Adaptive and fractional-order super-twisting (FO-STA) control for trajectory tracking of mobile robots with differential traction

Sahbi Boubaker; Jorge Uliarte; Flavio Capraro; Souad Kamel; Faisal S. Alsubaei; Farid Bourennani; Francisco Rossomando; Sahbi Boubaker; Jorge Uliarte; Flavio Capraro; Souad Kamel; Faisal S. Alsubaei; Farid Bourennani; Francisco Rossomando

doi:10.3934/math.2026559

AIMS Mathematics

2026, Volume 11, Issue 5: 13589-13616. doi: 10.3934/math.2026559

Previous Article Next Article

Research article

Adaptive and fractional-order super-twisting (FO-STA) control for trajectory tracking of mobile robots with differential traction

1.
Department of Computer and Network Engineering, College of Computer Science and Engineering, University of Jeddah, Jeddah 21959, Saudi Arabia
2.
Facultad de Ingenieria, Universidad Nacional de Cuyo (UNCu), Centro Universitario, M5502JMA, Mendoza, Argentina
3.
Instituto de Automatica, UNSJ-CONICET, San Juan, CP 5400, Argentina
4.
Department of Cybersecurity, College of Computer Science and Engineering, University of Jeddah, Jeddah 23218, Saudi Arabia
5.
Department of Information Systems and Technology, College of Computer Science and Engineering, University of Jeddah, Jeddah 23218, Saudi Arabia

Received: 01 March 2026 Revised: 20 April 2026 Accepted: 29 April 2026 Published: 15 May 2026
MSC : 93-10, 93D21

Differential-drive mobile robots (DDMRs) are extensively used in logistics applications such as warehouse automation, last-mile delivery, and material handling owing to their simple mechanical structure and high maneuverability. Nevertheless, achieving accurate trajectory tracking remains challenging due to nonholonomic constraints, parameter uncertainties, wheel slip, and external disturbances in dynamic environments. Motivated by the inherent symmetry in the kinematic and dynamic structure of DDMRs, this paper proposes an adaptive control and a fractional-order super-twisting Algorithm (FO-STA)-based control framework for robust trajectory tracking using a dynamic model. The proposed approach adopted a dual-loop control architecture composed of an external kinematic loop and an inner dynamic loop, forming a robust control structure. The kinematic controller ensures convergence of the robot position to the desired reference trajectory, while the dynamic controller compensates for model uncertainties and external disturbances to achieve stable velocity tracking. An adaptive FO-STA mechanism was incorporated to enhance robustness against time-varying dynamics and unknown parameter variations. Both control laws were systematically derived using Lyapunov stability theory, guaranteeing closed-loop convergence and boundedness of tracking errors. Simulation results confirmed the effectiveness of the proposed strategy, demonstrating accurate trajectory tracking and strong robustness under parameter uncertainties and external disturbances, thereby validating its suitability for logistics-oriented mobile robotic systems.
- differential drive mobile robot,
- stability analysis,
- trajectory tracking,
- fractional-order control,
- super-twisting algorithm,
- logistics
Citation: Sahbi Boubaker, Jorge Uliarte, Flavio Capraro, Souad Kamel, Faisal S. Alsubaei, Farid Bourennani, Francisco Rossomando. Adaptive and fractional-order super-twisting (FO-STA) control for trajectory tracking of mobile robots with differential traction[J]. AIMS Mathematics, 2026, 11(5): 13589-13616. doi: 10.3934/math.2026559

Related Papers:

Abstract

Differential-drive mobile robots (DDMRs) are extensively used in logistics applications such as warehouse automation, last-mile delivery, and material handling owing to their simple mechanical structure and high maneuverability. Nevertheless, achieving accurate trajectory tracking remains challenging due to nonholonomic constraints, parameter uncertainties, wheel slip, and external disturbances in dynamic environments. Motivated by the inherent symmetry in the kinematic and dynamic structure of DDMRs, this paper proposes an adaptive control and a fractional-order super-twisting Algorithm (FO-STA)-based control framework for robust trajectory tracking using a dynamic model. The proposed approach adopted a dual-loop control architecture composed of an external kinematic loop and an inner dynamic loop, forming a robust control structure. The kinematic controller ensures convergence of the robot position to the desired reference trajectory, while the dynamic controller compensates for model uncertainties and external disturbances to achieve stable velocity tracking. An adaptive FO-STA mechanism was incorporated to enhance robustness against time-varying dynamics and unknown parameter variations. Both control laws were systematically derived using Lyapunov stability theory, guaranteeing closed-loop convergence and boundedness of tracking errors. Simulation results confirmed the effectiveness of the proposed strategy, demonstrating accurate trajectory tracking and strong robustness under parameter uncertainties and external disturbances, thereby validating its suitability for logistics-oriented mobile robotic systems.

