doi: 10.3934/mfc.2022012
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Prescribed performance tracking control of multi-link robotic manipulator with uncertainties

1. 

School of Mechanical Engineering, Yangzhou University, Yangzhou, 225127, China

2. 

Jiangsu Engineering Center for Modern Agricultural Machinery and Agronomy Technology, Yangzhou, 225127, China

3. 

School of Electronic and Information Engineering, Harbin Institute of Technology, Shenzhen, 518055, China

4. 

China Academy of Information and Communications Technology, Beijing, 100191, China

*Corresponding author: Chao Chen

Received  January 2022 Revised  February 2022 Early access April 2022

Fund Project: The first author is supported by Jiangsu Agriculture Science and Technology innovation Fund (No.CX(21)3150), the Lvyangjinfeng Talent Program of Yangzhou(No.YZLYJF2020PHD048) and the Doctorate Project for Entrepreneurship and Innovation Talent Introduction Plan of Jiangsu Province (No.JSSCBS20211012)

This paper addresses the trajectory tracking problem with prescribed performance for a multi-link robotic manipulator subject to unknown dynamics and external disturbances. A predefined performance function is adopted to describe tracking errors' desired transient and steady-state performance. Then, the output error dynamics with performance constraints are transformed into an equivalent unconstrained system, whose stabilization is sufficient to guarantee the prescribed performance of the original system. An extended state observer with a friction model is designed to approximate unknown dynamics together with the unmeasurable velocity state, which extends the applicability of the proposed controller to manipulators with only position signals available. The friction model is lumped into it to improve the precision and velocity of estimation. It is proved via Lyapunov analysis that the proposed controller can theoretically guarantee the satisfaction of prescribed performance in the presence of uncertainties. The simulation results verify the reliability and effectiveness of the proposed method.

Citation: Chao Chen, Shanlin Yi, Feng Wang, Chengxi Zhang, Qingmin Yu. Prescribed performance tracking control of multi-link robotic manipulator with uncertainties. Mathematical Foundations of Computing, doi: 10.3934/mfc.2022012
References:
[1]

C. P. BechlioulisM. A. Demetriou and K. J. Kyriakopoulos, A distributed control and parameter estimation protocol with prescribed performance for homogeneous Lagrangian multi-agent systems, Auton. Robot., 42 (2018), 1525-1541.  doi: 10.1007/s10514-018-9700-2.

[2]

C. P. BechlioulisS. Heshmati-AlamdariG. C. Karras and K. J. Kyriakopoulos, Robust image-based visual servoing with prescribed performance under field of view constraints, IEEE Trans. Rob., 35 (2019), 1063-1070.  doi: 10.1109/TRO.2019.2914333.

[3]

C. P. Bechlioulis and G. A. Rovithakis, A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems, Automatica J. IFAC, 50 (2014), 1217-1226.  doi: 10.1016/j.automatica.2014.02.020.

[4]

A. CarronE. ArcariM. WermelingerL. Hewing and M. Hutter, Data-driven model predictive control for trajectory tracking with a robotic arm, IEEE Rob. Autom. Lett., 4 (2019), 3758-3765.  doi: 10.1109/LRA.2019.2929987.

[5]

W. ChangY. Li and S. Tong, Adaptive fuzzy backstepping tracking control for flexible robotic manipulator, IEEE/CAA J. Autom. Sin., 8 (2021), 1923-1930.  doi: 10.1109/JAS.2017.7510886.

[6]

C. L. P. ChenY.-J. Liu and G.-X. Wen, Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems, IEEE Trans. Cybern., 44 (2014), 583-593.  doi: 10.1109/TCYB.2013.2262935.

[7]

Z. ChuY. SunC. Wu and N. Sepehri, Active disturbance rejection control applied to automated steering for lane keeping in autonomous vehicles, Control Engrg. Pract., 74 (2018), 13-21.  doi: 10.1016/j.conengprac.2018.02.002.

[8]

J. J. Craig, Introduction to Robotics: Mechanics and Control, 3$^{rd}$ edition, Pearson Education India, Bengaluru, 2009.

