Asymmetric integral barrier function-based tracking control of constrained robots

Tan Zhang; Pianpian Yan; Tan Zhang; Pianpian Yan

doi:10.3934/math.2024019

AIMS Mathematics

2024, Volume 9, Issue 1: 319-339. doi: 10.3934/math.2024019

Previous Article Next Article

Research article

Asymmetric integral barrier function-based tracking control of constrained robots

Tan Zhang ,
Pianpian Yan ^,

School of Electrical and Optoelectronic Engineering, West Anhui University, Lu'an 237012, China

Received: 02 September 2023 Revised: 22 November 2023 Accepted: 23 November 2023 Published: 29 November 2023
MSC : 90C26, 90C30

In this paper, a new-type time-varying asymmetric integral barrier function is designed to handle the state constraint of nonlinear systems. The barrier Lyapunov function is developed by building an integral upper limit function with respect to transformation errors over an open set to cope with the position constraint of the robotic system. We know that the symmetric time-invariant constraint is only a particular situation of the asymmetric time-variant constraint, and thus compared to existing methods, it is capable of handling more general and broad practical engineering issues. We show that under the integral barrier Lyapunov function combining a disturbance observer-based tracking controller, the position vector tracks a desired trajectory successfully, while the constraint boundary is never violated. It can certify the exponential asymptotic stability of the robotic tracking system by using the given inequality relationship on barrier function and Lyapunov analysis. Finally, the feasibility of the presented algorithm is indicated by completing the simulations.
- integral barrier function,
- constraints,
- tracking control,
- nonlinear system,
- robot
Citation: Tan Zhang, Pianpian Yan. Asymmetric integral barrier function-based tracking control of constrained robots[J]. AIMS Mathematics, 2024, 9(1): 319-339. doi: 10.3934/math.2024019

Related Papers:

Abstract

In this paper, a new-type time-varying asymmetric integral barrier function is designed to handle the state constraint of nonlinear systems. The barrier Lyapunov function is developed by building an integral upper limit function with respect to transformation errors over an open set to cope with the position constraint of the robotic system. We know that the symmetric time-invariant constraint is only a particular situation of the asymmetric time-variant constraint, and thus compared to existing methods, it is capable of handling more general and broad practical engineering issues. We show that under the integral barrier Lyapunov function combining a disturbance observer-based tracking controller, the position vector tracks a desired trajectory successfully, while the constraint boundary is never violated. It can certify the exponential asymptotic stability of the robotic tracking system by using the given inequality relationship on barrier function and Lyapunov analysis. Finally, the feasibility of the presented algorithm is indicated by completing the simulations.

