper, the chang＇e 3 soft landing predictions and optimization problems are solved by using the dynamic model, based on the variable thrust engine with spiral search algorithm. First, physics model is established in Question 1 to work out the goddess of the moon landing to No.3 track point velocity near and far. Then, in the main reduction stage, main reduction variable thrust dynamics model is established. The polar angle of chang＇e 3 was studied, taking into consideration of the effects of rotation of the moon, landing for orbit determination in recent months, the position of the point and far point, and the goddess of the moon on the No.3 in the near and far points speed direction. In Question 2, optimization model of variable thrust engine fuel consumption is established for the problem of main reduction stage optimization. Comprehensive evaluation model for safety radius and velocity increment index is established. The coarse type of obstacle avoidance is the scope of safe landing. Pure phase of obstacle avoidance is a premise to ensure safety. Evaluation index for the uneven degree and average slope of the comprehensive evaluation model are established to determine the precise landing area. The mechanical model for each stage is established. Finally, the goddess of the moon landing orbit and the optimal control strategy in the six stages are determined. In Question 3, the error model is established for the design of landing trajectory and control strategy for the corresponding error analysis. The single factor sensitivity analysis is used for calculation of independent variable and dependent variable sensitivity in main reduction phase and residual phase 4.