Joint Design of Guidance and Control System for a Hypersonic Gliding Vehicle on Lie Groups

A new design architecture of guidance and control system for a hypersonic gliding vehicle is proposed on Lie groups. A novel translational model, including the coupling between the longitudinal and lateral motion of a hypersonic gliding vehicle, which satisfies the given terminal angular constraint, is established on SO(3) by combining the rotation transformations among the current line-of-sight (LOS) coordinate frame, the required LOS coordinate frame and the East-North-Up (ENU) coordinate frame and the rate of the angular velocity of the current LOS frame. Similarly, a rotational model, which contains the coupling existing in the pitching, yawing and rolling channels, is obtained on SO(3) by comprising the rotation transformations among the current body-fixed frame, the required body-fixed frame and the ballistic coordinate frame and the rate of the angular velocity of the current body-fixed frame. Then the two systems are stabilized using the proportional derivative (PD) control approach designed on SO(3), respectively. The numerical simulations conducted for the vehicle demonstrate the practicability and robustness of the proposed method.