Matematika i Matematičeskoe Modelirovanie (Jun 2016)
Automatic Generation of Complex Spatial Trajectories of the UAV and Synthesis of Control
Abstract
In this paper, we propose a new method and algorithms that allow us to design complex spatial trajectories for an unmanned aerial vehicle (UAV) passing through a given sequence of waypoints in the three-dimensional space.The nonlinear six-dimensional model of the UAV center-of-mass motion given in the trajectory frame is used for calculations. The state vector includes the altitude, the along-track deviation, the cross-track position, the velocity, the flight-path angle and the heading angle. The longitudinal and transverse overloads and the angle between the cross overload vector and vertical plane are considered as controls. This angle is often named as the roll angle.The feature of the problem is that both positions at waypoints and additional conditions are given. These conditions determine orientation of the velocity vector at each point (using the flight path angle and the heading angle). We also set either the point-visiting time or the pointvisiting velocity. The full state vector and controls are fixed at the starting waypoint.To construct a spatial trajectory, the concept of inverse dynamics problems is applied, as well as modern results of mathematical control theory of nonlinear dynamical systems. The introduction of new virtual controls allows us to represent the original system as an affine (linear in control) system. Then, the designed system is converted into the regular canonical form.When we set flight times between any two waypoints, the corresponding segments of the trajectory are designed using time-dependent polynomials of the fifth degree. These polynomials specify the altitude variation, the variation of the along-track deviation and that of the cross-track position. If the point-visiting times are not fixed, the transition to a new independent variable (the normalized mechanical energy of the system) is used. This transition is possible if the energy varies monotonically. In this case, the spatial trajectory is defined as a function of energy. The full trajectory is assembled from the separated segments which have various types of parameterization.Programmed and nonlinear stabilizing controls are calculated for the designed spatial trajectory. The efficiency of the developed algorithms is shown using computer simulations.DOI: 10.7463/mathm.0115.0778000
