Lyapunov Vector Fields for Autonomous UAV Flight Control

General techniques for constructing vector fields for UAV guidance are provided that incorporate Lyapunov stability properties to produce simple, globally stable vector fields in 3D. Use of these fields in circular loiter patterns is illustrated, along with simple switching algorithms for circular loiter vector fields to enable following of arbitrary way point paths or loops. Another variation is also developed, where a simple circular loiter is warped into other shapes, preserving global stability guarantees and accurate path tracking. An example of this technique is provided that produces a “racetrack ” loiter pattern, and three different variations in the warping technique are compared. Finally, tracking of the vector field is considered, using Lyapunov techniques to show global stability of heading and path position for several types of tracking control laws that are compatible with low cost UAV avionics. Nomenclature r = UAV position vector relative to an inertial reference frame ()z,y,x = Inertial frame coordinates of r ()ooo zyx,, = Loiter circle center