Application of Geometric Invariants in the Problem of Trajectory Tracking for UAVs

The study discusses approaches and an apply example of using geometric invariants in problems of control theory. An analytical review of modern papers in the field of trajectory tracking and path following control problems for unmanned aerial vehicles (UAVs) has been carried out. To increase the autonomy and ability to cope with uncertainties, it is proposed to use the theory of intelligent-geometric control. The problem of the trajectory tracking is considered in the framework of the pursuit-evasion differential game. Control invariants are considered in the form of ellipsoids, that can be used, for example, in pursuit-evasion problems. The task of determining the parameters of the pursuer’s motion to meet the evader on an ellipsoid is solved. The dependence of the pursuer’s speed on the parameters of the ellipse is shown. A modeling scheme is proposed aimed at joint application of optimal and intelligent control methods to solve trajectory tracking problem in difficult conditions. Simulations carried out in a disturbed environment on controlling the motion of a UAV group showed prospects of the proposed approach.