In this paper, a saturated proportional-integral (PI)-type controller for unicycle-type wheeled mobile robots (UWMRs) is designed. The advantages of the novel controller are the robustness to external disturbances and the ability to keep the control into admissible limits. The desired trajectory should satisfy the so-called virtual reference system and be bounded for all time. Lyapunov’s theory and Barbalat’s lemma are used to prove the convergence of the tracking errors. An analysis of when the system is affected by disturbances is also given. To assess the performance of the proposed controller, an experimental real-time comparison of five schemes, including the proposed one, is presented. All the tested controllers guarantee the motion control goal and can produce saturated control action. A circular reference trajectory for the tracking task is used to perform the comparison. The proposed PI-type controller presents the best trajectory tracking performance, while the generated control action remains bounded.
This is a preview of subscription content,to check access.
Access this article
J. C. M. Contreras, D. Herrera, J. M. Toibero, and R. Carelli, “Controllers design for differential drive mobile robots based on extended kinematic modeling,” Proc. of the European Conference on Mobile Robots, pp. 1–6, 2017.
L. Guo, L. Zhao, Y. Song, and J. Hu, “Design and control of a variable structure robot,” International Journal of Advanced Robotic Systems, vol. 17, no.1, pp. 1–21, January 2020.
J. R. García-Sánchez, R. Silva-Ortigoza, S. Tavera-Mosqueda, C. Márquez-Sánchez, V. M. Hernández-Guzmán, M. Antonio-Cruz, and H. Taud, “Tracking control for mobile robots considering the dynamics of all their subsystems: Experimental implementation,” Complexity, vol. 2017, pp. 1–18, December 2017.
J. M. L. N. Mezui, D. Nganga-Kouya, A. F. Okou, M. Saad, and B. Hernandez, “A novel control structure for a pioneer mobile robot: Simulation and practical implementation,” International Journal of Modelling, Identification and Control, vol. 33, no.2, pp. 108–119, December 2019.
M. Abdelwahab, V. Parque, A. M. F. Elbab, A. A. Abouelsoud, and S. Sugano, “Trajectory tracking of wheeled mobile robots using z-number based fuzzy logic,” IEEE Access, vol. 8, pp. 18426–18441, January 2020.
F. N. Martins, W. C. Celeste, R. Carelli, M. Sarcinelli-Filho, and T. F. Bastos-Filho, “An adaptive dynamic controller for autonomous mobile robot trajectory tracking,” Control Engineering Practice, vol. 16, no. 11, pp. 1354–1363, November 2008.
H. Chen, C. Wang, D. Zhang, and F. Yang, “Finite-time robust stabilization of dynamic feedback nonholonomic mobile robots based on visual servoing with input saturation,” Proc. of the 10th World Congress on Intelligent Control and Automation, pp. 3686–3691, 2012.
H. Chen, C. Wang, B. Zhang, and D. Zhang, “Saturated tracking control for nonholonomic mobile robots with dynamic feedback,” Transactions of the Institute of Measurement and Control, vol. 35, no. 2, pp. 105–116, January 2012.
J. Huang, C. Wen, W. Wang, and Z. P. Jiang, “Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance,” Systems & Control Letters, vol. 62, no. 3, 234–241, March 2013.
H. Chen, “Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation,” International Journal of Control, Automation, and Systems, vol. 12, no. 6, pp. 1216–1224, October 2014.
H. Chen, B. Li, B. Zhang, and L. Zhang, “Global finitetime partial stabilization for a class of nonholonomic mobile robots subject to input saturation,” International Journal of Advanced Robotic Systems, vol. 12, no. 11, pp. 1–11, January 2015.
X. Chen and Y. Jia “Simple tracking controller for unicycle-type mobile robots with velocity and torque constraints,” Transactions of the Institute of Measurement and Control, vol. 37, no. 2, pp. 211–218, June 2014.
K. Shojaei, “Neural adaptive robust output feedback control of wheeled mobile robots with saturating actuators,” International Journal of Adaptive Control and Signal Processing, vol. 29, no. 7, pp. 855–876, August 2014.
K. Shojaei and A. Chatraei, “A saturating extension of an output feedback controller for internally damped Euler-Lagrange systems,” Asian Journal of Control, vol. 17, no. 6, pp. 2175–2187, February 2015.
