To address the difficulty of simultaneously ensuring impact-time control accuracy and flight-trajectory feasibility in three-dimensional multi-vehicle cooperative engagement against a fixed target, where impact-time constraints, seeker field-of-view (FOV) constraints, time-varying velocity, and geometric coupling are involved, this paper proposes a three-dimensional analytical impact-time-control guidance law. The proposed method uses the standard engagement plane as a dynamic geometric reference and constructs a trajectory convergence channel to constrain the longitudinal evolution of the velocity direction. A three-dimensional equivalent time-control channel is then extracted, and a velocity decay model with aerodynamic drag is incorporated to analytically determine the reachable impact-time interval under the FOV constraint. The two channels are further mapped into closed-form three-dimensional acceleration commands through analytical control allocation. The convergence analysis shows that, within the operating domain where the control allocation matrix is uniformly nonsingular, the proposed method guarantees asymptotic alignment of the velocity direction with the standard engagement plane, continuous satisfaction of the FOV constraint, accurate convergence of the actual impact time to the desired impact time, and bounded control commands. Simulation results demonstrate that, under nominal conditions, the proposed method achieves satisfactory impact-time control accuracy while satisfying the FOV constraint. In Monte Carlo simulations with combined deviations of the initial states, aerodynamic parameters, and target position, the proposed method still maintains satisfactory impact-time control accuracy and homing accuracy, while the FOV and positive-altitude constraints are satisfied throughout the engagement, demonstrating considerable robustness.
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