In this paper we consider a trajectory planning problem arising from a lunar vertical landing with minimum fuel consumption.The vertical landing requirement is written as a final steering angle constraint,and a nonneg...In this paper we consider a trajectory planning problem arising from a lunar vertical landing with minimum fuel consumption.The vertical landing requirement is written as a final steering angle constraint,and a nonnegative regularization term is proposed to modify the cost functional.In this way,thefinal steering angle constraint will be inherently satisfied according to Pontryagin's Minimum Principle.As a result,the modified optimal steering angle has to be determined by solving a transcendental equation.To this end,a transforming procedure is employed,which allows forfinding the desired optimal steering angle by a simple bisection method.Consequently,the vertical landing trajectory can be found offline by the indirect shooting method.Finally,some numerical examples are presented to demonstrate and verify the developments of the paper.展开更多
借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软...借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软着陆轨迹。仿真结果表明,初值猜测技术得出的伴随变量初值均落在线性摄动法的收敛区间内,收敛速度快,优化精度高。最后研究了不同制动推力大小对软着陆性能的影响,结论为:增大制动发动机推力,既可缩短软着陆的时间,又能减少软着陆的燃料消耗。展开更多
基金supported by the National Natural Science Foundation of China under grant Nos.61903331 and 62088101.
文摘In this paper we consider a trajectory planning problem arising from a lunar vertical landing with minimum fuel consumption.The vertical landing requirement is written as a final steering angle constraint,and a nonnegative regularization term is proposed to modify the cost functional.In this way,thefinal steering angle constraint will be inherently satisfied according to Pontryagin's Minimum Principle.As a result,the modified optimal steering angle has to be determined by solving a transcendental equation.To this end,a transforming procedure is employed,which allows forfinding the desired optimal steering angle by a simple bisection method.Consequently,the vertical landing trajectory can be found offline by the indirect shooting method.Finally,some numerical examples are presented to demonstrate and verify the developments of the paper.
文摘借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软着陆轨迹。仿真结果表明,初值猜测技术得出的伴随变量初值均落在线性摄动法的收敛区间内,收敛速度快,优化精度高。最后研究了不同制动推力大小对软着陆性能的影响,结论为:增大制动发动机推力,既可缩短软着陆的时间,又能减少软着陆的燃料消耗。
