Comparison Between Some Nonlinear Controllers for the Position Control of Lagrangian-type Robotic Systems

Year 2022, , 179 - 196, 31.12.2022

Sahar Jenhani , Hassène Gritli , Professor Giuseppe Carbone

https://doi.org/10.51537/chaos.1184952

Cited By: 4

Abstract

This work addresses the set-point control problem of the position of fully-actuated Lagrangian-type robotic systems by means of some nonlinear control laws. We adopt four different nonlinear control laws: the PD plus gravity compensation controller, the PD plus desired gravity compensation controller, the computed-torque controller and the augmented PD plus gravity compensation controller. An in-depth comparison between these control laws and their application is achieved. Indeed, using some properties, we design some conditions on the feedback gains of the nonlinear controllers ensuring the stability in the closed loop of the zero-equilibrium point and its uniqueness. At the end of this work, we adopt a planar two-degree-of-freedom manipulator robot to illustrate via simulation the difference between and the efficiency of the adopted nonlinear controllers.

Keywords

Lagrangian robotic systems, Nonlinear dynamics, Approximated linear model, Position control, Nonlinear controllers, Stability, Stabilization, Solution uniqueness

References

• Abbas, M., S. Al Issa, and S. K. Dwivedy, 2021 Event-triggered adaptive hybrid position-force control for robot-assisted ultrasonic examination system. Journal of Intelligent & Robotic Systems 102: 84–102.
• Abdul-Adheem, W. R., I. K. Ibraheem, A. J. Humaidi, and A. T. Azar, 2021 Model-free active input–output feedback linearization of a single-link flexible joint manipulator: An improved active disturbance rejection control approach. Measurement and Control 54: 856–871.
• Ahmed, T.,M. Assad-Uz-Zaman, M. R. Islam, D. Gottheardt, E. Mc- Gonigle, et al., 2021 Flexohand: A hybrid exoskeleton-based novel hand rehabilitation device. Micromachines 12.
• Biswal, P. and P. K. Mohanty, 2021 Development of quadruped walking robots: A review. Ain Shams Engineering Journal 12: 2017–2031.
• Bjelonic, M., N. Kottege, and P. Beckerle, 2016 Proprioceptive control of an over-actuated hexapod robot in unstructured terrain. In 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2042–2049.
• Chai, H., Y. Li, R. Song, G. Zhang, Q. Zhang, et al., 2021 A survey of the development of quadruped robots: Joint configuration, dynamic locomotion control method and mobile manipulation approach. Biomimetic Intelligence and Robotics p. 100029.
• Chawla, I. and A. Singla, 2021 Real-time stabilization control of a rotary inverted pendulum using LQR-based sliding mode controller. Arabian Journal for Science and Engineering 46: 2589– 2596.
• Choukchou-Braham, A., B. Cherki, M. Djemai, and K. Busawon, 2014 Analysis and Control of Underactuated Mechanical Systems. Springer-Verlag, New York.
• da Costa Barros, I. R. and T. P. Nascimento, 2021 Robotic mobile fulfillment systems: A survey on recent developments and research opportunities. Robotics and Autonomous Systems 137: 103729.
• Gonzalez-Aguirre, J. A., R. Osorio-Oliveros, K. L. Rodriguez- Hernandez, J. Lizarraga-Iturralde, R. M. Menendez, et al., 2021 Service robots: Trends and technology. Applied Sciences 11: 10702.
• González, C., J. E. Solanes, A. Muñoz, L. Gracia, V. Girbés-Juan, et al., 2021 Advanced teleoperation and control system for industrial robots based on augmented virtuality and haptic feedback. Journal of Manufacturing Systems 59: 283–298.
• Gritli, H., 2020 LMI-based robust stabilization of a class of inputconstrained uncertain nonlinear systems with application to a helicopter model. Complexity 2020: 7025761.
• Gritli, H. and S. Belghith, 2018 Robust feedback control of the underactuated Inertia Wheel Inverted Pendulum under parametric uncertainties and subject to external disturbances: LMI formulation. Journal of The Franklin Institute 355: 9150–9191.