References

[1]	K. Lim, M. Eslami, Adaptive controller designs for robot manipulator systems using Lyapunov direct method, IEEE Trans. Autom. Control, 30 (1985), 1229–1233. https://doi.org/10.1109/TAC.1985.1103873 doi: 10.1109/TAC.1985.1103873
[2]	M. Hinze, A. Schmidt, R. I. Leine, The direct method of Lyapunov for nonlinear dynamical systems with fractional damping, Nonlinear Dyn., 102 (2020), 2017–2037. https://doi.org/10.1007/s11071-020-05962-3 doi: 10.1007/s11071-020-05962-3
[3]	K. P. Tee, S. S. Ge, E. Tay, Barrier lyapunov functions for the control of output-constrained nonlinear systems, Automatica, 45 (2009), 918–927. https://doi.org/10.1016/j.automatica.2008.11.017 doi: 10.1016/j.automatica.2008.11.017
[4]	T. Hu, Z. Lin, Control systems with actuator saturation: analysis and design, Birkhauser, 2001. https://doi.org/10.1007/978-1-4612-0205-9
[5]	E. Gilbert, I. Kolmanovsky, Nonlinear tracking control in the presence of state and control constraints: a generalized reference governor, Automatica, 38 (2002), 2063–2073. https://doi.org/10.1016/S0005-1098(02)00135-8 doi: 10.1016/S0005-1098(02)00135-8
[6]	Y. Li, Z. Ma, S. Tong, Adaptive fuzzy output-constrained fault-tolerant control of nonlinear stochastic large-scale systems with actuator faults, IEEE Trans. Cybern., 47 (2017), 2362–2376. https://doi.org/10.1109/TCYB.2017.2681683 doi: 10.1109/TCYB.2017.2681683
[7]	P. Du, H. Liang, S. Zhao, C. K. Ahn, Neural-based decentralized adaptive finite-time control for nonlinear large-scale systems with time-varying output constraints, IEEE Trans. Syst. Man Cybern. Syst., 51 (2019), 3136–3147. https://doi.org/10.1109/TSMC.2019.2918351 doi: 10.1109/TSMC.2019.2918351
[8]	X. Yuan, B. Chen, C. Lin, Prescribed finite-time adaptive fuzzy control via output feedback for output-constrained nonlinear systems, Int. J. Fuzzy Syst., 25 (2023), 1055–1068. https://doi.org/10.1007/s40815-022-01422-9 doi: 10.1007/s40815-022-01422-9
[9]	L. Wang, J. Dong, C. Xi, Event-triggered adaptive consensus for fuzzy output-constrained multi-agent systems with observers, J. Franklin Inst., 357 (2020), 82–105. https://doi.org/10.1016/j.jfranklin.2019.09.033 doi: 10.1016/j.jfranklin.2019.09.033
[10]	F. Chen, D. V. Dimarogonas, Leader follower formation control with prescribed performance guarantees, IEEE Trans. Control Networks Syst., 8 (2021), 450–461. https://doi.org/10.1109/TCNS.2020.3029155 doi: 10.1109/TCNS.2020.3029155
[11]	F. Fotiadis, G. A. Rovithakis, Prescribed performance control for discontinuous output reference tracking, IEEE Trans. Autom. Control, 66 (2021), 4409–4416. https://doi.org/10.1109/TAC.2020.3046216 doi: 10.1109/TAC.2020.3046216
[12]	W. He, Y. Chen, Z. Yin, Adaptive neural network control of an uncertain robot with full-state constraints, IEEE Trans. Cybern., 46 (2016), 620–629. https://doi.org/10.1109/TCYB.2015.2411285 doi: 10.1109/TCYB.2015.2411285
[13]	S. Zhang, Y. Dong, Y. Ouyang, Z. Yin, K. Peng, Adaptive neural control for robotic manipulators with output constraints and uncertainties, IEEE Trans. Neural Networks Learn. Syst., 29 (2018), 5554–5564. https://doi.org/10.1109/TNNLS.2018.2803827 doi: 10.1109/TNNLS.2018.2803827
[14]	W. He, H. Huang, S. S. Ge, Adaptive neural network control of a robotic manipulator with time-varying output constraintsv, IEEE Trans. Cybern., 47 (2017), 3136–3147. https://doi.org/10.1109/TCYB.2017.2711961 doi: 10.1109/TCYB.2017.2711961
[15]	Y. J. Liu, S. Lu, S. Tong, Neural network controller design for an uncertain robot with time-varying output constraint, IEEE Trans. Syst. Man Cybern. Syst., 47 (2017), 2060–2068. https://doi.org/10.1109/TSMC.2016.2606159 doi: 10.1109/TSMC.2016.2606159
[16]	X. Yu, W. He, H. Li, J. Sun, Adaptive fuzzy full-state and output-feedback control for uncertain robots with output constraint, IEEE Trans. Syst. Man Cybern. Syst., 51 (2021), 6994–7007. https://doi.org/10.1109/TSMC.2019.2963072 doi: 10.1109/TSMC.2019.2963072
[17]	W. Sun, S. F. Su, J. Xia, V. T. Nguyen, Adaptive fuzzy tracking control of flexible-joint robots with full-state constraints, IEEE Trans. Syst. Man Cybern. Syst., 49 (2019), 2201–2209. https://doi.org/10.1109/TSMC.2018.2870642 doi: 10.1109/TSMC.2018.2870642
[18]	Y. J. Liu, S. Tong, C. L. P. Chen, D. J. Li, Adaptive NN control using integral barrier lyapunov functionals for uncertain nonlinear block-triangular constraint systems, IEEE Trans. Cybern., 47 (2017), 3747–3757. https://doi.org/10.1109/TCYB.2016.2581173 doi: 10.1109/TCYB.2016.2581173
