Non-singular terminal sliding mode cooperative guidance law under impact angle constraint

This paper addresses the challenge of engaging maneuvering targets in 3-D space when multiple missiles are launched simultaneously. To overcome this problem, a cooperative guidance law with a fixed time constraint is developed. The objective is to enable multiple missiles to attack targets simultaneously while adhering to impact angle limitations. Initially, a relative kinematics model is established for the interaction between multiple missiles and the target. This model establishes the relationship between the terminal line-of-sight (LOS) angle and the impact angle in 3-D space. Subsequently, guidance laws are devised for the longitudinal and normal directions of the LOS coordinate system. For the LOS direction, the guidance law is designed based on the finite time consensus theory of multi-agent systems. This design ensures that multiple missiles reach the target simultaneously at a predetermined time. To account for the target's acceleration, which is considered an unknown disturbance, a fixed time disturbance observer is incorporated into the system to handle it. In the normal direction of the LOS, a fixed time sliding mode cooperative guidance law is formulated using nonsingular terminal sliding mode technology. This law guarantees the fulfillment of terminal LOS angle requirements. Furthermore, the paper provides theoretical proof of fixed time consensus. Finally, to assess the effectiveness of the proposed method, simulations are conducted under various scenarios, demonstrating its capability to guide multiple missiles in attacking a moving target at a fixed time.