• Gritli, H. and S. Belghith, 2021 LMI-based synthesis of a robust saturated controller for an underactuated mechanical system subject to motion constraints. European Journal of Control 57: 179–193.
• Gritli, H., S. Jenhani, and G. Carbone, 2022 Position control of robotic systems via an affine PD-based controller: Comparison between two design approaches. In 2022 5th International Conference on Advanced Systems and Emergent Technologies (IC_ASET), pp. 424–432.
• Gu, E. Y. L., 2013 Control of Robotic Systems, volume 1. Springer, Berlin, Heidelberg. Gualtieri, L., E. Rauch, and R. Vidoni, 2021 Development and validation of guidelines for safety in human-robot collaborative assembly systems. Computers & Industrial Engineering p. 107801.
• Hasan, S. K. and A. K. Dhingra, 2021 Development of a model reference computed torque controller for a human lower extremity exoskeleton robot. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 235: 1615–1637.
• Islam, M. R., M. Assad-Uz-Zaman, and M. H. Rahman, 2020 Design and control of an ergonomic robotic shoulder for wearable exoskeleton robot for rehabilitation. International Journal of Dynamics and Control 8: 312–325.
• Jafari, M., S. Mobayen, F. Bayat, and H. Roth, 2023 A nonsingular terminal sliding algorithm for swing and stance control of a prosthetic leg robot. Applied Mathematical Modelling 113: 13– 29.
• Jenhani, S., H. Gritli, and G. Carbone, 2022a Design and computation aid of command gains for the position control of manipulator robots. In 2022 International Conference on Decision Aid Sciences and Applications (DASA), pp. 1558–1564.
• Jenhani, S., H. Gritli, and G. Carbone, 2022b Design of an affine control law for the position control problem of robotic systems based on the development of a linear dynamic model. In 2022 5th International Conference on Advanced Systems and Emergent Technologies (IC_ASET), pp. 403–411.
• Jenhani, S., H. Gritli, and G. Carbone, 2022c Determination of conditions on feedback gains for the position control of robotic systems under an affine PD-based control law. In 2022 5th International Conference on Advanced Systems and Emergent Technologies (IC_ASET), pp. 518–526.
• Jenhani, S., H. Gritli, and G. Carbone, 2022d LMI-based optimization for the position feedback control of underactuated robotic systems via an affine PD controller: Case of the pendubot. In 2022 International Conference on Data Analytics for Business and Industry (ICDABI) (DATA’22), pp. 768–774, virtual, Bahrain.
• Jenhani, S., H. Gritli, and G. Carbone, 2022e Position control of Lagrangian robotic systems via an affine PID-based controller and using the LMI approach. In Advances in Italian Mechanism Science, edited by V. Niola, A. Gasparetto, G. Quaglia, and G. Carbone, pp. 727–737, Cham, Springer International Publishing.
• Jenhani, S., H. Gritli, and G. Carbone, 2022f Position feedback control of Lagrangian robotic systems via an affine PD-based control law. Part 1: Design of LMI conditions. In 2022 IEEE 2nd International Maghreb Meeting of the Conference on Sciences and Techniques of Automatic Control and Computer Engineering (MISTA), pp. 171–176
• Jenhani, S., H. Gritli, and G. Carbone, 2022g Position feedback control of Lagrangian robotic systems via an affine PD-based control law. Part 2: Improved results. In 2022 IEEE 2nd International Maghreb Meeting of the Conference on Sciences and Techniques of Automatic Control and Computer Engineering (MI-STA), pp. 177– 182.
• Jiang, Y., K. Lu, C. Gong, and H. Liang, 2020 Robust composite nonlinear feedback control for uncertain robot manipulators. International Journal of Advanced Robotic Systems 17: 1729881420914805.
