Guidance Laws to Control Impact Angle and Time for Missiles with Field-of-View Constraint

Abstract

Homing guidance aims at guiding a missile to its intended target using information acquired from an on-board seeker. In real applications of homing guidance laws, a field-of-view restriction of the missile seeker is a significant issue because maintaining the seeker lock-on condition is an important task for acquiring the target information. Especially, when implementing advanced guidance laws to impose terminal constraints on impact angle and time, considering the field-of-view constraint is particularly essential since the curved trajectory may let the seeker's look angle exceed the confined field-of-view limit.<br/> <br/> This dissertation presents guidance laws whose contributions are classified into three parts: i) impact angle control guidance law with the field-of-view constraint, ii) impact time control guidance law with the field-of-view constraint, and $iii)$ impact angle and time control guidance law with the field-of-view constraint.<br/> <br/> First, an impact angle control guidance law that confines the missile look angle during homing in order not to exceed a seeker's field-of-view limit is proposed. A sliding surface variable whose regulation guarantees the interception of a stationary target at the desired impact angle is designed, and the guidance law is derived to make the surface variable go to the sliding mode. Using a magnitude-limited sigmoid function in the surface variable, the proposed law prohibits the look angle from exceeding the specified limit during the entire homing. This capability to confine the missile look angle is valuable when a seeker's field-of-view is restricted, since imposing the terminal impact angle constraint demands the missile to fly a curved trajectory. Furthermore, the proposed law only needs the line-of-sight angle and look angle among the target information. Thus, the proposed law can easily be implemented into a homing missile equipped with a structurally simple passive strapdown seeker. Theoretical analysis in this part indicates that the proposed law accomplishes the impact angle constraint without violating the look angle limit although it only uses the information of bearing angles.<br/> <br/> Second, a guidance law that achieves the desired impact time without violating the seeker's field-of-view limit is presented. For the development of the law, kinematic conditions for impact time control are defined, and the backstepping control-based approach is adopted for the satisfaction of the conditions. The missile look angle is utilized as a virtual control input for the backstepping structure, and its magnitude is limited by a prescribed limit by restricting the controller gain. Consequently, the impact time constraint can be achieved with satisfying the look angle limit under the proposed law. Since few papers considering the field-of-view limit under the impact time control are available in open literature, the capability to confine the seeker's look angle with achieving the desired impact time is the main contribution of this part.<br/> <br/> Finally, a guidance law for impact angle and time control with taking into account the field-of-view constraint is developed. Basically, the law in this part is formed as a look angle-limited impact angle control guidance law that has an additional guidance gain. Since the length of the trajectory under this law is calculated as a function of this gain, the terminal impact time can be controlled by adjusting the gain. As a result, the proposed guidance law in this part can intercept the stationary target at the desired impact angle and time with satisfying the field-of-view limit. The proposed law is expected to achieve the accurate performance in real applications owing to its closed-loop structure without using any numerical routine such as off-line optimization or the shooting method.<br/> <br/> To evaluate the performance of the proposed laws, numerical simulations are conducted for each part. The results demonstrate that the proposed laws accomplish the desired terminal tasks with preventing the look angle from exceeding the prescribed limit.