Unicycle Robot’s Navigation Control with Obstacle Avoidance and Asymptotic Stability

Abstract

This study builds upon the groundbreaking research of Asymptotic stability of unicycle-like robots with the Bessel’s controller continuing the exploration of asymptotic stability for non-holonomic robots through kinematic modeling that allows for obstacle avoidance. utilizing the previously derived Bessel's controller, the study defines an avoidance region containing obstacles, presenting an algorithm that relies solely on the distance to the obstacle. This novel algorithm introduces a new set of Ordinary Differential Equations (ODEs) to recalibrate the controller. A MATLAB/Simulink example demonstrates the exact algorithm using Bessel's functions and an approximate solution, emphasizing a more tractable hardware implementation. The paper contributes a significant advancement in the field, combining asymptotic stability, obstacle avoidance, and efficient hardware implementation. In conclusion, this study introduces and validates a pioneering navigation algorithm tailored for unicycle-like robots, ensuring asymptotic stability even in the presence of obstacles. Building upon the earlier research framework utilizing Bessel's controllers, the paper highlights instances of asymptotic stability and convergence near the origin, addressing a notable gap in the existing literature regarding path planning and navigation algorithms for obstacle avoidance with asymptotic stability. The research trajectory initiated by previous paper proves instrumental in advancing the understanding and practical implementation of stable navigation algorithms for robotic systems, particularly in scenarios involving obstacles. This study not only extends the achievements of the previous work but also provides valuable insights and recommendations for future research directions in the pursuit of robust and efficient robotic navigation.