Vector field following for quadrotors using differential flatness

Abstract

This paper proposes a differential flatness-based method for maneuvering a quadrotor so that its position follows a specified velocity vector field. Existing planning and control algorithms often give a 2D or 3D velocity vector field to be followed by a robot. However, quadrotors have complex nonlinear dynamics that make vector field following difficult, especially in aggressive maneuvering regimes. This paper exploits the differential flatness property of a quadrotor's dynamics to control its position along a given vector field. Differential flatness allows for the analytical derivation of control inputs in order to control the 12D dynamical state of the quadrotor such that the 2D or 3D position of the quadrotor follows the flow specified by a given vector field. The method is derived mathematically, and demonstrated in numerical simulations and in experiments with a quadrotor robot for three different vector fields.