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Mathematical analysis of a line-follower robot, a stable controller design using Lyapunov approach, and experimental tests

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Abstract

Line-follower robots are used in industry to transport materials and objects autonomously by following certain paths. These paths may be drawn lines or magnetic tapes on the floor that are detected by a sensor array. In this research, a mathematical model of the dynamics of the tracking error of a line-follower differential robot is derived. The derived mathematical form of the rate of change of the tracking error shows its dependency on the direction of the tangent of the desired path, the current direction of the robot, and the angular and linear velocities. Based on this error model and using the Lyapunov approach, a variable structure controller is designed to guarantee a stable tracking performance. In addition, it is shown how the controller parameters can be chosen based on the robot’s maximum velocities and the maximum expected angle between the robot’s linear velocity and the tangent of the path. Then, the effect of the dynamics of the robot is investigated. The introduced controller is experimentally tested using a small differential robot using two different tracks. The results show that the robot successfully followed the test tracks using different parameter settings. However, some settings give better performance than others, which are explained.

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Authors and Affiliations

  1. Egyptian Academy for Engineering and Advanced Technology, Al Salam First, Cairo, Egypt

    Amin Danial Asham

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  1. Amin Danial Asham
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Correspondence to Amin Danial Asham.

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Asham, A.D. Mathematical analysis of a line-follower robot, a stable controller design using Lyapunov approach, and experimental tests. Int. J. Dynam. Control 11, 385–395 (2023). https://doi.org/10.1007/s40435-022-00973-x

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  • DOI: https://doi.org/10.1007/s40435-022-00973-x

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