Nonlinear three-dimensional constrained guidance law: An analytical higher-order shaping approach

This paper presents a novel analytical framework for three-dimensional (3-D) guidance that simultaneously satisfies constraints on impact time, seeker's field-of-view (FOV), and overload throughout the entire engagement. The proposed Heading Error Shaping-based Variable-Gain Proportional Navigation (HES-VPN) law shapes the heading error profile as an nth order generalized polynomial in the relative range, enabling the derivation of a closed-form guidance solution through explicit coefficient solving. A core contribution of this work is the establishment of a priori feasibility for the guidance mission through the analytical derivation of a shaping parameter safe set. This framework precisely delineates the achievable impact time interval, ensuring strict compliance with FOV and acceleration limits while predetermining feasible mission constraints. The resulting deterministic trajectory commands direct the missile toward the target with zero terminal acceleration and guaranteed stability. Extensive numerical simulations and Monte Carlo tests validate the effectiveness and evaluate the robustness of the HES-VPN law under various engagement scenarios.