Predictor-Corrector Nonlinear Arrival-Time Control Guidance under Time-Varying Velocity

Guiding fixed-wing uncrewed aerial vehicles to a destination at a designated arrival time is a fundamental challenge, as highly nonlinear nonholonomic kinematics and maneuver-coupled velocity decay severely complicate the arrival time control. This paper proposes a predictor-corrector guidance scheme to achieve accurate arrival time control under severe speed variations. Relying on the assumption that the speed remains constant during each guidance cycle, the look angle is parameterized by a cubic polynomial. The predictor then estimates the physically flyable range capacity via forward integration that accounts for aerodynamic drag. Subsequently, the corrector iteratively enforces this constraint to update the guidance parameter. In addition, an analytical initialization for the guidance parameter is employed to improve convergence performance, making the proposed method promising for onboard implementation. Numerical simulations demonstrate that, even under extreme velocity decay, the proposed method yields near-optimal solutions, achieving a level of performance typically reserved for computationally intensive nonlinear programming methods.