[9]

H. Q. Du, Uncertain robotic manipulator system's tracking control based on fuzzy adaptive method, Int. J. Control Autom., 8 (2015), 153-160.  doi: 10.14257/ijca.2015.8.9.15.

[10]

Z. Q. Gao, Scaling and bandwidth-parameterization based controller tuning, Proceedings of the 2003 American Control Conference, Denver, CO, USA, 2003, 4989–4996. doi: 10.1109/ACC.2003.1242516.

[11]

J. Q. Han, From PID to active disturbance rejection control, IEEE Trans. Ind. Electron., 56 (2009), 900-906.  doi: 10.1109/TIE.2008.2011621.

[12]

S. Jung, Improvement of tracking control of a sliding mode controller for robot manipulators by a neural network, Int. J. Control Autom. Syst., 16 (2018), 937-943.  doi: 10.1007/s12555-017-0186-z.

[13]

G. LiD. SongS. XuL. Sun and J. Liu, A hybrid model and model-free position control for a reconfigurable manipulator, IEEE/ASME Trans. Mechatron., 24 (2019), 785-795.  doi: 10.1109/TMECH.2019.2893227.

[14]

H. LiuX. TianG. Wang and T. Zhang, Finite-time ${h_\infty }$ control for high-precision tracking in robotic manipulators using backstepping control, IEEE Trans. Ind. Electron., 63 (2016), 5501-5513.  doi: 10.1109/TIE.2016.2583998.

[15]

H. Liu and T. Zhang, Adaptive neural network finite-time control for uncertain robotic manipulators, J. Intell. Rob. Syst., 75 (2014), 363-377.  doi: 10.1007/s10846-013-9888-5.

[16]

J. NaQ. ChenX. Ren and Y. Guo, Adaptive prescribed performance motion control of servo mechanisms with friction compensation, IEEE Trans. Ind. Electron., 61 (2014), 486-494.  doi: 10.1109/TIE.2013.2240635.

[17]

P. R. OuyangJ. Acob and V. Pano, PD with sliding mode control for trajectory tracking of robotic system, Rob. Comput. Integr. Manuf., 30 (2014), 189-200.  doi: 10.1016/j.rcim.2013.09.009.

[18]

X. ShaoQ. Hu and Y. Shi, Adaptive pose control for spacecraft proximity operations with prescribed performance under spatial motion constraints, IEEE Trans. Control Syst. Technol., 29 (2021), 1405-1419.  doi: 10.1109/TCST.2020.3005966.

[19]

X. ShaoQ. HuY. Shi and B. Jiang, Fault-tolerant prescribed performance attitude tracking control for spacecraft under input saturation, IEEE Trans. Control Syst. Technol., 28 (2020), 574-582.  doi: 10.1109/TCST.2018.2875426.

[20]

M. Wang and A. Yang, Dynamic learning from adaptive neural control of robot manipulators with prescribed performance, IEEE Trans. Syst. Man Cybern. Syst., 47 (2017), 2244-2255.  doi: 10.1109/TSMC.2016.2645942.

[21]

W. Wang and Z. Gao, A comparison study of advanced state observer design techniques, Proceedings of the 2003 American Control Conference, Denver, CO, USA, 2003, 4754–4759. doi: 10.1109/ACC.2003.1242474.

[22]

J. WilsonM. Charest and R. Dubay, Non-linear model predictive control schemes with application on a 2 link vertical robot manipulator, Rob. Comput. Integr. Manuf., 41 (2016), 23-30.  doi: 10.1016/j.rcim.2016.02.003.

[23]

Y. WuR. HuangX. Li and S. Liu, Adaptive neural network control of uncertain robotic manipulators with external disturbance and time-varying output constraints, Neurocomputing, 323 (2019), 108-116.  doi: 10.1016/j.neucom.2018.09.072.

[24]

Y. YangJ. Tan and D. Yue, Prescribed performance control of one-DOF link manipulator with uncertainties and input saturation constraint, IEEE/CAA J. Autom. Sin., 6 (2019), 148-157.  doi: 10.1109/JAS.2018.7511099.

[25]

Z.-J. YangY. Fukushima and P. Qin, Decentralized adaptive robust control of robot manipulators using disturbance observers, IEEE Trans. Control Syst. Technol., 20 (2012), 1357-1365.  doi: 10.1109/TCST.2011.2164076.