References

[1]	H. Wang, Y. Huang, Y. Ge, W. Gao, Trajectory tracking control for mobile robots based on second order fast terminal sliding mode, In: 2018 33rd Youth Academic Annual Conference of Chinese Association of Automation (YAC), 2018,581–584. https://doi.org/10.1109/YAC.2018.8406441
[2]	V. Nguyen, M. T. Vu, S. H. Kim, A finite-time non-singular fast terminal sliding mode control of wheeled mobile robots with prescribed performance, IET Control Theory A., 19 (2025), e70013. https://doi.org/10.1049/cth2.70013 doi: 10.1049/cth2.70013
[3]	H. Ríos, M. Mera, A. Polyakov, Perturbed unicycle mobile robots: A second-order sliding-mode trajectory tracking control, IEEE T. Ind. Electron., 71 (2024), 2864–2872. https://doi.org/10.1109/TIE.2023.3270520 doi: 10.1109/TIE.2023.3270520
[4]	G. J. E. Scaglia, M. E. Serrano, S. A. Godoy, F. Rossomando, Linear algebra-based controller for trajectory tracking in mobile robots with additive uncertainties estimation, IMA J. Math. Control I., 37 (2020), 607–624. https://doi.org/10.1093/imamci/dnz016 doi: 10.1093/imamci/dnz016
[5]	Z. Sun, H. Xie, J. Zheng, Z. Man, D. He, Path-following control of mecanum-wheels omnidirectional mobile robots using nonsingular terminal sliding mode, Mech. Syst. Signal Pr., 147 (2021), 107128. https://doi.org/10.1016/j.ymssp.2020.107128 doi: 10.1016/j.ymssp.2020.107128
[6]	A. H. Nezhad, M. R. Soltanpour, S. Zaare, Observer-based robust finite-time tracking control for two-wheeled balancing mobile robots in the presence of uncertainties, Robot. Auton. Syst., 202 (2026), 105456. https://doi.org/10.1016/j.robot.2026.105456 doi: 10.1016/j.robot.2026.105456
[7]	S. Yin, C. Chen, Z. Xiang, Distributed predefined-time leader-follower formation control for heterogeneous wheeled mobile robots, IEEE T. Autom. Sci. Eng., 23 (2026), 6687–6697. https://doi.org/10.1109/TASE.2026.3673594 doi: 10.1109/TASE.2026.3673594
[8]	J. Uliarte, E. O. Freire, F. U. Vázquez, F. Camargo, H. Secchi, R. Carelli, et al., Trajectory tracking of a wmr using a neuro-adaptive mrac control with dynamic uncertainties, IEEE Access, 14 (2026), 37871–37884. https://doi.org/10.1109/ACCESS.2026.3670760 doi: 10.1109/ACCESS.2026.3670760
[9]	S. Boubaker, J. Gaia, E. Zavalla, S. Kamel, F. S. Alsubaei, Fa. Bourennani, et al., Trajectory tracking of wmr with neural adaptive correction, Mathematics, 13 (2025), 3178. https://doi.org/10.3390/math13193178 doi: 10.3390/math13193178
[10]	L. Caracciolo, A. de Luca, S. Iannitti, Trajectory tracking for a four-wheel differentially driven mobile robot, In: Proceedings 1999 IEEE International Conference on Robotics and Automation, 4 (1999), 2632–2638. https://doi.org/10.1109/ROBOT.1999.773994
[11]	J. Moreno, E. Slawiñski, F. A. Chicaiza, F. G. Rossomando, V. Mut, M. A. Morán, Design and analysis of an input–output linearization-based trajectory tracking controller for skid-steering mobile robots, Machines, 11 (2023), 988. https://doi.org/10.3390/machines11110988 doi: 10.3390/machines11110988
[12]	C Canudas de Wit, H. Khennouf, C. Samson, O. J. Sordalen, Nonlinear control design for mobile robots, In: Recent trends in mobile robots, 1993,121–156. https://doi.org/10.1142/9789814354301_0005
[13]	H. Xie, J. Zheng, Z. Sun, H. Wang, R. Chai, Finite-time tracking control for nonholonomic wheeled mobile robot using adaptive fast nonsingular terminal sliding mode, Nonlinear Dyn., 110 (2022), 1437–1453. https://doi.org/10.1007/s11071-022-07682-2 doi: 10.1007/s11071-022-07682-2
[14]	T. N. T. Cao, B. T. Pham, N. T. Nguyen, D. Vu, N. Truong, Second-order terminal sliding mode control for trajectory tracking of a differential drive robot, Mathematics, 12 (2024), 2657, 2024. https://doi.org/10.3390/math12172657 doi: 10.3390/math12172657
