Solving the Problem of Optimal Control for a Gliding Projectile Motion Using a Genetic Algorithm

Abstract

Increasing the projectile flight range is a critical objective for rocket and artillery systems. The aim of this work is to develop optimal control methods for the motion of a gliding projectile to increase its flight range. The paper proposes a mathematical model for the gliding flight of a controlled rocket-assisted projectile. The model accounts for the relations of aerodynamic forces and moments to geometric parameters of the wings, stabilizers, and control fins. The considered scenario involves the ignition of a boost engine during the trajectory, in addition to the initial launch motor. The wings, which provide the projectile's gliding capability, are extendable and deploy at the optimal point of the trajectory. The projectile's motion is controlled by generating an attack angle through the deflection of the control fins. Transient processes are not considered; it is assumed that control surface deflection instantaneously results in changes in the attack and sideslipangles (the case of ideal control). A fourth-order Runge-Kutta method was implemented to integrate the system of differential equations describing the gliding projectile motion. To construct the optimal control function for the projectile motion, a genetic algorithm with real-valued encoding was implemented. The continuity and smoothness of the attack angle relation to time is achieved by a special solution-splicing algorithm during crossover and approximation by a third-degree polynomial. Three methods for increasing the firing range of a gliding projectile were considered: by setting a constant flight path angle during the controlled phase;by selecting a constant attack angle;by variable attack angle, which time-relation function was determined by the genetic algorithm. Optimal parameters for each motion control method were determined, as well as the optimal angle-of-attack function for the third method, ensuring the maximum gliding flight range. The mathematical models and software developed during this research enable the calculation of the flight trajectory for a controlled rocket-assisted projectile and allow for solving the problem of optimal motion control for a gliding projectile with the goal of increasing its flight range.