UAV Trajectory Tracking Based on Local Interpolating Splines and Optimal Choice of Knots

We consider trajectory-tracking problem for an unmanned aerial vehicle (UAV) based on optimal choice of knots of the interpolating spline. As examples, we use typical second-order curves: ellipses, parabolas, hyperbolas, obtained by cutting a cone with planes. The rules are proposed for rational placement of a given number of knots for curves given in parametric form. The use of spline interpolation methods opens the way to developing mathematical tools for tracking complex trajectories, storing geometrical information in a compact form and reproducing trajectories with a predetermined accuracy on a general basis. The research is focused on parametric cubic Hermite spline and Bezier curves, which are characterized by simplicity of computational implementation. We have conducted experimental studies to search for the optimal allocation of knots. The problem of moving along the route represented by a parabola has been investigated under wind loads taking into account the mathematical model of the aerial vehicle. We consider an approach to dynamic motion planning based on strategies and rules that imitate actions of a pilot when rapid actions are needed.