Trajectory optimization for agile-turn of vertically launched missile

This paper studies the optimization problem of agile-turn for the vertically launched missiles. The objective of this problem is to minimize the flight range. Compared with the previous studies, there are three major difficulties in solving this problem: (1) the problem is based on the six-degree-of-freedom dynamic model; (2) Due to the large angle attitude maneuvers, there exists singularity phenomenon of attitude in addition to the problem of strongly nonlinear coupling; (3) the missile adopts the integrated control system including thrust vector and tail fin controls, which causes that the nonlinear optimal control problem of the agile-turn is multiple-phased. The six-degree-of-freedom flight dynamics model of the missile is established in detail. Then the optimal control problem is solved by hp-adaptive Radau pseudospectral method. It is found that due to the disparity in the capability of attitude maneuvering, the missile uses the thrust vector control as the major mean to accomplish the agile-turn in the first flight phase. In the second flight phase, by operating the tail fins, the velocity and attitude of missile get stabilized and the terminal constraints are satisfied. The simulation results demonstrate the feasibility of agile-turn from vertical launch to attack ground targets, and the efficiency of the integrated control system.