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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]

This paper proposes a robust tracking control method for wheeled mobile robot (WMR) against uncertainties, including wind disturbances and slipping. Through the application of the differential flatness methodology, the under-actuated WMR model is transformed into a linear canonical form, simplifying the design of a stabilizing feedback controller. To handle uncertainties from wheel slip and wind disturbances, the proposed feedback controller uses sliding mode control (SMC). However, increased uncertainties lead to chattering in the SMC approach due to higher control inputs. To mitigate this, a boundary layer around the switching surface is introduced, implementing a continuous control law to reduce chattering. Although increasing the boundary layer thickness reduces chattering, it may compromise the robustness achieved by SMC. To address this challenge, an active disturbance rejection control (ADRC) is integrated with boundary layer sliding mode control. ADRC estimates lumped uncertainties via an extended state observer and eliminates them within the feedback loop. This combined feedback control method aims to achieve practical control and robust tracking performance. Stability properties of the closed-loop system are established using the Lyapunov theory. Finally, simulations and experimental results are conducted to compare and evaluate the efficiency of the proposed robust tracking controller against other existing control methods. [ABSTRACT FROM AUTHOR]

In this article, we present an innovative approach to 2D visual servoing (IBVS), aiming to guide an object to its destination while avoiding collisions with obstacles and keeping the target within the camera's field of view. A single monocular sensor's sole visual data serves as the basis for our method. The fundamental idea is to manage and control the dynamics associated with any trajectory generated in the image plane. We show that the differential flatness of the system's dynamics can be used to limit arbitrary paths based on the number of points on the object that need to be reached in the image plane. This creates a link between the current configuration and the desired configuration. The number of required points depends on the number of control inputs of the robot used and determines the dimension of the flat output of the system. For a two-wheeled mobile robot, for instance, the coordinates of a single point on the object in the image plane are sufficient, whereas, for a quadcopter with four rotating motors, the trajectory needs to be defined by the coordinates of two points in the image plane. By guaranteeing precise tracking of the chosen trajectory in the image plane, we ensure that problems of collision with obstacles and leaving the camera's field of view are avoided. Our approach is based on the principle of the inverse problem, meaning that when any point on the object is selected in the image plane, it will not be occluded by obstacles or leave the camera's field of view during movement. It is true that proposing any trajectory in the image plane can lead to non-intuitive movements (back and forth) in the Cartesian plane. In the case of backward motion, the robot may collide with obstacles as it navigates without direct vision. Therefore, it is essential to perform optimal trajectory planning that avoids backward movements. To assess the effectiveness of our method, our study focuses exclusively on the challenge of implementing the generated trajectory in the image plane within the specific context of a two-wheeled mobile robot. We use numerical simulations to illustrate the performance of the control strategy we have developed. [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 paper deals with 3D visual servoing applied to mobile robots in the presence of measurement disturbances, caused in particular by target occlusion. We propose a new approach based on the flatness concept. In 3D visual servoing, the task is performed out of image coordinate space and targets may leave the camera field of view during navigation (servoing). Forced to navigate blindly during one or more periods of time, the robot will use our new open-loop control algorithm inspired by the flatness concept. The 3D visual servoing method is performed using robot pose estimation. This estimation generally contains some errors. The exact position of the robot is therefore not guaranteed, and robust feedback control is necessary to reject these errors in the input. To solve this problem, we propose a new pose estimation method that uses neural networks. We reduce the complexity of the architecture of the neural networks used (the number of variables to estimate) by proving that the location and the orientation of the robot can be ensured by using a single point in the image coordinate space for mobile robots with two degrees of freedom. To show the efficiency of the proposed algorithm, we use the RVCTOOLS MATLAB toolbox. [ABSTRACT FROM AUTHOR]