An Innovative Collision-Free Image-Based Visual Servoing Method for Mobile Robot Navigation Based on the Path Planning in the Image Plan

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.