Look-angle-shaped impact time control guidance with field-of-view constraints

This paper addresses the impact time control guidance problem against stationary targets, explicitly accounting for field-of-view (FOV) constraints and nonlinear kinematics. Leveraging key geometric properties, we design a guidance law that shapes the look angle using a hyperbolic tangent function of the range. This approach ensures that the look angle intrinsically satisfies the FOV constraint. Consequently, the guidance problem is reduced to a univariate equation with respect to the guidance gain. While solving this equation typically yields two solutions associated with different control efforts, we utilize a geometric property of the look angle to constrain the guidance gain, thereby selecting the solution with lower control effort. Based on this property, theoretical analysis demonstrates the monotonicity of the univariate equation, establishing the existence and uniqueness of the solution. Furthermore, we derive an analytical, conservative lower bound for the impact time in series form, which explicitly incorporates the initial look angle and the FOV constraint. An approximate upper bound on the impact time is also derived by explicitly considering the acceleration constraint. An analytical initialization scheme is developed to enhance convergence when solving the resulting equation. As a result, the guidance law can be solve very efficiently. On this basis, an analytical compensation scheme is further developed to enhance the robustness of the guidance law against speed variations. The effectiveness of the method is validated through comprehensive numerical simulations.