K. Shojaei, “Saturated output feedback control of uncertain nonholonomic wheeled mobile robots,” Robotica, vol. 33, no. 1, pp. 87–105, January 2015.
Y. Wu and Y. Wang, “Asymptotic tracking control of uncertain nonholonomic wheeled mobile robot with actuator saturation and external disturbances,” Neural Computing and Applications, vol. 32, pp. 1–11, July 2019.
K. Liu, H. Ji, and Y. Zhang, “Extended state observer based adaptive sliding mode tracking control of wheeled mobile robot with input saturation and uncertainties,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 233, no. 15, pp. 5460–5476, May 2019.
M. M. Rayguru, S. Roy, and I. N. Kar, “Time-scale redesign-based saturated controller synthesis for a class of MIMO nonlinear systems,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, pp. 1–12, October 2019.
T. C. Lee, K. T. Song, C. H. Lee, and C. C. Teng, “Tracking control of unicycle-modeled mobile robots using a saturation feedback controller,” IEEE Transactions on Control Systems Technology, vol. 9, no. 2, pp. 305–318, March 2001.
Z. P. Jiang, E. Lefeber, and H. Nijmeijer, “Saturated stabilization and tracking of a nonholonomic mobile robot,” Systems & Control Letters, vol. 42, no. 5, pp. 327–332, April 2001.
W. J. Evers and H. Nijmeijer, “Practical stabilization of a mobile robot using saturated control,” Proc. of the 45th IEEE Conference on Decision and Control, pp. 2394–2399, 2006.
M. Defoort, J. Palos, A. Kokosy, T. Floquet, W. Perruquetti, and D. Boulinguez, “Experimental motion planning and control for an autonomous nonholonomic mobile robot,” Proc. of the 2007 IEEE International Conference on Robotics and Automation, pp. 2221–2226, 2007.
G. Antonelli, S. Chiaverini, and G. Fusco, “A fuzzy-logicbased approach for mobile robot path tracking,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 2, pp. 211–221, April 2007.
C. Wang, “Semiglobal practical stabilization of nonholonomic wheeled mobile robots with saturated inputs,” Automatica, vol. 44, no. 3, pp. 816–822, March 2008.
H. Chen, C. Wang, D. Zhang, and F. Yang, “Robust saturated finite-time stabilization for nonholonomic mobile robots based on visual serving feedback,” Proc. of the 24th Chinese Control and Decision Conference (CCDC), pp. 1268–1272, 2012.
C. Z. Resende, R. Carelli, and M. Sarcinelli-Filho, “A nonlinear trajectory tracking controller for mobile robots with velocity limitation via fuzzy gains,” Control Engineering Practice, vol. 21, no. 10, pp. 1302–1309, October 2013.
K. Izumi, H. Tanaka, and T. Tsujimura, “Nonholonomic control considering with input saturation for a mobile robot,” Proc. of the 55th Annual Conference of the Society of Instrument and Control Engineers of Japan, pp. 1173–1178, 2016.
C. Liu and J. Gao, “Lyapunov-based model predictive control for tracking of nonholonomic mobile robots under input constraints,” International Journal of Control, Automation and Systems, vol. 15, no. 5, pp. 2313–2319, July 2017.
M. Meza-Sánchez, E. Clemente, M. C. Rodríguez-Liñán, and G. Olague, “Synthetic-analytic behavior-based control framework: Constraining velocity in tracking for nonholonomic wheeled mobile robots,” Information Sciences, vol. 501, pp. 436–459, October 2019.
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.
S. Sharma and S. Jain, “Speed control of mobile robotic system using PI, PID and pole placement controller,” Proc. of the 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), pp. 1–5, 2016.
A. Sheikhlar, A. Fakharian, and A. Adhami-Mirhosseini, “Fuzzy adaptive PI control of omni-directional mobile robot,” Proc. of the 13th Iranian Conference on Fuzzy Systems (IFSC), pp. 1–4, 2013.
Z. Cao, Y. Zhao, and Q. Wu, “Genetic fuzzy+ PI path tracking control of a nonholonomic mobile robot,” Chinese Journal of Electronics, vol. 20, no. 1, pp. 31–34, January 2011.
