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Volume 7 Issue 1
Jan.  2020

IEEE/CAA Journal of Automatica Sinica

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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)
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  • 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.


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    • 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.


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