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Technical Brief

Fixed-Time Inverse Dynamics Control for Robot Manipulators

[+] Author and Article Information
Yuxin Su

School of Electro-Mechanical Engineering,
Xidian University,
Xi'an 710071, China
e-mail: yxsu@mail.xidian.edu.cn

Chunhong Zheng

School of Electronic Engineering,
Xidian University,
Xi'an 710071, China
e-mail: chzheng@xidian.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received August 15, 2018; final manuscript received January 23, 2019; published online February 27, 2019. Assoc. Editor: Richard Bearee.

J. Dyn. Sys., Meas., Control 141(6), 064502 (Feb 27, 2019) (7 pages) Paper No: DS-18-1378; doi: 10.1115/1.4042743 History: Received August 15, 2018; Revised January 23, 2019

This paper concerns with global fixed-time trajectory tracking of robot manipulators. A simple nonlinear inverse dynamics control (IDC) is proposed by using bi-limit homogeneity technique. Lyapunov stability theory and geometric bi-limit homogeneity technique are employed to prove global fixed-time tracking stability. It is proved that there exists a convergence time that is uniformly bounded a priori and such a bound is independent of the initial states such that the tracking errors converge to zero globally. The appealing advantages of the proposed control are that it is fairly easy to construct and has the global fixed-time tracking stability featuring faster transient and higher steady-state precision. Numerical simulation comparisons are provided to demonstrate the improved performance of the proposed approach.

