Regular Papers

International Journal of Control, Automation and Systems 2015; 13(3): 718-724

Published online February 2, 2015

https://doi.org/10.1007/s12555-014-0024-5

© The International Journal of Control, Automation, and Systems

Sliding Mode Tracking Control of Mobile Robots with Approach Angle in Cartesian Coordinates

Jun Ku Lee, Yoon Ho Choi, and Jin Bae Park*

Yonsei University

Abstract

In this paper, we propose a method for designing the sliding mode based tracking control of a mobile robot in Cartesian coordinates with an approach angle and an improved reaching law. In the proposed method, to solve the singular point problem, we consider the kinematics in Cartesian coordinates instead of the kinematics in polar coordinates. We consider the bounded disturbances of the dynamics. Next, we design a new sliding surface by using an approach angle to solve the sliding surface constraint problem. Also, we propose an improved reaching law which can reduce the chattering phenomenon and the reaching time. Then, we derive the new matrix to use the sliding mode control method to the kinematics and dynamics equations. Based on the proposed control law, we can derive the control input for the given arbitrary trajectories. We prove that the position tracking error asymptotically converges to zero by using the Lyapunov stability theory. Finally, we demonstrate the effectiveness of the proposed control system through computer simulations.

Keywords Approach angle, Cartesian coordinates, disturbance, Lyapunov function, mobile robot, reaching law, sliding mode control, tracking control.

Article

Regular Papers

International Journal of Control, Automation and Systems 2015; 13(3): 718-724

Published online June 1, 2015 https://doi.org/10.1007/s12555-014-0024-5

Copyright © The International Journal of Control, Automation, and Systems.

Sliding Mode Tracking Control of Mobile Robots with Approach Angle in Cartesian Coordinates

Jun Ku Lee, Yoon Ho Choi, and Jin Bae Park*

Yonsei University

Abstract

In this paper, we propose a method for designing the sliding mode based tracking control of a mobile robot in Cartesian coordinates with an approach angle and an improved reaching law. In the proposed method, to solve the singular point problem, we consider the kinematics in Cartesian coordinates instead of the kinematics in polar coordinates. We consider the bounded disturbances of the dynamics. Next, we design a new sliding surface by using an approach angle to solve the sliding surface constraint problem. Also, we propose an improved reaching law which can reduce the chattering phenomenon and the reaching time. Then, we derive the new matrix to use the sliding mode control method to the kinematics and dynamics equations. Based on the proposed control law, we can derive the control input for the given arbitrary trajectories. We prove that the position tracking error asymptotically converges to zero by using the Lyapunov stability theory. Finally, we demonstrate the effectiveness of the proposed control system through computer simulations.

Keywords: Approach angle, Cartesian coordinates, disturbance, Lyapunov function, mobile robot, reaching law, sliding mode control, tracking control.

IJCAS
February 2025

Vol. 23, No. 2, pp. 359~682

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