Computational analysis of the effect of speed on tracking accuracy in differential mobile robots
DOI:
https://doi.org/10.62059/m3r4cr73Keywords:
Mobile robot, Differential traction, Trajectory tracking, Operating speed, Tracking errorAbstract
This work analyzes how operating speed affects the path-tracking accuracy of a differentially driven mobile robot. A computational simulation was developed in Python using a proportional controller with constant parameters and a fixed reference path. Speeds between 0.2 and 1.0 m/s were evaluated using tracking error, RMSE, maximum error, and final error. The results show that increasing speed reduces travel time but progressively increases error. The RMSE increased from 0.000308 m to 0.005664 m, while the maximum error increased from 0.000516 m to 0.008836 m. The influence of curvature, initial disturbances, measurement noise, and numerical convergence were also analyzed. The results confirm a clear relationship between speed and accuracy, providing a basis for selecting operating conditions that balance speed and precision.
References
1] N. Leena and K. K. Saju, Modelling and Trajectory Tracking of Wheeled Mobile Robots, Procedia Technology, vol. 24, pp. 538–545, 2016, doi: 10.1016/j.protcy.2016.05.094.
[2] G. Klančar, D. Matko, and S. Blažič, A control strategy for platoons of differential drive 11 wheeled mobile robot, Robotics and Autonomous Systems, vol. 9, no. 2, pp. 57–64, 2011, doi: 10.1016/j.robot.2010.12.002.
[3] H. Rodríguez-Cortés and M. Velasco-Villa, A new geometric trajectory tracking controller for the unicycle mobile robot, Systems & Control Letters, vol. 168, p. 105360, 2022, doi: 10.1016/j.sysconle.2022.105360.
[4] I. Estrada-Sánchez, M. Velasco-Villa, and H. Rodríguez-Cortés, A new trajectory tracking controller for the unicycle mobile robot, Congreso Nacional de Control Automático, Monterrey, Nuevo León, México, 2017.
[5] G. Campion, G. Bastin, and B. D’Andrea-Novel, Structural properties and classification of kinematic and dynamic models of wheeled mobile robots, IEEE Transactions on Robotics and Automation, vol. 12, no. 1, pp. 47–62, 1996, doi: 10.1109/70.481750.
[6] Y. Kanayama, Y. Kimura, F. Miyazaki, and T. Noguchi, A stable tracking control method for a non-holonomic mobile robot, Proceedings of the IEEE/RSJ International Workshop on Intelligent Robots and Systems, pp. 1236–1241, 1991, doi: 10.1109/IROS.1991.174669.
[7] Z.-P. Jiang and H. Nijmeijer, Tracking control of mobile robots: A case study in backstepping, Automatica, vol. 33, no. 7, pp. 1393–1399, 1997, doi: 10.1016/S0005-1098(97)00055-1.
[8] R. Fierro and F. L. Lewis, Control of a nonholonomic mobile robot: Backstepping kinematics into dynamics, Journal of Robotic Systems, vol. 14, no. 3, pp. 149–163, 1997, doi: 10.1002/(SICI)1097-4563(199703)14:3<149::AID-ROB1>3.0.CO;2-R.
[9] G. Antonelli, S. Chiaverini, and G. Fusco, A fuzzy-logic-based approach for mobile robot path tracking, IEEE Transactions on Fuzzy Systems, vol. 15, no. 2, pp. 211–221, 2007, doi: 10.1109/TFUZZ.2006.879998.
[10] C.-L. Shih and L.-C. Lin, Trajectory Planning and Tracking Control of a Differential-Drive Mobile Robot in a Picture Drawing Application, Robotics, vol. 6, no. 3, p. 17, 2017, doi: 10.3390/robotics6030017.
[11] M. Yue, F. Tang, B. Liu, and B. Yao, Trajectory-tracking control of a nonholonomic mobile robot: Backstepping kinematics into dynamics with uncertain disturbances, Applied Artificial Intelligence, vol. 26, no. 10, pp. 952–966, 2012, doi: 10.1080/08839514.2012.731347.
[12] S. K. Saha, A. R. Mandal, and S. M. Bandyopadhyay, Trajectory Tracking of Autonomous Mobile Robots Using Nonlinear Dynamic Inversion, IFAC-PapersOnLine, vol. 51, no. 1, pp. 202–207, 2018, doi: 10.1016/j.ifacol.2018.05.041.
[13] Y. Wang, Y. Zhang, and X. Wang, Finite-time output feedback tracking control for a nonholonomic wheeled mobile robot, Aerospace Science and Technology, vol. 78, pp. 574–579, 2018, doi: 10.1016/j.ast.2018.05.005.
