Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-10T22:06:46.814Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust approximate constraint following control design for collaborative robots system and experimental validation

Published online by Cambridge University Press:  03 January 2025

Haohua Liu ,
Shengchao Zhen Open the ORCID record for Shengchao Zhen [Opens in a new window] ,
Xiaoli Liu Open the ORCID record for Xiaoli Liu [Opens in a new window] ,
Hongmei Zheng ,
Liansheng Gao  and
Ye-Hwa Chen
Haohua Liu
Affiliation:
School of Mechanical Engineering, Hefei University of Technology, Hefei, Anhui 230009, PR China
Shengchao Zhen*
Affiliation:
School of Mechanical Engineering, Hefei University of Technology, Hefei, Anhui 230009, PR China Intelligent Manufacturing Institute Of Hefei University Of Technology, Hefei, Anhui 230051, PR China
Xiaoli Liu
Affiliation:
School of Artificial Intelligence, Anhui University, Hefei, Anhui 230601, PR China
Hongmei Zheng
Affiliation:
School of Mechanical Engineering, Hefei University of Technology, Hefei, Anhui 230009, PR China
Liansheng Gao
Affiliation:
Hangzhou Huger Medical Robotics Co., Ltd., Hangzhou, Zhejiang 310002, PR China
Ye-Hwa Chen
Affiliation:
The George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology, Atlanta, Georgia 30332, USA
*
Corresponding author: Shengchao Zhen; Email: zhenshengchao@qq.com
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper presents a novel control method aimed at enhancing the trajectory tracking accuracy of two-link mechanical systems, particularly nonlinear systems that incorporate uncertainties such as time-varying parameters and external disturbances. Leveraging the Udwadia–Kalaba equation, the algorithm employs the desired system trajectory as a servo constraint. First, the system’s constraints to construct its dynamic equation and apply generalized constraints from the constraint equation to an unconstrained system. Second, we design a robust approximate constraint tracking controller for manipulator control and establish its stability using Lyapunov’s law. Finally, we numerically simulate and experimentally validate the controller on a collaborative platform using model-based design methods.

