A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 7 Issue 1
Jan.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 6.171, Top 11% (SCI Q1)
    CiteScore: 11.2, Top 5% (Q1)
    Google Scholar h5-index: 51, TOP 8
Turn off MathJax
Article Contents
Keyvan Majd, Mohammad Razeghi-Jahromi and Abdollah Homaifar, "A Stable Analytical Solution Method for Car-Like Robot Trajectory Tracking and Optimization," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 39-47, Jan. 2020. doi: 10.1109/JAS.2019.1911816
Citation: Keyvan Majd, Mohammad Razeghi-Jahromi and Abdollah Homaifar, "A Stable Analytical Solution Method for Car-Like Robot Trajectory Tracking and Optimization," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 39-47, Jan. 2020. doi: 10.1109/JAS.2019.1911816

A Stable Analytical Solution Method for Car-Like Robot Trajectory Tracking and Optimization

doi: 10.1109/JAS.2019.1911816
Funds:  This work was partially supported by the Air Force Research Laboratory and Office of the Secretary of Defense (OSD) (FA8750-15-2-0116), the US Department of Transportation (USDOT), and Research and Innovative Technology Administration (RITA) under University Transportation Center (UTC) Program (DTRT13-G-UTC47)
More Information
  • In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.


  • loading
  • [1]
    R. W. Brockett et al., " Asymptotic stability and feedback stabilization,” Differential Geometric Control Theory, vol. 27, no. 1, pp. 181–191, 1983.
    B. Paden, M. Čáp, S. Z. Yong, D. Yershov, and E. Frazzoli, " A survey of motion planning and control techniques for self-driving urban vehicles,” IEEE Trans. Intelligent Vehicles, vol. 1, no. 1, pp. 33–55, 2016. doi: 10.1109/TIV.2016.2578706
    Y. Kanayama, Y. Kimura, F. Miyazaki, and T. Noguchi, " A stable tracking control method for an autonomous mobile robot, ” in Proc. IEEE Int. Conf. Robotics and Automation, 1990.
    A. De Luca, G. Oriolo, and C. Samson, " Feedback control of a nonholonomic car-like robot,” Robot Motion Planning and Control, pp. 171–253, 1998.
    B. d’Andréa Novel, G. Campion, and G. Bastin, " Control of nonholo-nomic wheeled mobile robots by state feedback linearization,” The Int. J. Robotics Research, vol. 14, no. 6, pp. 543–559, 1995. doi: 10.1177/027836499501400602
    P. Gáspár, Z. Szabó, and J. Bokor, " LPV design of fault-tolerant control for road vehicles,” Int. J. Applied Mathematics and Computer Science, vol. 22, no. 1, pp. 173–182, 2012. doi: 10.2478/v10006-012-0013-x
    J. Fu, F. Tian, T. Chai, Y. Jing, Z. Li, and C.-Y. Su, " Motion tracking control design for a class of nonholonomic mobile robot systems,” IEEE Trans. Systems, Man, and Cybernetics: Systems, no. 99, pp. 1–7,
    R. Postoyan, M. C. Bragagnolo, E. Galbrun, J. Daafouz, D. Neši ć, and E. B. Castelan, " Event-triggered tracking control of unicycle mobile robots,” Automatica, vol. 52, pp. 302–308, 2015. doi: 10.1016/j.automatica.2014.12.009
    D. Gu and H. Hu, " Receding horizon tracking control of wheeled mobile robots,” IEEE Trans. Control Systems Technology, vol. 14, no. 4, pp. 743–749, 2006. doi: 10.1109/TCST.2006.872512
    Y. Zhang, S. Li, and X. Liu, " Neural network-based model-free adaptive near-optimal tracking control for a class of nonlinear systems,” IEEE Trans. Neural Networks and Learning Systems, 2018.
    G. V. Raffo, G. K. Gomes, J. E. Normey-Rico, C. R. Kelber, and L. B. Becker, " A predictive controller for autonomous vehicle path tracking,” IEEE Trans. Intell. Trans. Sys., vol. 10, no. 1, pp. 92–102, 2009. doi: 10.1109/TITS.2008.2011697
    D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. Scokaert, " Constrained model predictive control: stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, 2000. doi: 10.1016/S0005-1098(99)00214-9
    G. Klančar and I. Škrjanc, " Tracking-error model-based predictive control for mobile robots in real time,” Robotics and Autonomous Systems, vol. 55, no. 6, pp. 460–469, 2007. doi: 10.1016/j.robot.2007.01.002
    I. Škrjanc and G. Klančar, " A comparison of continuous and discrete tracking-error model-based predictive control for mobile robots,” Robotics and Autonomous Systems, vol. 87, pp. 177–187, 2017. doi: 10.1016/j.robot.2016.09.016
    H. K. Khalil and J. Grizzle, Nonlinear Systems. Prentice hall Upper Saddle River, NJ, vol. 3, 2002.
    R. Rajamani, Vehicle Dynamics and Control. Springer Science & Business Media, 2011.
    D. E. Kirk, Optimal Control Theory: An Introduction. Courier Corporation, 2012.
    W. J. Rugh, Linear System Theory. Prentice hall Upper Saddle River, NJ, vol. 2, 1996.
    K. Majd, M. Razeghi-Jahromi, and A. Homaifar, " Optimal Kinematicbased Trajectory Planning and Tracking Control of Autonomous Ground Vehicle Using the Variational Approach, ” in Proc. IEEE Intelligent Vehicles Symposium, 2018.


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(6)  / Tables(3)

    Article Metrics

    Article views (8886) PDF downloads(212) Cited by()


    • The car-like robot kinematic model trajectory tracking, and control problem is revisited.
    • A globally exponentially stable trajectory optimization and tracking framework is proposed.
    • The analytical solution using variational approach is proposed to solve the trajectory optimization problem.
    • The method can tackle the optimal trajectory optimization of higher dimensional kinematic models.


    DownLoad:  Full-Size Img  PowerPoint