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This article presents an innovative method for planning and tracking the trajectory in the image plane for the visual control of a quadrotor. The community of researchers working on 2D control widely recognizes this challenge as complex, because a trajectory defined in image space can lead to unpredictable movements of the robot in Cartesian space. While researchers have addressed this problem for mobile robots, quadrotors continue to face significant challenges. To tackle this issue, the adopted approach involves considering the separation of altitude control from the other variables, thus reducing the workspace. Furthermore, the movements of the quadrotor (pitch, roll, and yaw) are interdependent. Consequently, the connection between the inputs and outputs cannot be reversed. The task complexity becomes significant. To address this issue, we propose the following scenario: When the quadrotor is equipped with a downward-facing camera, flying at high altitude is sensible to spot a target. However, to minimize disturbances and conserve energy, the quadrotor needs to descend in altitude. This can result in the target being lost. The solution to this problem is a new methodology based on the principle of differential flatness, allowing the separation of altitude control from the other variables. The system first detects the target at high altitude, then plots a trajectory in the image coordinate system between the acquired image and the desired image. It is crucial to emphasize that this step is performed offline, ensuring that the image processing time does not affect the control frequency. Through the proposed trajectory planning, complying with the constraints of differential flatness, the quadrotor can follow the imposed dynamics. To ensure the tracking of the target while following the generated trajectory, the proposed control law takes the form of an Image Based Visual Servoing (IBVS) scheme. We validated this method using the RVCTOOLS environment in MATLAB. The DJI Phantom 1 quadrotor served as a testbed to evaluate, under real conditions, the effectiveness of the proposed control law. We specifically designed an electronic card to transfer calculated commands to the DJI Phantom 1 control joystick via Bluetooth. This card integrates a PIC18F2520 microcontroller, a DAC8564 digital-to-analogue converter, and an RN42 Bluetooth module. The experimental results demonstrate the effectiveness of this method, ensuring the precise tracking of the target as well as the accurate tracking of the path generated in the image coordinate system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work proposes guaranteed trajectory tracking control for a quadrotor based on feedforward flatness control and an interval observer. Since the quadrotor is subject to bounded uncertainties (parameters, disturbances and noise), the state of this latter cannot be measured properly. Therefore, based on the information of the upper and lower limits of the initial condition, the uncertain parameters, the disturbance and the measurement noise, an interval observer that generates an envelope enclosing every feasible state trajectory is developed. After that, based on the centre of the obtained interval observer, flatness feedforward control, combined with estimated feedback control, is proposed to improve the tracking performance of the quadrotor subject to bounded uncertainties. The closed-loop stability of the system is proven analytical using the Lyapunov theorem. The numerical simulation is done in order to evaluate the proposed tracking control scheme and the interval observer design. [ABSTRACT FROM AUTHOR]

Byline: Hassen Mekki, Mohamed Chtourou, Nabil Derbel Feedback linearisation is an approach applied to non-linear control design and has attracted a great deal of research interest in recent years. The common assumptions are that the full state is measurable, and that the system is exactly linearly parameterised and feedback linearisable (input/state or input/output). With few exceptions, the robustness issue is not addressed. In practical implementation of exactly linearising control laws, the chief drawback is that they are based on exact cancellation of non-linear terms. If there is any uncertainty in the knowledge of the non-linear functions, the cancellation is not exact and the resulting inputoutput equation is not linear. The aim of this paper discusses the use of Neural Network (NN)-based adaptive control to get asymptotically exact cancellation.