Research ArticleTrajectory-Shaping Guidance with final speed and load factor constraints

- A guidance law meeting the impact angle, speed and load factor requirements is proposed.
- The generalized closed form solutions of Trajectory Shaping Guidance (TSG) are obtained where the speed of the vehicle can arbitrarily change with time.
- A novel approach based on spectral decomposition is proposed for solving a special type of linear time-varying system.
- The stability domain of the guidance coefficients is obtained such that the acceleration command goes to zero finally.

This paper describes the design of a guidance law used for guiding a hypersonic gliding vehicle against a ground target from a near-vertical orientation with a specified final speed and a near-zero final load factor. The guidance law consists of two terms: one is Trajectory-Shaping Guidance (TSG) used for steering the vehicle to the target from the specified orientation; the other is Final-Speed-Control Scheme (FSCS) used for controlling the vehicle to perform lateral maneuver to adjust the final speed. Further, the generalized closed form solutions of TSG are obtained from a more general linearized engagement model, where the speed of the vehicle can be an arbitrary positive function of time. By analyzing these solutions, the stability domain of the guidance coefficients is obtained such that the final load factor is zero. This domain is not affected by the change rate of the speed. Thus, according to this analysis, the proposed guidance law can achieve a near zero final load factor by properly selecting the guidance coefficients in the stability domain.