基于伪光谱方法的有限推力轨道转移优化设计

Optimal Design of Orbital Transfer with Finite Thrust Based on Legendre Pseudospectral Method

研究了伪光谱方法在空间飞行器有限推力轨道转移最优化问题中的应用。首先给出了空间飞行器轨道转移最优化控制问题模型,其中运动方程为三自由度模型,性能指标选为轨道转移过程中燃料消耗最小,控制变量为推力攻角。终端状态受到航迹角、高度和速度的约束。然后,应用伪光谱方法将最优控制问题离散化为非线性规划问题,即将动态优化问题转化为静态参数最优化问题。选取各配点上的状态量和控制量作为优化参数。最后应用基于Matlab语言的SNOPT软件包对参数最优化问题进行求解,该软件包对于求解大型非线性规划问题具有很好的收敛性。仿真结果表明伪光谱方法对于空间飞行器转移轨道初始参数取值不敏感,具有一定的鲁棒性,生成的轨道能够较好地满足各种约束条件。因此,伪光谱方法对于空间飞行器有限推力轨道转移问题的求解是可行的。

In this paper, the application of Legendre pseudospectral method to space vehicle orbital transfer with finite thrust optimization problem was studied. Firstly, the model of orbital transfer optimization control problem was established, while equations of motion were simplified based on some reasonable hypotheses. Performance was selected to minimize the total fuel consumption. The control variable was thrust attack angle. Terminal state variable constraints were path angle, altitude and velocity constraints. Then, the optimal control problem was transformed into nonlinear programming problem （NLP） using Legendre pseudospectral method. And dynamic optimization problem was transformed into static parameter optimization problem. The state variables and control variables were selected as optimal parameters at all collocation nodes. At last, parameter optimization problem was solved using the SNOPT software package. The SNOPT software package has high convergence to nonlinear programming problem. The simulation results demonstrate that Legendre pseudospectral method is not sensitive to orbital transfer initial conditions; they also show that the optimal solutions of orbital transfer optimization problem are fairly good in robustness. Therefore, Legendre pseudospectral method is a viable approach to the space vehicle orbital transfer with finite thrust optimization problem.