Properties of reentry dynamics and their application in trajectory optimization

The reentry trajectory optimization problem with terminal constraints and path constraints of a lunar return vehicle is considered in this paper. By defining the performance index functional as a square sum of the reentry terminal position errors, the reentry trajectory design problem is transformed into the optimization problem with the terminal constraints and state equation constraints. Firstly, only considering the state equation constraints, the necessary conditions are obtained of the optimization problem using the maximum principle, and the optimal control is solved using the conjugate gradient method. Then, for the problem of path constraints, it is studied that the relationship between the overload and the distance of the orbit phase and the flight path angle and the bank angle. On the basis, a method of initial bank angle value adjustment is presented to satisfy the path constraints. This algorithm circumvents the problem of parameter adjustment in the punishment function method, with definite physical meaning and simple implementation. Finally, a numerical example for Apollo reentry trajectory optimization is given to illustrate the effectiveness of the algorithm.