• Drilon Bunjaku
  • Jovan Stankovski
  • Mile Stankovski


In this paper, we present the dynamic modelling of two differential wheeled mobile robot, and also propose an easily implementable control strategy, for stabilizing the nonlinear and nonholonomic WMR system around the desired final posture. The asymptotic stability is approached by using two PI controllers. The dynamic model of WMR is used in the simulation environment of Matlab/Simulink, for testing the proposed stabilizing control strategy. The validity of control strategy is verified by the simulation results.

Key words: wheeled mobile robot; dynamic modelling; nonholonomic robots; stabilization control; linear controller

[1] G. M. Dimirovski: “Vuk and Georgi: An Adventure into Active Systems via Mechatronics, Robotics and Manufacturing Engineering” (Plenary Lecture). In: SISY2013. Proceedings of the IEEE 11 th International Conference on Intelligent Systems and Informatics – Remembering Miomir K. Vukobratović, (I. J. Rudas, B. Borovać, J. Fodor, General Chairs; I. Stajner-Papuga, technical Program Chair). The IEEE and Obuda University, Budapest, HU (ISBN 978-1-4799-0303-0; IEEE Catalog CEP1384C), September 2013, Subotica, RS. IEEE, 2013, pp. 11–19.
[2] M. Vukobratović, G. Dimirovski: Modelling, simulation and control of robots and robotized FMS (flexible manufacturing systems), Facta Universitatis, Series: Mechanics, Automatic Control and Robotics, 1, 3, 241–280 (1993).
[3] A. Pajaziti, S. Buza, D. Bunjaku: Development and programming of the mobile platform with manipulation arm for rescue operations. In: The 12th International Symposium ”MINE ACTION 2015”, 13th IARP WS. HCRCTRO, 2015, pp. 157–160.
[4] G. Lee, S. Jung: Line tracking control of a two-wheeled mobile robot using visual feedback, International Journal of Advanced Robotic Systems, 10, 177 (2013), DOI: 10.5772/53729.
[5] H. N. Pishkenari, S. Mahboobi, A. Alasty: Optimum synthesis of fuzzy logic controller for trajectory tracking by differential evolution, Scientia Iranica, 18, 2, 261–267 (2011).
[6] H. Aithal, S. Janardhanan: Trajectory tracking of two wheeled mobile robot using higher order sliding mode control. In International Conference on Control Computing Communication & Materials, 2013, pp. 1–4.
[7]  Y. Wang, S. Wang, R. Tan, Y. Jiang: Motion control of a wheeled mobile robot using digital acceleration control method, Int J Innov Comput Inf Control (ICIC), 9 (1), 2013.
[8] E. Abbott, D. Powell: Land-vehicle navigation using gps, Proceedings of the IEEE, 87, 1, 145–162 (1999). [9] L. Cordesses, B. Thuilot, P. Martinet, C. Cariou: Curved path following of a farm tractor using a CP-DGPS. In: Proceedings of the 6th Symposium on Robot Control, 2000, pp. 489–494.
[10] Z. M. Gacovski, G. M. Dimirovski: Mobile non-holonomic robots: Trajectory generation and obstacle avoidance, Computational Intelligence for Modelling, Control & Automation: Evolutionary Computation & Fuzzy Logic for Intelligent Control, Knowledge Acquisition & Information Retrieval, vol. 2, pp. 166–171 (1999).
[11] J. Barraquand, J.-C. Latombe: Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles, Algorithmica, 10, 2–4, 121–155 (1993).
[12] F. G. Pin, H. A. Vasseur: Autonomous trajectory generation for mobile robots with non-holonomic and steering angle constraints, Intelligent Motion Control, 1990, pp. 295–299.
[13] M. Amoozgar, Y. Zhang: Trajectory tracking of wheeled mobile robots: A kinematical approach. In: Mechatronics and Embedded Systems and Applications (MESA), 2012 IEEE/ASME International Conference, IEEE, 2012, pp. 275–280.
[14] I. Zohar, A. Ailon, R. Rabinovici: Mobile robot characterized by dynamic and kinematic equations and actuator dynamics: Trajectory tracking and related application, Robotics and autonomous systems, 59, 6, 343–353 (2011).
[15] Y.-T. Wang, Y.-C. Chen, M.-C. Lin: Dynamic object tracking control for a non-holonomic wheeled autonomous robot, Tamkang Journal of Science and Engineering, 12, 3, 339–350 (2009).
[16] F. Kuhne, W. F. Lages, J. M. G. da Silva Jr: Point stabilization of mobile robots with nonlinear model predictive control. In: Mechatronics and Automation, 2005 IEEE International Conference, vol. 3. IEEE, 2005, pp. 1163–1168.
[17] P. Shi, Y. Zhao, Y. Cui: Modelling and control of wheeled mobile robot based on hybrid automata, In: Control and Decision Conference (CCDC), 2010 Chinese. IEEE, 2010, pp. 3375–3379.
[18] Aguiar, A. P., Pascoal, A.: Stabilization of the extended nonholonomic double integrator via logic-based hybrid control. In: Proc. of the 6th Int. IFAC Symposium on Robot Control, vol. 1. The IFAC and Pergamon Press, Oxford, 2001, pp. 307–312.
[19] G. Campion, W. Chung: Wheeled robots. In: Springer Handbook of Robotics. Springer, 2008, pp. 391–410. [20] R. W. Brockett et al.: Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, 27, 1, 181–191 (1983).
[21] E. Ivanjko, T. Petrinić, I. Petrović: Modelling of mobile robot dynamics. In: 7th EUROSIM Congress on Modelling and Simulation, vol. 2, 2010.

Jan 26, 2017
How to Cite
BUNJAKU, Drilon; STANKOVSKI, Jovan; STANKOVSKI, Mile. DYNAMIC MODELLING AND ASYMPTOTIC POINT STABILIZATION CONTROL OF TWO DIFFERENTIAL WHEELED MOBILE ROBOT. Journal of Electrical Engineering and Information Technologies - JEEIT, [S.l.], v. 1, n. 1-2, p. 25–35, jan. 2017. ISSN 2545-4269. Available at: <http://jeeit.feit.ukim.edu.mk/index.php/jeeit/article/view/24>. Date accessed: 26 mar. 2017.