Feedback Equivalence Between Curve & Straight Line Tracking for Unmanned Aerial Vehicles

We present a feedback equivalence transformation for the Dubins airplane model, which maps a monotone reference curve in space, to a straight line. This enables one to reduce path following and trajectory tracking for UAVs to the following and tracking of a straight line. We show that under this equivalence map, the system's equations remain invariant. Thus, in the new transformed space, one can use existing controllers, simplify them for straight lines, and apply them for tracking. We analyse the requirements of the reference curves which allow bijectivity and showcase simulation results using existing controllers.