[15]	Y. Liu, G. Cui, Z. Li, Fixed-time consensus control of stochastic nonlinear multi-agent systems with input saturation using command-filtered backstepping, AIMS Math., 9 (2024), 1476514785. https://doi.org/10.3934/math.2024718 doi: 10.3934/math.2024718
[16]	J. Zhai, Z. Song, Adaptive sliding mode trajectory tracking control for wheeled mobile robots, Int. J. Control, 92 (2019), 2255–2262. https://doi.org/10.1080/00207179.2018.1436194 doi: 10.1080/00207179.2018.1436194
[17]	S. Ahmed, A. T. Azar, I. K. Ibraheem, Model-free scheme using time delay estimation with fixed-time fsmc for the nonlinear robot dynamics, AIMS Math., 9 (2024), 9989–10009. https://doi.org/10.3934/math.2024489 doi: 10.3934/math.2024489
[18]	A. Mallem, S. Nourredine, W. Benaziza, Mobile robot trajectory tracking using pid fast terminal sliding mode inverse dynamic control, In: 2016 4th International Conference on Control Engineering & Information Technology (CEIT), 2016, 1–6. https://doi.org/10.1109/CEIT.2016.7929057
[19]	I. Salgado, D. Cruz-Ortiz, O. Camacho, I. Chairez, Output feedback control of a skid-steered mobile robot based on the super-twisting algorithm, Control Eng. Pract., 58 (2017), 193–203. https://doi.org/10.1016/j.conengprac.2016.10.003 doi: 10.1016/j.conengprac.2016.10.003
[20]	Y. B. Shtessel, J. A. Moreno, F. Plestan, L. M. Fridman, A. S. Poznyak, Super-twisting adaptive sliding mode control: A lyapunov design, In: 49th IEEE Conference on Decision and Control (CDC), 2010, 5109–5113. https://doi.org/10.1109/CDC.2010.5717908
[21]	A. Tattersall, B. McGuinness, H. Lim, C. K. Au, H. Williams, M. Duke, The effect of dimensional parameters on the performance of ddmrs, In: 2023 IEEE 19th International Conference on Automation Science and Engineering (CASE), 2023, 1–6. https://doi.org/10.1109/CASE56687.2023.10260635
[22]	Y. Chen, I. Petras, D. Xue, Fractional order control-a tutorial, In: 2009 American control conference, 2009, 1397–1411. https://doi.org/10.1109/ACC.2009.5160719
[23]	J. E. Macías-Díaz, Fractional calculus—theory and applications, 11 (2022), 43. https://doi.org/10.3390/axioms11020043
[24]	Z. Li, L. Liu, S. Dehghan, Y. Chen, D. Xue, A review and evaluation of numerical tools for fractional calculus and fractional order controls, Int. J. Control, 90 (2017), 1165–1181. https://doi.org/10.1080/00207179.2015.1124290 doi: 10.1080/00207179.2015.1124290
[25]	A. P. Singh, K. Bingi, Applications of fractional-order calculus in robotics, Fractal Fract., 8 (2024), 403. https://doi.org/10.3390/fractalfract8070403 doi: 10.3390/fractalfract8070403
[26]	V. Mihaly, M. Şuşcă, D. Morar, M. Stănese, P. Dobra, $\mu$-Synthesis for fractional-order robust controllers, Mathematics, 9 (2021), 911. https://doi.org/10.3390/math9080911 doi: 10.3390/math9080911
[27]	I. Matraji, K. Al-Wahedi, A. Al-Durra, Higher-order super-twisting control for trajectory tracking control of skid-steered mobile robot, IEEE Access, 8 (2020), 124712–124721. https://doi.org/10.1109/ACCESS.2020.3007784 doi: 10.1109/ACCESS.2020.3007784
[28]	I. Matraji, A. Al-Durra, A. Haryono, K. Al-Wahedi, M. Abou-Khousa, Trajectory tracking control of skid-steered mobile robot based on adaptive second order sliding mode control, Control Eng. Pract., 72 (2018), 167–176. https://doi.org/10.1016/j.conengprac.2017.11.009 doi: 10.1016/j.conengprac.2017.11.009
[29]	C. Rosales, C. V. Sisterna, F. Rossomando, D. Gandolfo, C. Soria, R. Carelli, Super-twisting adaptive control of a quadrotor, ISA T., 166 (2025), 241–249. https://doi.org/10.1016/j.isatra.2025.07.029 doi: 10.1016/j.isatra.2025.07.029
[30]	J. J. E. Slotine, W. Li, Applied nonlinear control, Prentice Hall, 1991.

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)