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
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.