Three-Dimensional Generalized Nominal Effort Miss Guidance Law in Endo-Atmosphere Boost Phase

This paper presents an analytical guidance law for the boost phase within the atmosphere, specifically tailored for multistage boosters. Initially, an analytical solution for the trajectory increment corresponding to a non-zero sideslip angle is derived, and a sideslip angle curve that satisfies terminal velocity and terminal heading angle constraints is designed. By leveraging the analytical solution of the trajectory, the dynamic constraints of the boost phase are transformed into constraint functions of the sideslip angle values at interpolation nodes, discretizing the sideslip angle curve optimization problem into a nonlinear programming problem. The optimal solution is obtained through sequential quadratic programming. In each guidance cycle, the nominal effort miss under the sideslip angle curve is analytically predicted based on the current state, and a correction to the guidance command in analytical form is derived using linear-quadratic optimal control, achieving closed-loop correction of terminal errors. Simulation results demonstrate that the proposed guidance method not only has a low computational demand but also offers high guidance accuracy and a wide range of applicability.