A multi-scroll chaotic system for a higher coverage path planning of a mobile robot using flatness controller

In this paper, we present a study of higher-coverage path planning desired for mobile robots for some special tasks using a flatness controller based on the dynamic features of a multi-scroll chaotic system. The trajectory construction is envisaged for field exploration missions or for the specific purpose of research where fast scanning of a complete workplace of the robot is required. For these types of applications or missions, researchers have opted for using a chaotic trajectory. The chaotic systems that are often used are: the Lorenz system, the Standard-map system, the Arnold system, etc. The problem for this type of chaotic systems is the density of these orbits that appear in the robot trajectory, which begets a loss of energy and time. For that, we propose a multi-scroll chaotic system to avoid the redundancy of orbits. At the boundary conditions, in order not to leave the workspace, a mirror mapping method is utilized, which constrains all the mobile robot positions in the workspace and which can reflect all the overflow waypoints returning to it. The major problem of this type of chaotic trajectory is how to determine the control law which makes it possible to guarantee the system commendability. However, a flatness controller, which shows great advantages providing an integrated structure for planning and control, is utilized to ensure the commendability of the chaotic robot. Compared to simply using the double-scroll chaotic systems in the whole workspace, the suggested new multi-scroll chaotic system, combined with the mirror mapping method, shows good results that can achieve a higher coverage for a larger workplace of the mobile robot.