• Kalita, B., J. Narayan, and S. K. Dwivedy, 2021 Development of active lower limb robotic-based orthosis and exoskeleton devices: A systematic review. International Journal of Social Robotics 3: 775–793.
• Kelly, R., V. S. Davila, and A. Loría, 2005 Control of Robot Manipulators in Joint Space. Advanced Textbooks in Control and Signal Processing, Springer-Verlag, London.
• Koditschek, D. E., 2021 What is robotics? why do we need it and how can we get it? Annual Review of Control, Robotics, and Autonomous Systems 4: 1–33.
• Krafes, S., Z. Chalh, and A. Saka, 2018 A review on the control of second order underactuated mechanical systems. Complexity 2018: 9573514.
• Kurdila, A. J. and P. Ben-Tzvi, 2019 Dynamics and Control of Robotic Systems. Control Process & Measurements, Wiley, first edition.
• Li, X., B. Liu, and L. Wang, 2020 Control system of the six-axis serial manipulator based on active disturbance rejection control. International Journal of Advanced Robotic Systems 17: 1729881420939476.
• Liu, P., M. N. Huda, L. Sun, and H. Yu, 2020 A survey on underactuated robotic systems: Bio-inspiration, trajectory planning and control. Mechatronics 72: 102443.
• Liu, Y. and H. Yu, 2013 A survey of underactuated mechanical systems. IET Control Theory Applications 7: 921–935.
• Mobayen, S., F. Tchier, and L. Ragoub, 2017 Design of an adaptive tracker for n-link rigid robotic manipulators based on supertwisting global nonlinear sliding mode control. International Journal of Systems Science 48: 1990–2002.
• Narayan, J. and S. K. Dwivedy, 2021 Robust LQR-based neuralfuzzy tracking control for a lower limb exoskeleton system with parametric uncertainties and external disturbances. Applied Bionics and Biomechanics 2021: 5573041.
• Nho, H. C. and P. Meckl, 2003 Intelligent feedforward control and payload estimation for a two-link robotic manipulator. IEEE/ASME transactions on mechatronics 8: 277–282.
• Parulski, P., P. Bartkowiak, and D. Pazderski, 2021, 11 Evaluation of linearization methods for control of the pendubot. Applied Sciences 11: 1–13.
• Perrusquia, A., J. A. Flores-Campos, and C. R. Torres-San-Miguel, 2020 A novel tuning method of PD with gravity compensation controller for robot manipulators. IEEE Access 8: 114773–114783.
• Singla, A. and G. Singh, 2017 Real-time swing-up and stabilization control of a cart-pendulum system with constrained cart movement. International Journal of Nonlinear Sciences and Numerical Simulation 18: 525–539.
• Spong, M. W., 2022 An historical perspective on the control of robotic manipulators. Annual Review of Control, Robotics, and Autonomous Systems 5: 1–31.
• Spong, M.W., S. Hutchinson, and M. Vidyasagar, 2020 Robot Modeling and Control. Robotics, John Wiley & Sons Inc, second edition. Tarnita, D., I. D. Geonea, D. Pisla, G. Carbone, B. Gherman, et al., 2022 Analysis of dynamic behavior of parreex robot used in upper limb rehabilitation. Applied Sciences 12.
• Tipary, B. and G. Erdos, 2021 Generic development methodology for flexible robotic pick-and-place workcells based on digital twin. Robotics and Computer-Integrated Manufacturing 71: 102140.
• Turki, F., H. Gritli, and S. Belghith, 2020 An LMI-based design of a robust state-feedback control for the master-slave tracking of an impact mechanical oscillator with double-side rigid constraints and subject to bounded-parametric uncertainty. Communications in Nonlinear Science and Numerical Simulation 82: 105020.
• Wang, J., W. Chen, X. Xiao, Y. Xu, C. Li, et al., 2021 A survey of the development of biomimetic intelligence and robotics. Biomimetic Intelligence and Robotics 1: 100001.
• Zhang, C. and Y. Wu, 2021 P-Rob six-degree-of-freedom robot manipulator dynamics modeling and anti-disturbance control. IEEE Access 9: 141403–141420.
• Zilong Zhang, C. S. S., 2022 Underactuated mechanical systems – a review of control design. Journal of Vibration Testing and System Dynamics 6: 21–51.