[26]

C. Zhang, M.-Z. Dai, J. Wu, B. Xiao and B. Li, et al., Neural-networks and event-based fault-tolerant control for spacecraft attitude stabilization, Aerosp. Sci. Technol., 114 (2021). doi: 10.1016/j.ast.2021.106746.

[27]

C. ZhangP. DongH. LeungJ. Wu and K. Shen, Reset and prescribed performance approach to spacecraft attitude regulation, Aircraft Engrg. Aerospace Technol., 93 (2021), 1573-1581.  doi: 10.1108/AEAT-02-2021-0046.

[28]

C. ZhangJ. WangD. Zhang and X. Shao, Fault-tolerant adaptive finite-time attitude synchronization and tracking control for multi-spacecraft formation, Aerosp. Sci. Technol., 73 (2018), 197-209.  doi: 10.1016/j.ast.2017.12.004.

[29]

C. ZhangJ. WuC. K. AhnZ. Fei and C. Wei, Learning observer and performance tuning-based robust consensus policy for multiagent systems, IEEE Systems J., 16 (2022), 431-439.  doi: 10.1109/JSYST.2020.3047644.

[30]

H. ZhangJ. XianJ. ShiS. Wu and Z. Ma, High performance decoupling current control by linear extended state observer for three-phase grid-connected inverter with an LCL filter, IEEE Access, 8 (2020), 13119-13127.  doi: 10.1109/ACCESS.2020.2965650.

[31]

Q. Zheng, L. Q. Gaol and Z. Gao, On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics, 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, 2007. doi: 10.1109/CDC.2007.4434676.

[32]

Q. Zheng and F. Wu, Adaptive control design for uncertain polynomial nonlinear systems with parametric uncertainties, Internat. J. Adapt. Control Signal Process., 25 (2011), 502-518.  doi: 10.1002/acs.1215.

show all references

References:
[1]

C. P. BechlioulisM. A. Demetriou and K. J. Kyriakopoulos, A distributed control and parameter estimation protocol with prescribed performance for homogeneous Lagrangian multi-agent systems, Auton. Robot., 42 (2018), 1525-1541.  doi: 10.1007/s10514-018-9700-2.

[2]

C. P. BechlioulisS. Heshmati-AlamdariG. C. Karras and K. J. Kyriakopoulos, Robust image-based visual servoing with prescribed performance under field of view constraints, IEEE Trans. Rob., 35 (2019), 1063-1070.  doi: 10.1109/TRO.2019.2914333.

[3]

C. P. Bechlioulis and G. A. Rovithakis, A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems, Automatica J. IFAC, 50 (2014), 1217-1226.  doi: 10.1016/j.automatica.2014.02.020.

[4]

A. CarronE. ArcariM. WermelingerL. Hewing and M. Hutter, Data-driven model predictive control for trajectory tracking with a robotic arm, IEEE Rob. Autom. Lett., 4 (2019), 3758-3765.  doi: 10.1109/LRA.2019.2929987.

[5]

W. ChangY. Li and S. Tong, Adaptive fuzzy backstepping tracking control for flexible robotic manipulator, IEEE/CAA J. Autom. Sin., 8 (2021), 1923-1930.  doi: 10.1109/JAS.2017.7510886.

[6]

C. L. P. ChenY.-J. Liu and G.-X. Wen, Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems, IEEE Trans. Cybern., 44 (2014), 583-593.  doi: 10.1109/TCYB.2013.2262935.

[7]

Z. ChuY. SunC. Wu and N. Sepehri, Active disturbance rejection control applied to automated steering for lane keeping in autonomous vehicles, Control Engrg. Pract., 74 (2018), 13-21.  doi: 10.1016/j.conengprac.2018.02.002.

[8]

J. J. Craig, Introduction to Robotics: Mechanics and Control, 3$^{rd}$ edition, Pearson Education India, Bengaluru, 2009.

[9]

H. Q. Du, Uncertain robotic manipulator system's tracking control based on fuzzy adaptive method, Int. J. Control Autom., 8 (2015), 153-160.  doi: 10.14257/ijca.2015.8.9.15.