Keywords

robust controlU–K equationLyapunov methodnonlinear controlconstraint followingcollaborative robots
Type
Research Article
Information
Robotica , First View , pp. 1 - 19
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Corless, M. J. and Leitmann, G., “Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems,” IEEE Trans. Automatic Control 26(5), 1139–1144 (2003).CrossRefGoogle Scholar
CHEN, Y. H., “On the deterministic performance of uncertain dynamical systems,” Int. J. Control 43(5), 1557–1579 (1986).CrossRefGoogle Scholar
Corless, M., “Control of uncertain nonlinear systems,” J. Dyn. Syst. Meas. Control 115(2B), 362–372 (1993).CrossRefGoogle Scholar
Lee, J., Chang, P. H., Yu, B. and Jin, M., “An adaptive pid control for robot manipulators under substantial payload variations,” IEEE Access 8(99), 1–1 (2020).Google Scholar
Li, T., Yang, S.-H., Sun, Z.-Y. and Tan, Q.-Q., “Tracking control design for a class of generalized high-order nonlinearsystems with serious uncertainties,” in 2016 35th Chinese Control Conference (CCC), Chengdu, China. IEEE, 692–697 (2016).CrossRefGoogle Scholar
Maggi, G. and Rodriguez-Clare, A., “On countervailing incentives,” J. Econ. Theory 66(1), 238–263 (1995).CrossRefGoogle Scholar
Gibbs, J. W., “On the fundamental formulae of dynamics,” Am. J. Math. 2(1), 49–64 (1879).CrossRefGoogle Scholar
Udwadia, F. E. and Kalaba, R. E., “A new perspective on constrained motion,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, (1992).Google Scholar
Abramova, I. and Latyshev, S., “Using the fundamental equation of constrained motion with inequality constraints,” Appl. Math. Comput. 215(8), 2858–2876 (2009).Google Scholar
Udwadia, F. E. and Kalaba, R. E., “Nonideal constraints and lagrangian dynamics,” J. Aerospace Eng. 13(1), 17–22 (2000).CrossRefGoogle Scholar
Udwadia, F. E., “On constrained motion,” Appl. Math. Comput. 164(2), 313–320 (2005).Google Scholar
Udwadia, F. E. and Kalaba, R. E., “Explicit equations of motion for mechanical systems with nonideal constraints,” J. Appl. Mech. 68(3), 462–467 (2001).CrossRefGoogle Scholar
Chen, Y. H., “Equations of motion of constrained mechanical systems: Given force depends on constraint force,” Mechatronics 9(4), 411–428 (1999).CrossRefGoogle Scholar
Chen, Y.-H., “Second-order constraints for equations of motion of constrained systems,” IEEE/ASME Trans. Mechatronics 3(3), 240–248 (1998).CrossRefGoogle Scholar
Chen, Y. H., “Mechanical systems under servo constraints: The Lagrange’s approach,” Mechatronics 15(3), 317–337 (2005).CrossRefGoogle Scholar
Chen, Y.-H., “Constraint-following servo control design for mechanical systems,” J. Vib. Control 15(3), 369–389 (2009).CrossRefGoogle Scholar
Chen, Y. H., “Approximate constraint-following of mechanical systems under uncertainty,” Nonlinear Dyn. Syst. Theory 8(4), 329–337 (2008).Google Scholar
Chen, Y. H. and Zhang, X., “Adaptive robust approximate constraint-following control for mechanical systems,” J. Frankl. Inst. 347(1), 69–86 (2010).CrossRefGoogle Scholar
Schutte, A. D., “Permissible control of general constrained mechanical systems,” J. Frankl. Inst. 347(1), 208–227 (2010).CrossRefGoogle Scholar
Avanzini, G. B., Zanchettin, A. M. and Rocco, P., “Constrained model predictive control for mobile robotic manipulators,” Robotica 36(1), 19–38 (2018).CrossRefGoogle Scholar
Qin, Q. and Gao, G., “Screw dynamic modeling and novel composite error-based second-order sliding mode dynamic control for a bilaterally symmetrical hybrid robot,” Robotica 39(7), 1–17 (2021).CrossRefGoogle Scholar
Oh, S.-R., Bien, Z. and Suh, I. H., “A model algorithmic learning method for continuous-path control of a robot manipulator,” Robotica 8(1), 31–36 (1990).CrossRefGoogle Scholar
Guo, Q., Yu, T. and Jiang, D., “Robust h∞ positional control of 2-dof robotic arm driven by electro-hydraulic servo system,” Isa Trans. 59, 55–64 (2015).CrossRefGoogle ScholarPubMed
Rigatos, G., Siano, P. and Raffo, G., “A nonlinear h-infinity control method for multi-dof robotic manipulators,” Nonlinear Dyn. 88(1), 1–20 (2017).CrossRefGoogle Scholar
Truong, L. V., Huang, S. D., Yen, V. T. and Cuong, P. V., “Adaptive trajectory neural network tracking control for industrial robot manipulators with deadzone robust compensator,” Int. J. Control Autom. 18(3), 2423–2434 (2020).CrossRefGoogle Scholar
Truong, T. N., Kang, H. J. and Le, T. D., “Adaptive neural sliding mode control for 3-dof planar parallel manipulators,” ISCSIC 2019: 2019 3rd International Symposium on Computer Science and Intelligent Control, (2019).CrossRefGoogle Scholar
Islam, S. and Liu, P. X., “Output feedback sliding mode control for robot manipulators,” Robotica 28(7), 975–987 (2010).CrossRefGoogle Scholar
Van, M., Ge, S. S. and Ren, H., “Finite time fault tolerant control for robot manipulators using time delay estimation and continuous nonsingular fast terminal sliding mode control,” IEEE T. Cybernetics 47(7), 1681–1693 (2017).CrossRefGoogle Scholar
Huang, K., Xian, Y., Zhen, S. and Sun, H., “Robust control design for a planar humanoid robot arm with high strength composite gear and experimental validation,” Mech. Syst. Signal Pr. 155, 107442 (2021).CrossRefGoogle Scholar
Ma, J., Cheng, Z., Zhang, X., Tomizuka, M. and Lee, T. H., “Optimal decentralized control for uncertain systems by symmetric gauss–seidel semi-proximal alm,” IEEE Trans. Automat. Contr. 66(11), 5554–5560 (2021).CrossRefGoogle Scholar
Chen, Y. H., “Second-order constraints for equations of motion of constrained systems,” IEEE/ASME Trans. mechatronics: A joint publication of the IEEE Industrial Electronics Society and the ASME Dynamic Systems and Control Division 3, 3 (1998).Google Scholar
Kovincic, N., Müller, A., Gattringer, H., Weyrer, M., Schlotzhauer, A. and Brandstötter, M., “Dynamic parameter identification of the universal robots ur5,” Proceedings of the Austrian Robotics Workshop, 42, (2019).Google Scholar