Quadrotor UAV Dynamic Visual Servoing Based on Differential Flatness Theory

Abstract

In this paper, we propose 2D dynamic visual servoing (Dynamic IBVS), where a quadrotor UAV tries to track a moving target using a single facing-down perspective camera. As an application, we propose the tracking of a car-type vehicle. In this case, data related to the altitude and the lateral angles have no importance for the visual system. Indeed, to perform the tracking, we only need to know the longitudinal displacements (along the x and y axes) and the orientation along the z-axis. However, those data are necessary for the quadrotor’s guidance problem. Thanks to the concept of differential flatness, we demonstrate that if we manage to extract the displacements according to the three axes and the orientation according to the yaw angle (the vertical axis) of the quadrotor, we can control all the other variables of the system. For this, we consider a camera equipped with a vertical stabilizer that keeps it in a vertical position during its movement (a gimbaled camera). Other specialized sensors measure information regarding altitude and lateral angles. In the case of classic 2D visual servoing, the elaboration of the kinematic torsor of the quadrotor in no way guarantees the physical realization of instructions, given that the quadrotor is an under-actuated system. Indeed, the setpoint has a dimension equal to six, while the quadrotor is controlled only by four inputs. In addition, the dynamics of a quadrotor are generally very fast, which requires a high-frequency control law. Furthermore, the complexity of the image processing stage can cause delays in motion control, which can lead to target loss. A new dynamic 2D visual servoing method (Dynamic IBVS) is proposed. This method makes it possible to generate in real time the necessary movements for the quadrotor in order to carry out the tracking of the target (vehicle) using a single point of this target as visual information. This point can represent the center of gravity of the target or any other part of it. A control by flatness has been proposed, which guarantees the controllability of the system and ensures the asymptotic convergence of the generated trajectory in the image plane. Numerical simulations are presented to show the effectiveness of the proposed control strategy.