[10]

Z. Q. Gao, Scaling and bandwidth-parameterization based controller tuning, Proceedings of the 2003 American Control Conference, Denver, CO, USA, 2003, 4989–4996. doi: 10.1109/ACC.2003.1242516.

[11]

J. Q. Han, From PID to active disturbance rejection control, IEEE Trans. Ind. Electron., 56 (2009), 900-906.  doi: 10.1109/TIE.2008.2011621.

[12]

S. Jung, Improvement of tracking control of a sliding mode controller for robot manipulators by a neural network, Int. J. Control Autom. Syst., 16 (2018), 937-943.  doi: 10.1007/s12555-017-0186-z.

[13]

G. LiD. SongS. XuL. Sun and J. Liu, A hybrid model and model-free position control for a reconfigurable manipulator, IEEE/ASME Trans. Mechatron., 24 (2019), 785-795.  doi: 10.1109/TMECH.2019.2893227.

[14]

H. LiuX. TianG. Wang and T. Zhang, Finite-time ${h_\infty }$ control for high-precision tracking in robotic manipulators using backstepping control, IEEE Trans. Ind. Electron., 63 (2016), 5501-5513.  doi: 10.1109/TIE.2016.2583998.

[15]

H. Liu and T. Zhang, Adaptive neural network finite-time control for uncertain robotic manipulators, J. Intell. Rob. Syst., 75 (2014), 363-377.  doi: 10.1007/s10846-013-9888-5.

[16]

J. NaQ. ChenX. Ren and Y. Guo, Adaptive prescribed performance motion control of servo mechanisms with friction compensation, IEEE Trans. Ind. Electron., 61 (2014), 486-494.  doi: 10.1109/TIE.2013.2240635.

[17]

P. R. OuyangJ. Acob and V. Pano, PD with sliding mode control for trajectory tracking of robotic system, Rob. Comput. Integr. Manuf., 30 (2014), 189-200.  doi: 10.1016/j.rcim.2013.09.009.

[18]

X. ShaoQ. Hu and Y. Shi, Adaptive pose control for spacecraft proximity operations with prescribed performance under spatial motion constraints, IEEE Trans. Control Syst. Technol., 29 (2021), 1405-1419.  doi: 10.1109/TCST.2020.3005966.

[19]

X. ShaoQ. HuY. Shi and B. Jiang, Fault-tolerant prescribed performance attitude tracking control for spacecraft under input saturation, IEEE Trans. Control Syst. Technol., 28 (2020), 574-582.  doi: 10.1109/TCST.2018.2875426.

[20]

M. Wang and A. Yang, Dynamic learning from adaptive neural control of robot manipulators with prescribed performance, IEEE Trans. Syst. Man Cybern. Syst., 47 (2017), 2244-2255.  doi: 10.1109/TSMC.2016.2645942.

[21]

W. Wang and Z. Gao, A comparison study of advanced state observer design techniques, Proceedings of the 2003 American Control Conference, Denver, CO, USA, 2003, 4754–4759. doi: 10.1109/ACC.2003.1242474.

[22]

J. WilsonM. Charest and R. Dubay, Non-linear model predictive control schemes with application on a 2 link vertical robot manipulator, Rob. Comput. Integr. Manuf., 41 (2016), 23-30.  doi: 10.1016/j.rcim.2016.02.003.

[23]

Y. WuR. HuangX. Li and S. Liu, Adaptive neural network control of uncertain robotic manipulators with external disturbance and time-varying output constraints, Neurocomputing, 323 (2019), 108-116.  doi: 10.1016/j.neucom.2018.09.072.

[24]

Y. YangJ. Tan and D. Yue, Prescribed performance control of one-DOF link manipulator with uncertainties and input saturation constraint, IEEE/CAA J. Autom. Sin., 6 (2019), 148-157.  doi: 10.1109/JAS.2018.7511099.

[25]

Z.-J. YangY. Fukushima and P. Qin, Decentralized adaptive robust control of robot manipulators using disturbance observers, IEEE Trans. Control Syst. Technol., 20 (2012), 1357-1365.  doi: 10.1109/TCST.2011.2164076.

