  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, the
final 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 for finding the desired
optimal steering angle by a simple bisection method. Consequently, the modified
optimal control problem can be solved by the indirect shooting method. Finally,
some numerical examples are presented to demonstrate and verify the
developments of the paper.
