基于间接法的最优小推力逃逸轨道设计

Indirect Optimization of Low Thrust Escape Trajectories

目前,小推力逃逸轨道优化的大部分研究限于平面内逃逸或对发动机模型做无约束简化处理。通过在性能指标中引入一个待定参数,采用间接法将系统两点边值问题的待定参数约束在多维单位球里;同时结合同伦思想和曲线拟合技术,由短时间无约束平面内燃料最优逃逸问题开始,逐步求解长时间有约束平面外燃料最优逃逸问题。数值仿真结果表明该方法收敛性好,能求解复杂逃逸问题,是一种高效的逃逸轨道设计方法。

At present, most of the research on low thrust escape trajectory optimization were limited to planar escape or unconstrained engine model. Using the indirect method, the unknown parameters of the two-point-boundary-value-problem were bounded in a hyper unit sphere by multiplying a positive unknown parameter to the fuel optimal performance index. Firstly, the two-dimensional short-time fuel-optimal escape trajectory without control constraint was solved by the homotopy method and curve fits technology. Finally, the three-dimensional long-time fuel-optimal escape trajectory with control constraint was solved. This method is validated to be high-accuracy, good-convergence and efficient for low thrust escape trajectory optimization.