[26]

C. Zhang, M.-Z. Dai, J. Wu, B. Xiao and B. Li, et al., Neural-networks and event-based fault-tolerant control for spacecraft attitude stabilization, Aerosp. Sci. Technol., 114 (2021). doi: 10.1016/j.ast.2021.106746.

[27]

C. ZhangP. DongH. LeungJ. Wu and K. Shen, Reset and prescribed performance approach to spacecraft attitude regulation, Aircraft Engrg. Aerospace Technol., 93 (2021), 1573-1581.  doi: 10.1108/AEAT-02-2021-0046.

[28]

C. ZhangJ. WangD. Zhang and X. Shao, Fault-tolerant adaptive finite-time attitude synchronization and tracking control for multi-spacecraft formation, Aerosp. Sci. Technol., 73 (2018), 197-209.  doi: 10.1016/j.ast.2017.12.004.

[29]

C. ZhangJ. WuC. K. AhnZ. Fei and C. Wei, Learning observer and performance tuning-based robust consensus policy for multiagent systems, IEEE Systems J., 16 (2022), 431-439.  doi: 10.1109/JSYST.2020.3047644.

[30]

H. ZhangJ. XianJ. ShiS. Wu and Z. Ma, High performance decoupling current control by linear extended state observer for three-phase grid-connected inverter with an LCL filter, IEEE Access, 8 (2020), 13119-13127.  doi: 10.1109/ACCESS.2020.2965650.

[31]

Q. Zheng, L. Q. Gaol and Z. Gao, On stability analysis of active disturbance rejection control for nonlinear time-varying plants with unknown dynamics, 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, 2007. doi: 10.1109/CDC.2007.4434676.

[32]

Q. Zheng and F. Wu, Adaptive control design for uncertain polynomial nonlinear systems with parametric uncertainties, Internat. J. Adapt. Control Signal Process., 25 (2011), 502-518.  doi: 10.1002/acs.1215.

Figure 1.  The two-link planar manipulator
Figure 2.  The position tracking errors
Figure 3.  The control torques
Figure 4.  The disturbance estimation errors
Table 1.  Controller parameters
Controller Joint Parameters
PPC-FESO 1
2
${\mu _0} = 0.025, {\mu _\infty } = 0.005, l = 4, {\rho _1} = 1, {\rho _2} = 1, $
${k_1} = 0.5, {k_2} = 30$, ${\omega _{\rm{o}}} = 120, $ $ f_c = 2.6, f_v = 6$
${\mu _0} = 0.025, {\mu _\infty } = 0.005, l = 4, {\rho _1} = 1, {\rho _2} = 1, $
$ {k_1} = 0.5, {k_2} = 40$, ${\omega _{\rm{o}}} = 120, $ $ f_c = 4.8, f_v = 1.8 $
PD-SMC 1
2
${k_p} = 180, {k_d} = 50, {\omega _o} = 150$
${k_p} = 200, {k_d} = 35, {\omega _o} = 150$
ADRC 1
2
${k_p} = 350, {k_d} = 100, H = 65, \varphi = 0.3$
${k_p} = 300, {k_d} = 40, H = 25, \varphi = 0.3$
Controller Joint Parameters
PPC-FESO 1
2
${\mu _0} = 0.025, {\mu _\infty } = 0.005, l = 4, {\rho _1} = 1, {\rho _2} = 1, $
${k_1} = 0.5, {k_2} = 30$, ${\omega _{\rm{o}}} = 120, $ $ f_c = 2.6, f_v = 6$
${\mu _0} = 0.025, {\mu _\infty } = 0.005, l = 4, {\rho _1} = 1, {\rho _2} = 1, $
$ {k_1} = 0.5, {k_2} = 40$, ${\omega _{\rm{o}}} = 120, $ $ f_c = 4.8, f_v = 1.8 $
PD-SMC 1
2
${k_p} = 180, {k_d} = 50, {\omega _o} = 150$
${k_p} = 200, {k_d} = 35, {\omega _o} = 150$
ADRC 1
2
${k_p} = 350, {k_d} = 100, H = 65, \varphi = 0.3$
${k_p} = 300, {k_d} = 40, H = 25, \varphi = 0.3$
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