[14] X. Wang, J. Wang, and Y. Zhao, Event-based tracking control for nonholonomi mobile robots, Nonlinear Analysis: Hybrid Systems, vol. 38, p. 100945, 2020, doi: 10.1016/j.nahs.2020.100945.12
[15] M. Ou, H. Sun, Z. Zhang, L. Li, and X.-A. Wang, Fixed-time tracking control for nonholonomic mobile robot, Kybernetika, vol. 57, no. 2, pp. 220–235, 2021, doi: 10.14736/kyb-2021-2-0220.
[16] H. Zhang, Y. Wang, and X. Li, Robust tracking control of a differential drive wheeled mobile robot using fast nonsingular terminal sliding mode, Computers & Electrical Engineering, vol. 96, p. 107488, 2021, doi: 10.1016/j.compeleceng.2021.107488.
[17] S. I. C. Gulo and T. Tamba, Design of trajectory tracking control for an differential drive wheeled mobile robot, Jurnal Nasional Teknik Elektro dan Teknologi Informasi, vol. 10, no. 3, 2021, doi: 10.22146/jnteti.v10i3.1454.
[18] L. Yan, B. Ma, and Y. Jia, Trajectory tracking control of nonholonomic wheeled mobile robots using only measurements for position and velocity, Automatica, vol. 159, p. 111374, 2024, doi: 10.1016/j.automatica.2023.111374.
[19] P. Morin and C. Samson, Motion control of wheeled mobile robots, Springer Handbook of Robotics, Springer, Berlin, Heidelberg, pp. 799–826, 2008, doi: 10.1007/978-3-540-30301-535.
[20] A. De Luca and G. Oriolo, Trajectory planning and control for robots, Robotics and Automation Handbook, CRC Press, 2002.
[21] L. Marton, Robust control of a differential drive mobile robot, International Journal of Robust and Nonlinear Control, vol. 20, no. 9, pp. 969–980, 2010, doi: 10.1002/rnc.1492.
[22] H. Cheng, Y. Zhang, and J. Wu, Adaptive tracking control of differential drive mobile robots with unknown parameters, IEEE Transactions on Industrial Electronics, vol. 68, no. 12, pp. 12545–12554, 2021, doi: 10.1109/TIE.2020.3047045.
[23] Y. Zhang, X. Li, and C. Yang, Sliding mode control for trajectory tracking of mobile robots with unknown disturbances, Journal of the Franklin Institute, vol. 357, no. 3, pp. 1421–1439, 2020, doi: 10.1016/j.jfranklin.2019.11.064.
[24] Z. Li, H. Wang, and B. Xu, Neural network based tracking control for nonholonomic mobile robots with input saturation, Neurocomputing, vol. 503, pp. 32–42, 2022, doi: 10.1016/j.neucom.2022.06.084.
[25] Y. Sun, X. Wang, and J. Zhou, Event-triggered control for trajectory tracking of mobile robots with unknown disturbances, International Journal of Control, vol. 96, no. 5, pp. 1221–1233, 2023, doi: 10.1080/00207179.2022.2055512.
[26] H. Wang, Y. Liu, and Z. Guo, Robust trajectory tracking of mobile robots using adaptive control with unknown disturbances, IEEE Access, vol. 7, pp. 152234–152243, 2019, doi: 10.1109/ACCESS.2019.2948362.
[27] S. Guo, Z. Zhang, and L. Li, Fixed-time tracking control for mobile robots with disturbances and input saturation, ISA Transactions, vol. 128, pp. 315–325, 2022, doi: 10.1016/j.isatra.2022.01.012.
[28] X. Li, C. Yang, and Y. Zhang, Adaptive neural network control for trajectory tracking of mobile robots with input dead-zone, Applied Soft Computing, vol. 106, p. 107335, 2021, doi: 10.1016/j.asoc.2021.107335.13
[29] T. Fukao, H. Nakagawa, and K. Adachi, Adaptive tracking control of a nonholonomic mobile robot, IEEE Transactions on Robotics and Automation, vol. 16, no. 5, pp. 609–615, 2000, doi: 10.1109/70.852605.
[30] Y. Liu, X. Wang, and S. Zhang, Finite-time control of mobile robots with unknown disturbances and actuator saturation, Nonlinear Dynamics, vol. 94, pp. 365–378, 2018, doi: 10.1007/s11071-018-4366-2.
Downloads
Downloads
Posted
Categories
Data Availability Statement
The data supporting the findings of this study are available from the corresponding author upon reasonable request.
License
Copyright (c) 2026 José Luis Guamán Chacha, Ronal Javier Alejandro Castro, Cecibell Alexandra Malavé Vivar (Autor/a)
This work is licensed under a Creative Commons Attribution 4.0 International License.
This preprint contains the reported license and associated copyright. Once published in an associated journal or other publisher, the published version assumes the publisher's terms and conditions.
