Combined Vector Field Approach for 2D and 3D Arbitrary Twice Differentiable Curved Path Following with Constrained UAVs

Path following is an essential requirement for unmanned aerial vehicles (UAVs). Path following problems of 2-dimensional (2D) straight lines and planar circles have been studied and many approaches have been proposed during the past few years. In this paper the problem of following arbitrary twice differentiable curved paths in both 2D and 3D spaces is investigated. Based on the Helmholtz theorem, respective combined guidance vector fields for any given 2D and 3D arbitrary twice differentiable curved paths are constructed by trading off the respective conservative and solenoidal vector fields making use of the defined distance between the UAV and the desired path. Conditions for the two combined vector fields to be globally feasible are given. UAV input constraints and constant wind disturbance are assumed to be present. By tracking the constructed combined vector fields, a saturated course rate controller for 2D curved path following and a jointly saturated course rate and climb rate controller for 3D curved path following are designed. The Lyapunov stability of the saturated course rate controller for 2D curved path following is proved. Numerical simulations are given to assess the proposed approach.