Polynomial Time-to-Go Design for Impact Time Control and Cooperative Guidance

A superior baseline homing guidance law plays a crucial role in further deriving advanced laws with different impact constraints. To this end, a class of polynomial-form trajectory shaping modulation functions with admissible ranges of coefficients is proposed. Then, a specific parametric design process is developed to improve the performance of conventional pure proportional navigation (PPN) under nonlinear intercept geometries. The baseline guidance law along with its extended three-dimensional form features a closed-form solution for time-to-go, parameterized control efficiency, and optimal approximation to PPN under small heading error. Next, an impact time control guidance law with analytical capture conditions is developed by introducing a fixed-time convergence bias term. Furthermore, a three-dimensional nonsaturated cooperative guidance law with field-of-view constraints is developed on basis of the time-to-go consensus mechanism. Both physical interpretations and selection criteria for guidance parameters are thoroughly considered. The proposed methods eliminate the need for small-angle approximation, model linearization, or numerical iterations. Numerical simulations validate the effectiveness, robustness, and superiority of the advanced guidance laws.