This paper investigates the trajectory optimization problem of hypersonic vehicles in the dive phase with both angle of attack and bank angle as control inputs and multiple practical constraints on impact velocity and angle as well as path constraints are all considered. To efficiently and reliably solve such a highly nonlinear problem, a new set of control inputs is defined and a relaxation method for the new controls is proposed. A regularization is employed to guarantee the exactness of the relaxation. Then, a series of convexification methods is used to transform the original nonlinear problem into a convex optimization problem. The simulation results show the effectiveness and performance of the proposed method, with average solution time under 3.0 s and terminal precision achieving less than 0.2 km in position and 4 m/s in velocity.
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