Near-Optimal Spatial Midcourse Guidance Law with an Angular Constraint

Abstract

Dividing the guidance stages into two main phases, a midcourse phase and a terminal phase, is a common practice in long-range interceptions. The midcourse guidance task is to keep the interceptor on an optimal trajectory under various problem constraints toward a predicted interception point, whereas the terminal guidance task is to hit the target. This study develops a novel near-optimal spatial midcourse guidance to the predicted interception point under a terminal angular constraint. The angular constraint is formulated in terms of a required difference between the interceptor and the target flight directions at impact. The paper consists of two main parts: the planar case and the spatial case. The first part revisits the linear planar guidance problem with a terminal angular constraint between the velocities. Then, a nonlinear optimal control problem is solved numerically, either by minimizing the total squared acceleration or by maximizing the total terminal energy. Finally, a new closed-loop guidance law is proposed, with performances matching the optimal results for the nonlinear case. The second part extends the new guidance law to the spatial case by determining the preferred spatial maneuver plane based on energy considerations. The proposed law is demonstrated for two important special cases: the arrival with an angular constraint of 90 deg, and the arrival with the angular constraint of 0 deg (head-on arrival).