3D-Nonlinear Vector Guidance and Exo-Atmospheric Interception

This paper presents a nonlinear 3D-vector guidance law. It is based on kinematic vector equations, where the commanded thrust is bounded, and the interceptor does not know the target evasive strategy. The resulting game theoretic guidance law with miss-distance as the cost, is nonlinear, aligned along the zero-effort-miss (ZEM) direction, and the time-to-go is a solution of a quartic polynomial equation in feedback form. This time-to-go is the actual one provided both players play optimal. If the evader does not play optimal, capture occurs earlier. Moreover, optimal strategies in line-of-sight (LOS) coordinates are also presented. It is found that these strategies are functions of the range, range rate, and the LOS rate. Simulations demonstrate the possibility of a miss at the first pass, but eventual capture.