Proportional navigation versus high-g barrel roll maneuvers from optimal control of view

Abstract

Our preceding studies showed that the high-g barrel roll maneuver generally produces very large miss distance against proportional navigation missiles. The performance of this maneuver is discussed from optimal control of view. Numerically obtained three-dimensional optimal evasive maneuvers of a fighter agaist a proportinal navigation missile were those of vertical-S type and horizontal-S typc,which are two-dimensional in their nature. It is shown that the high-g barrel roll is regarded as a kind of approximation of these optimal maneuvers, however, it is easier to be implemented than the latter, and we may still insist on its practical effectiveness. Introduction Many studies have been performed on the optimal evasive maneuver of an aircraft agaist a proportional navigation guidance (PNG) missile. In order to obtain the optimal aircraft maneuver, a high-dimensional, nonlinear, two-point boundary value problem must be solved. Because of the difficulty inherent to this problem, most of the earlier works use very simple aircraft and missile models, and only a few deal with the threedimensional problems. The results of the earlier two-dimensional studies showed that optimal evasive maneuvers become a split-S type or a vertical-S type.' As these maneuvers arc two-dimensional in their nature, the previous results are valid and may be proved to be optimum in the neighboring extremal sense. The high-g barrel roll (HGB) maneuver,' which is well-known to pilots, however, cannot be analyzed by a two-dimensional sudy because of its essentially three-dimensional naturc.' As the maneuver surely produces very large miss distance, we are interested in the maneuver from the point of view of its optimality. Unfortunately, by the lack of our optimizing algorithm ability, we could not have obtained three-dimensional optimal maneuvers, but the recent improvement of our algorithm has made it possible. In this paper, the mathematical model for threedimensional pursuit-evasion problem of the aircraft against PNG missile is shown first. Next, some features of the aircraft optimal evasive maneuvers, and HGB are explained. Finally, the exact numerical solution for the three-dimensional pursuit-evasion problem is illustrated and the nonoptimality of the HGB is shown. The relation between the optimal maneuver and the HGB is also discussed. American Institute of Aeronautics and Astronautics 1 Copyright © 1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Mathematical model Figure 1 shows symbols of a missile and an aircraft. Point-mass models are used, and constant mass and velocity are assumed for both vehicles.