Constrained Pole Placement Optimization Using the Flower Pollination Algorithm for Velocity Tracking of Differential-Drive Mobile Robots

Anh-Minh Duc Tran; Tri-Vien Vu

doi:10.48084/etasr.18761

Authors

Anh-Minh Duc Tran Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Tri-Vien Vu Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Volume: 16 | Issue: 4 | Pages: 37710-37716 | August 2026 | https://doi.org/10.48084/etasr.18761

Received: 15 March 2026 | Revised: 11 May 2026, 29 May 2026, and 8 June 2026 | Accepted: 9 June 2026 | Online: 18 June 2026

Corresponding author: Anh-Minh Duc Tran

Abstract

This paper proposes a Flower Pollination Algorithm (FPA)-based constrained pole-placement framework for velocity-tracking control of Differential-Drive Mobile Robots (DDMRs) subject to actuator-voltage limitations and external disturbances. A fourth-order state-space model is derived from Newton-Euler principles, including coupled electromechanical dynamics and disturbance inputs. The pole-placement problem is formulated as a constrained multi-objective optimization task balancing tracking performance, Cross-Coupling (CC) reduction, and actuator saturation penalties. A reference prefilter is included to improve nominal steady-state tracking, while closed-loop stability is ensured by restricting the poles to the open left-half plane. The proposed controller is compared with classical pole placement, Linear Quadratic Regulator (LQR), and Model Reference Adaptive Control (MRAC). The simulation results show that although LQR achieves good nominal tracking, it requires 102.9 V, exceeding the 48 V actuator limit, whereas MRAC exhibits higher tracking errors and severe cross-coupling (CC = 1.94). In contrast, the proposed method maintains a feasible control effort while achieving satisfactory tracking performance under external disturbances.

Keywords:

constrained pole placement, differential-drive, mobile, robots, flower pollination algorithm, actuator saturation, velocity tracking, cross-coupling analysis

References

[1] R. Siegwart, Introduction to autonomous mobile robots, 2nd ed. Cambridge, Massachusetts: MIT Press, 2011.

[2] A. D. Luca, "Modelling and Control of Nonholonomic Mechanical Systems," in Kinematics and Dynamics of Multi-Body Systems, vol. 360, J. Angeles and A. Kecskeméthy, Eds. Vienna: Springer Vienna, 1995, pp. 277-342.

[3] L. Wang and G. Liu, "Research on multi-robot collaborative operation in logistics and warehousing using A3C optimized YOLOv5-PPO model," Frontiers in Neurorobotics, vol. 17, Jan. 2024.

[4] A. M. Abed et al., "Trajectory tracking of differential drive mobile robots using fractional-order proportional-integral-derivative controller design tuned by an enhanced fruit fly optimization," Measurement and Control, vol. 55, no. 3–4, pp. 209–226, Mar. 2022.

[5] I. A. Hameed et al., "A New Nonlinear Dynamic Speed Controller for a Differential Drive Mobile Robot," Entropy, vol. 25, no. 3, Mar. 2023, Art. no. 514.

[6] F. Hamerlain, K. Achour, T. Floquet, and W. Perruquetti, "Higher Order Sliding Mode Control of wheeled mobile robots in the presence of sliding effects," in Proceedings of the 44th IEEE Conference on Decision and Control, Dec. 2005, pp. 1959-1963.

[7] R. C. Dorf and R. H. Bishop, Modern control systems, Fourteenth edition, Global Edition. Harlow: Pearson, 2022.

[8] A. S. Alkabaa, O. Taylan, M. Balubaid, C. Zhang, and A. Mohammadzadeh, "A practical type-3 Fuzzy control for mobile robots: predictive and Boltzmann-based learning," Complex & Intelligent Systems, vol. 9, no. 6, pp. 6509–6522, Dec. 2023.

[9] M. Cui, H. Liu, X. Wang, and W. Liu, "Adaptive Control for Simultaneous Tracking and Stabilization of Wheeled Mobile Robot with Uncertainties," Journal of Intelligent & Robotic Systems, vol. 108, no. 3, July 2023, Art. no. 46.

[10] G. Oriolo, A. De Luca, and M. Vendittelli, "WMR control via dynamic feedback linearization: design, implementation, and experimental validation," IEEE Transactions on Control Systems Technology, vol. 10, no. 6, pp. 835-852, Nov. 2002.

[11] A.M. D. Tran and T. V. Vu, "Robust MIMO LQR Control with Integral Action for Differential Drive Robots: A Lyapunov-Cost Function Approach," Engineering, Technology & Applied Science Research, vol. 15, no. 4, pp. 24775-24781, Aug. 2025.

[12] J. Moreno-Valenzuela, L. Montoya-Villegas, R. Pérez-Alcocer, and J. Sandoval, "A family of saturated controllers for UWMRs," ISA Transactions, vol. 100, pp. 495-509, May 2020.

[13] F.-G. Wang, H.-M. Wang, S.-K. Park, and X.-S. Wang, "Linear pole-placement anti-windup control for input saturation nonlinear system based on Takagi Sugeno fuzzy model," International Journal of Control, Automation and Systems, vol. 14, no. 6, pp. 1599-1606, Dec. 2016.

[14] S. B. Joseph, E. G. Dada, A. Abidemi, D. O. Oyewola, and B. M. Khammas, "Metaheuristic algorithms for PID controller parameters tuning: review, approaches and open problems," Heliyon, vol. 8, no. 5, May 2022.

[15] X.-S. Yang, Nature-inspired optimization algorithms, 1st ed. Amsterdam Waltham, MA: Elsevier, 2014.

[16] A.-M. D. Tran, T.-V. Vu, and Q.-D. Nguyen, "A Study on General State Model of Differential Drive Wheeled Mobile Robots," Journal of Advanced Engineering and Computation, vol. 7, no. 3, Sept. 2023, Art. no. 174.

[17] H. K. Khalil, Nonlinear Systems, 3rd ed. Upper Saddle River, N.J: Prentice Hall, 2002.

[18] K. J. Åström and T. Hägglund, PID controllers: theory, design, and tuning, 2nd ed. Research Triangle Park, NC: Instrument Society of America, 1995.

[19] G. Kaczmarczyk, R. Stanisławski, Ł. Knypiński, D. D. Ferreira, and M. Kamiński, "Flower pollination algorithm optimization applied for Lyapunov-based fuzzy logic speed controller of a complex drive system," Bulletin of the Polish Academy of Sciences Technical Sciences, vol. 73, no. 5, Apr. 2025, Art. no. 154205.

[20] N. H. Rohiem, A. Soeprijanto, and M. Syai’in, "Enhancing Voltage Stability under GCC Constraints with the AI-Driven Optimization of Distributed Generators," Engineering, Technology & Applied Science Research, vol. 15, no. 5, pp. 28063-28070, Oct. 2025.

[21] X. S. Yang, "Flower Pollination Algorithm for Global Optimization," in Unconventional Computation and Natural Computation, Springer Berlin Heidelberg, 2012, vol. 7445, pp. 240-249.