Maneuvering Trajectory Planning During the Whole Phase Based on Piecewise Radau Pseudospectral Method

As the whole trajectory planning of ballistic missile are difficult in the following aspects: changed widely in flight area. different phase linked complicated, control variables coupled largely, different phases have different objective function. In this paper, a method of maneuvering trajectory planning based on piecewise Radau pseudo spectral method (RPM) is proposed to solve the problem of full trajectory optimization. Firstly, the dynamic model of maneuvering trajectory in different phase are built. as well as the constraints. Then, to satisfy the demand of penetration, several maneuvering strategies are designed, including changing the launch plane in boost phase, large-scale maneuvering during the mid-course trajectory and maneuvering against interception during the terminal phase. To evaluate the effect of the maneuverings in different trajectory phases, the optimal control problem is established based on pseudo-spectral method. After that, the full trajectory are got through connecting conditions, and the corresponding objective function is obtained by weighting average of several different objective functions, thus realizing the whose maneuvering trajectory programming. Lastly, choosing Minuteman III missile for trajectory optimization simulation, the results show that the ability of trajectory maneuvering in different phase can be made full use of by the whole phase trajectory maneuvering optimization method, and the full trajectory optimization results are better than the trajectory maneuverings in mid course phase only.