Indirect method for solving the reentry trajectory with maximum cross range

The indirect method cannot obtain the solution of global trajectory optimization, since the difficulty of evaluating initial values of conjugate variables which are highly sensitive. To overcome that disadvantage, a hybrid genetic algorithm is introduced in this paper to search initial value of conjugate variables and the equations are solved to obtain the reentry trajectory with maximum cross range. In the optimization process, the constraints of equations, such as heating rate, dynamic pressure and overload, could be handled as penalty functions which could convert the feasible solution to unconstrained problem by penalty conversion. Numerical simulations confirm the applicability of the presented algorithm and some typical spacecraft gliding trajectories are optimized.