[19]	L. Liu, T. Gao, Y. J. Liu, S. Tong, C. L. P. Chen, L. Ma, Time-varying IBLFs-based adaptive control of uncertain nonlinear systems with full state constraints, Automatica, 129 (2021), 109595. https://doi.org/10.1016/j.automatica.2021.109595 doi: 10.1016/j.automatica.2021.109595
[20]	Z. L. Tang, S. S. Ge, K. P. Tee, W. He, Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints, IEEE Trans. Syst. Man Cybern. Syst., 46 (2016), 1618–1629. https://doi.org/10.1109/TSMC.2015.2508962 doi: 10.1109/TSMC.2015.2508962
[21]	K. P. Tee, S. S. Ge, Control of state-constrained nonlinear systems using integral barrier Lyapunov functionals, 2012 IEEE 51st IEEE Conference on Decision and Control, 2012. https://doi.org/10.1109/CDC.2012.6426196 doi: 10.1109/CDC.2012.6426196
[22]	B. S. Kim, S. J. Yoo, Approximation-based adaptive control of uncertain non-linear pure-feedback systems with full state constraints, IET Control Theory Appl., 8 (2014), 2070–2081. https://doi.org/10.1049/iet-cta.2014.0254 doi: 10.1049/iet-cta.2014.0254
[23]	D. J. Li, J. Li, L. Shu, Adaptive control of nonlinear systems with full state constraints using integral barrier Lyapunov functionals, Neurocomputing, 186 (2016), 90–96. https://doi.org/10.1016/j.neucom.2015.12.075 doi: 10.1016/j.neucom.2015.12.075
[24]	T. Gao, T. Li, Y. J. Liu, S. Tong, IBLF-based adaptive neural control of state-constrained uncertain stochastic nonlinear systems, IEEE Trans. Neural Networks Learn. Syst., 33 (2022), 7345–7356. https://doi.org/10.1109/TNNLS.2021.3084820 doi: 10.1109/TNNLS.2021.3084820
[25]	Y. Wei, Y. Wang, C. K. Ahn, D. Duan, IBLF-based finite-time adaptive fuzzy output-feedback control for uncertain mimo nonlinear state-constrained systems, IEEE Trans. Fuzzy Syst., 29 (2021), 3389–3400. https://doi.org/10.1109/TFUZZ.2020.3021733 doi: 10.1109/TFUZZ.2020.3021733
[26]	D. Zhang, P. Ma, Y. Du, T. Chao, Integral barrier Lyapunov function-based three-dimensional low-order integrated guidance and control design with seeker's field-of-view constraint, Aerosp. Sci. Technol., 116 (2021), 106886. https://doi.org/10.1016/j.ast.2021.106886 doi: 10.1016/j.ast.2021.106886
[27]	Y. H. Liu, Y. Liu, Y. F. Liu, C. Y. Su, Adaptive fuzzy control with global stability guarantees for unknown strict-feedback systems using novel integral barrier Lyapunov functions, IEEE Trans. Syst. Man Cybern. Syst., 52 (2022), 4336–4348. https://doi.org/10.1109/TSMC.2021.3094975 doi: 10.1109/TSMC.2021.3094975
[28]	L. Tang, K. He, Y. Chen, Y. J. Liu, S. Tong, Integral BLF-based adaptive neural constrained regulation for switched systems with unknown bounds on control gain, IEEE Trans. Neural Networks Learn. Syst., 34 (2023), 8579–8588. https://doi.org/10.1109/TNNLS.2022.3151625 doi: 10.1109/TNNLS.2022.3151625
[29]	X. Liang, H. Wang, Y. Zhang, Adaptive nonsingular terminal sliding mode control for rehabilitation robots, Comput. Electron. Eng., 99 (2022), 107718. https://doi.org/10.1016/j.compeleceng.2022.107718 doi: 10.1016/j.compeleceng.2022.107718
[30]	K. P. Tee, B. Ren, S. S. Ge, Control of nonlinear systems with time-varying output constraints, Automatica, 47 (2011), 2511–2516. https://doi.org/10.1016/j.automatica.2011.08.044 doi: 10.1016/j.automatica.2011.08.044
[31]	Z. Zheng, M. Feroskhan, Path following of a surface vessel with prescribed performance in the presence of input saturation and external disturbances, IEEE ASME Trans. Mechatron., 22 (2017), 2564–2575. https://doi.org/10.1109/TMECH.2017.2756110 doi: 10.1109/TMECH.2017.2756110
[32]	W. Sun, S. F. Su, G. Dong, W. Bai, Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints, IEEE Trans. Syst. Man Cybern. Syst., 51 (2021), 1496–1506. https://doi.org/10.1109/TSMC.2019.2898204 doi: 10.1109/TSMC.2019.2898204
[33]	Q. Zhang, D. He, Adaptive fuzzy sliding exact tracking control based on high-order log-type time-varying blfs for high-order nonlinear systems, IEEE Trans. Fuzzy Syst., 31 (2023), 14–24. https://doi.org/10.1109/TFUZZ.2022.3176681 doi: 10.1109/TFUZZ.2022.3176681
[34]	D. Cui, W. Zou, J. Guo, Z. Xiang, Adaptive fault-tolerant decentralized tracking control of switched stochastic uncertain nonlinear systems with time-varying delay, Int. J. Adapt. Control Signal Process., 36 (2022), 2971-2987. https://doi.org/10.1002/acs.3491 doi: 10.1002/acs.3491
[35]	Y. Zhang, J. Guo, Z. Xiang, Finite-time adaptive neural control for a class of nonlinear systems with asymmetric time-varying full-state constraints, IEEE Trans. Neural Networks Learn. Syst., 2022. https://doi.org/10.1109/TNNLS.2022.3164948 doi: 10.1109/TNNLS.2022.3164948

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)