Y. Liang, L. Xu, R. Wei, and H. Hu, “Adaptive fuzzy control for trajectory tracking of mobile robot,” Proc. of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4755–4760, 2010.
M. Manel and B. Faouzi, “Comparative study of PI controller and model based predictive control for mobile robot,” Universal Journal of Control and Automation, vol. 5, no. 1, pp. 1–11, February 2017.
M. Seyr, S. Jakubek, and G. Novak, “Neural network predictive trajectory tracking of an autonomous two-wheeled mobile robot,” IFAC Proceedings Volumes, vol. 38, no. 1, pp. 385–390, 2005.
Y. Su and C. Zheng, “Global asymptotic stabilization and tracking of wheeled mobile robots with actuator saturation”. Proc. of the IEEE International Conference on Robotics and Biomimetics, pp. 345–350, 2010.
H. K. Khalil, Nonlinear Systems, Prentice Hall, New Jersey, 2002.
J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, New Jersey, 1991.
W. E. Dixon, A. Behal, D. M. Dawson, and S. P. Nagarkatti, Nonlinear Control of Engineering Systems, Birkhäuser Basel, New York, 2003.
Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work was supported in part by the Instituto Politécnico Nacional under research grant 20201203, and by the Consejo Nacional de Ciencia y Tecnología, CONACYT-Fondo Sectorial de Investigación para la Educación under Project A1-S-24762. Proyecto Apoyado por el Fondo Sectorial de Investigación para la Educación, Mexico.
Javier Moreno-Valenzuela received his Ph.D. degree in automatic control from the CICESE Research Center, Ensenada, México, in 2002. From 2004 to 2005, he was a Postdoctoral Fellow with the Université de Liége, Belgium. He is currently with the Instituto Politécnico Nacional-CITEDI, Tijuana, México. He is the author of many peer-reviewed journal and international conference papers. He authored the book entitled: Motion Control of Underactuated Mechanical Systems (Springer-Verlag, 2018). His research interests include nonlinear systems, mechatronics, and intelligent systems. He has served as a Reviewer of a number of prestigious scientific journals. He is currently an Associate Editor of the IEEE LATIN AMERICA TRANSACTIONS and Mathematical Problems in Engineering.
Luis Gonzalo Montoya-Villegas was born in Tijuana, México, in 1992. He received his B.S. degree in electromechanical engineering from the Instituto Tecnológico de Tijuana, Tijuana, México, in 2015 and his M.S. degree in digital systems with specialization in control systems from the Instituto Politécnico Nacional-CITEDI, Tijuana, México, in 2017, where he is currently pursuing a Ph.D. degree in digital systems. His research interests include the analysis and control of wheeled mobile robots, nonlinear control, multiagents systems and consensus problems.
Ricardo Pérez-Alcocer was born in Mérida, México, in 1981. He received his B.Sc. degree in Computer Sciences from the University of Yucatán, México, in 2004, his M.Sc. in Mathematics from the University of Yucatán, México, in 2007, and a Ph.D. degree in Robotics and Advanced Manufacturing from CINVESTAV Research Center, Saltillo, México, in 2013. He is currently a Research Fellow with the CONACYT-Instituto Politécnico Nacional-CITEDI. His research interests include unmanned vehicles (aerial, aquatic and wheeled), linear and nonlinear control, multiagent systems, computer vision and intelligent systems.
Raúl Rascón received his B.S. degree in electrical engineering from Tecnológico Nacional de México, Mexicali, México, in 2005, an M.S. degree in automatic control from the Instituto Politécnico Nacional-CITEDI, Tijuana, México, in 2008, and a Ph.D. degree in automatic control from the CICESE Research Center, Ensenada, México, in 2012. He is currently a Fulltime Professor and a Researcher with the Facultad de Ingeniería, Universidad Autónoma de Baja California, Mexicali, México. His research interests include robust control, nonlinear control, observers, and applications to mechanical systems.
About this article
Cite this article
Moreno-Valenzuel, J., Montoya-Villegas, L.G., Pérez-Alcocer, R. et al. Saturated Proportional-integral-type Control of UWMRs with Experimental Evaluations. Int. J. Control Autom. Syst. 20, 184–197 (2022). https://doi.org/10.1007/s12555-020-0428-3