Three-dimensional impact angle constrained nonlinear guidance with predefined convergence time

In this paper, we address the challenge of maximizing the effectiveness of warheads by targeting the structurally vulnerable points of the intended targets in three-dimensional engagements. We first transform the problem of achieving the target interception at the desired impact angles into the one of tracking desired line-of-sight (LOS) angles and their corresponding rates. The guidance strategies, derived considering coupled and nonlinear kinematics in three-dimensional engagements, guarantee the interception of non-maneuvering and maneuvering targets from desired impact directions within a finite time. The proposed approach allows the designer to specify the times of convergence, regardless of initial engagement geometries. Owing to the sliding mode control approach and the predefined-time stability notion, the proposed guidance methods are robust enough to compensate for the effects of target's maneuver and satisfy the response time constraints. To achieve the guidance objectives with enhanced transient and terminal performances, we construct the sliding surfaces using the LOS angles errors and their rates, with predefined times. The choices of such sliding functions allow us to derive the guidance laws that drive the error variables and their rates to the origin within assigned times. Moreover, we analyze the effect of tuning parameters on the dynamics using the Lyapunov stability theory. Such analysis allows us to obtain continuous guidance commands without necessitating any approximation of the signum function, eliminates singularity and chattering in the lateral accelerations and enables a better guidance precision and disturbance attenuation. Guidance strategies for the planar engagement are obtained as the special cases of proposed guidance schemes. Finally, we perform numerical simulations using the proposed guidance strategies for various engagement geometries and terminal conditions, where the pursuer moves at a constant speed, and the results are satisfactory.