Cascade Control for Trajectory-Tracking Mobile Robots Based on Synergetic Control Theory and Lyapunov Functions

Nguyen Xuan Chiem

Abstract


This paper aims to synthesize a synergetic control law using a cascade approach for trajectory-tracking robots. A nonlinear model was established for a differential two-wheeled mobile robot. The robot’s operation can either stabilize along a desired trajectory or deviate due to model uncertainty and external disturbances. The cascade approach is utilized to reduce system complexity while maintaining the robustness of the control law. The kinematic control law in the outer loop is designed using Lyapunov functions, while the dynamic control law is derived using synergetic control theory. This law ensures system control quality under model uncertainties and external disturbances. Finally, simulation results demonstrate that the proposed controller provides robust stability for the mobile robot, along with excellent disturbance rejection and robustness against model uncertainties.

Keywords


Synergetic Control Law, Lyapunov Functions, Mobile Robot, Trajectory-Tracking Robot, Cascade Approach

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References


C. Samson and K. Ait-Abderrahim, "Feedback control of a nonholonomic wheeled cart in Cartesian space," Proceedings. 1991 IEEE International Conference on Robotics and Automation, Sacramento, vol. 2, pp. 1136-1141, 1991, https://doi.org/10.1109/ROBOT.1991.131748.

M. Aicardi, G. Casalino, A. Bicchi and A. Balestrino, "Closed loop steering of unicycle like vehicles via Lyapunov techniques," IEEE Robotics & Automation Magazine, vol. 2, no. 1, pp. 27-35, 1995, https://doi.org/10.1109/100.388294.

Byung Moon Kim and P. Tsiotras, "Controllers for unicycle-type wheeled robots: Theoretical results and experimental validation," IEEE Transactions on Robotics and Automation, vol. 18, no. 3, pp. 294-307, 2002, https://doi.org/10.1109/TRA.2002.1019460.

G. Zidani, S. Drid, L. Chrifi-Alaoui, A. Benmakhlouf and S. Chaouch, "Backstepping controller for a wheeled mobile robot," 2015 4th International Conference on Systems and Control (ICSC), pp. 443-448, 2015, https://doi.org/10.1109/ICoSC.2015.7153286.

I. Hassania, C. Rekik, “Backstepping Controller for Mobile Robot in Presence of Disturbances and Uncertainties,” International Journal of Robotics and Control Systems, vol. 3, no. 4, pp. 934-954, 2023, https://doi.org/10.31763/ijrcs.v3i4.1110.

T. P. Nascimento, C. E. T. Dórea, and L. M. G. Gonçalves, “Nonlinear model predictive control for trajectory tracking of nonholonomic mobile robots: A modified approach,” International Journal of Advanced Robotic Systems, vol. 15, no. 1, 2018, https://doi.org/10.1177/1729881418760461.

S. Bouzoualegh, E.-H. Guechi, and R. Kelaiaia, “Model predictive control of a differentialdrive mobile robot,” Acta Universitatis Sapientiae, Electrical and Mechanical Engineering, vol. 10, no. 1, pp. 20-41, 2018, https://doi.org/10.2478/auseme-2018-0002.

J. Yang and J. Kim, "Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots," IEEE Transactions on Robotics and Automation, vol. 15, no. 3, pp. 578-587, 1999, https://doi.org/10.1109/70.768190.

Felipe N. Martins, Wanderley C. Celeste, Ricardo Carelli, Mário Sarcinelli-Filho, Teodiano F. Bastos-Filho, “An adaptive dynamic controller for autonomous mobile robot trajectory tracking Author links open overlay panel,” Control Engineering Practice, vol 16, no 11, pp. 1354-1363, 2008, https://doi.org/10.1016/j.conengprac.2008.03.004.

R. Barzamini, A. R. Yazdizadeh and A. H. Rahmani, "A New Adaptive Tracking Control For Wheeled Mobile Robot," 2006 IEEE Conference on Robotics, Automation and Mechatronics, pp. 1-6, 2006, https://doi.org/10.1109/RAMECH.2006.252750.

H. Omrane, M. S. Masmoudi, M. Masmoudi, “Fuzzy Logic Based Control for Autonomous Mobile Robot Navigation,” Computational Intelligence and Neuroscience, vol. 2016, no. 1, pp. 1-10, 2016, https://doi.org/10.1155/2016/9548482.

F. Cupertino, V. Giordano, D. Naso and L. Delfine, "Fuzzy control of a mobile robot," IEEE Robotics & Automation Magazine, vol. 13, no. 4, pp. 74-81, 2006, https://doi.org/10.1109/MRA.2006.250563.

M. Akbarzadeh-T, “Agencies of Intelligence: From the Macro to the Nano,” Control and Systems Engineering, Springer, pp. 289-311, 2015, https://doi.org/10.1007/978-3-319-14636-2_15.

N. X. Chiem, N. D. Anh, A. D. Lukianov, P. D. Tung, H. D. Long, and N. D. Linh, “Design real-time embedded optimal PD fuzzy controller by PSO algorithm for autonomous vehicle mounted camera,” AIP Conference Proceedings, vol. 2188, no. 1, p. 030008, 2019, https://doi.org/10.1063/1.5138401.

A. A. Kolesnikov, "Introduction of synergetic control," 2014 American Control Conference, pp. 3013-3016, 2014, https://doi.org/10.1109/ACC.2014.6859397.

A. A. Kolesnikov, "Introduction of synergetic control," 2014 American Control Conference, pp. 3013-3016, 2014, https://doi.org/10.1109/ACC.2014.6859397.

C. S. Nguyen, C. V. Tran, H. N. Phan, “Control Law Synthesis for Flexible Joint Manipulator Based on Synergetic Control Theory,” Mechatronics, Automation, Control, vol. 24, no. 8, pp. 395-402, 2023, https://doi.org/10.17587/mau.24.395-402.

Nguyen Xuan Chiem, Le Tran Thang, “Synthesis of an Orbit Tracking Controller for a 2DOF Helicopter based on Sequential Manifolds with Stabilization Time in the Presence of Disturbances,” Engineering, Technology & Applied Science Research, vol. 14, no. 4, pp. 15083-15089, 2024, https://doi.org/10.48084/etasr.7512.

N. X. Chiem, B. X. Hai, T. C. Phan, “Synthesis of Adaptive Sliding Mode Control for Twin Rotor MIMO System with Mass Uncertainty based on Synergetic Control Theory,” International Journal of Robotics and Control Systems, vol. 4, no. 1, pp. 174-187, 2024, https://doi.org/10.31763/ijrcs.v4i1.1307.




DOI: https://doi.org/10.59247/csol.v3i1.169

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Control Systems and Optimization Letters
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