Trajectory shaping guidance law based on virtual angle with terminal constraints

A trajectory shaping guidance law based on virtual angle (TSGLBVA) is proposed for a re-entry vehicle with the constraints of terminal impact angles and their time derivatives. In the view of differential properties of the maneuvering trajectory, a virtual angle and a virtual radius are defined. Also, the shaping trajectory of the vehicle is established by the polynomials of the virtual angle. Then, four optimized parameters are selected according to the theorem of parameters transformation presented in this paper. Finally, a convergent variant of the Nelder-Mead algorithm is adopted to obtain the reference trajectory, and a trajectory feedback tracking guidance law is designed. The simulation results demonstrate that the TSGLBVA ensures the re-entry vehicle to impact a target precisely from a specified direction with small terminal load factor command, as well as to obtain a maximum or constrained terminal velocity according to various requirements.