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References

Incremona, G. P. , and Ferrara, A. , 2017, “ MPC for Robot Manipulators With Integral Sliding Modes Generation,” IEEE/ASME Trans. Mechatronics, 22(3), pp. 1299–1307. [CrossRef]
Zirkohi, M. M. , 2017, “ Direct Adaptive Function Approximation Techniques Based Control of Robot Manipulators,” ASME J. Dyn. Syst., Meas., Control, 140(1), p. 011006. [CrossRef]
Richter, H. , 2015, “ A Framework for Control of Robots With Energy Regeneration,” ASME J. Dyn. Syst., Meas., Control, 137(9), p. 0910041. [CrossRef]
Bhat, S. P. , and Bernstein, D. S. , 1998, “ Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrators,” IEEE Trans. Autom. Control, 43(5), pp. 678–682. [CrossRef]
Hong, Y. , Xu, Y. , and Huang, J. , 2002, “ Finite-Time Control for Robot Manipulators,” Syst. Control Lett., 46(4), pp. 243–253. [CrossRef]
Venkataraman, S. T. , and Gulati, S. , 1993, “ Control of Nonlinear Systems Using Terminal Sliding Modes,” ASME J. Dyn. Syst., Meas., Control, 115(3), pp. 554–560. [CrossRef]
Man, Z. , Paplinski, P. A. , and Wu, H. , 1994, “ A Robust MIMO Terminal Sliding Mode Control Scheme for Rigid Robotic Manipulators,” IEEE Trans. Autom. Control, 39(12), pp. 2464–2469. [CrossRef]
Tang, Y. , 1998, “ Terminal Sliding Mode Control for Rigid Robots,” Automatica, 34(1), pp. 51–56. [CrossRef]
Park, K.-B. , and Lee, J.-J. , 1996, “ Comments on ‘A Robust MIMO Terminal Sliding Mode Control Scheme for Rigid Robotic Manipulators’,” IEEE Trans. Autom. Control, 41(5), pp. 761–762. [CrossRef]
Feng, Y. , Yu, X. , and Man, Z. , 2002, “ Non-Singular Terminal Sliding Mode Control of Rigid Manipulators,” Automatica, 38(12), pp. 2159–2167. [CrossRef]
Yu, S. H. , Yu, X. H. , Shirinzadeh, B. J. , and Man, Z. , 2005, “ Continuous Finite-Time Control for Robotic Manipulators With Terminal Sliding Mode,” Automatica, 41(11), pp. 1957–1964. [CrossRef]
Jin, M. , Lee, J. , Chang, P. H. , and Choi, C. , 2009, “ Practical Nonsingular Terminal Sliding-Mode Control of Robot Manipulators for High-Accuracy Tracking Control,” IEEE Trans. Ind. Electron., 56(9), pp. 3593–3601. [CrossRef]
Yang, L. , and Yang, J. Y. , 2011, “ Nonsingular Fast Terminal Sliding-Mode Control for Nonlinear Dynamical Systems,” Int. J. Robust Nonlinear Control, 21(16), pp. 1865–1879. [CrossRef]
Barambones, O. , and Etxebarria, V. , 2002, “ Energy-Based Approach to Sliding Composite Adaptive Control for Rigid Robots With Finite Error Convergence Time,” Int. J. Control, 75(5), pp. 352–359. [CrossRef]
Zhao, D. Y. , Li, S. Y. , and Gao, F. , 2009, “ A New Terminal Sliding Mode Control for Robotic Manipulators,” Int. J. Control, 82(10), pp. 1804–1813. [CrossRef]
Su, Y. X. , 2017, “ Comments on ‘A New Terminal Sliding Mode Control for Robotic Manipulators’,” Int. J. Control, 90(2), pp. 247–254. [CrossRef]
Wang, L. Y. , Chai, T. Y. , and Zhai, L. F. , 2009, “ Neural-Network-Based Terminal Sliding-Mode Control of Robotic Manipulators Including Actuator Dynamics,” IEEE Trans. Ind. Electron., 56(9), pp. 3296–3304. [CrossRef]
Chiu, C.-S. , 2012, “ Derivative and Integral Terminal Sliding Mode Control for a Class of MIMO Nonlinear Systems,” Automatica, 48(2), pp. 316–326. [CrossRef]
Galicki, M. , 2015, “ Finite-Time Control of Robotic Manipulators,” Automatica, 51, pp. 49–54. [CrossRef]
Galicki, M. , 2016, “ Finite-Time Trajectory Tracking Control in a Task Space of Robotic Manipulators,” Automatica, 67, pp. 165–170. [CrossRef]
Van, M. , Ge, S. S. , and Ren, H. L. , 2017, “ Finite Time Fault Tolerant Control for Robot Manipulators Using Time Delay Estimation and Continuous Nonsingular Fast Terminal Sliding Mode Control,” IEEE Trans. Cybern., 47(7), pp. 1681–1693. [CrossRef]
Su, Y. X. , 2009, “ Global Continuous Finite-Time Tracking of Robot Manipulators,” Int. J. Robust Nonlinear Control, 19(17), pp. 1871–1885. [CrossRef]
Su, Y. X. , and Zheng, C. H. , 2011, “ Global Finite-Time Inverse Tracking Control of Robot Manipulators,” Rob. Comput.-Integr. Manuf., 27(3), pp. 550–557. [CrossRef]
Su, Y. X. , and Swevers, J. , 2014, “ Finite-Time Tracking Control for Robot Manipulators With Actuator Saturation,” Rob. Comput.-Integr. Manuf., 30(2), pp. 91–98. [CrossRef]
Andrieu, V. , Praly, L. , and Astolfi, A. , 2008, “ Homogeneous Approximation, Recursive Observer Design and Output Feedback,” SIAM J. Control Optim., 47(4), pp. 1814–1850. [CrossRef]
Polyakov, A. , 2012, “ Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems,” IEEE Trans. Autom. Control, 57(8), pp. 2106–2110. [CrossRef]
Polyakov, A. , Efimov, D. , and Perruquetti, W. , 2015, “ Finite-Time and Fixed-Time Stabilization: Implicit Lyapunov Function Approach,” Automatica, 51, pp. 332–340. [CrossRef]
Zuo, Z. Y. , 2015, “ Non-Singular Fixed-Time Consensus Tracking for Second-Order Multi-Agent Networks,” Automatica, 54, pp. 305–309. [CrossRef]
Zuo, Z. Y. , 2015, “ Non-Singular Fixed-Time Terminal Sliding Mode Control of Non-Linear Systems,” IET Control Theory Appl., 9(4), pp. 545–552. [CrossRef]
Ni, J. K. , Liu, L. , Liu, C. X. , Hu, X. Y. , and Li, S. L. , 2017, “ Fast Fixed-Time Nonsingular Terminal Sliding Mode Control and Its Application to Chaos Suppression in Power System,” IEEE Trans. Circuits Syst. II, 64(2), pp. 151–155. [CrossRef]
Tian, B. L. , Zuo, Z. Y. , Yan, X. M. , and Wang, H. , 2017, “ A Fixed-Time Output Feedback Control Scheme for Double Integrator System,” Automatica, 80(11), pp. 17–24. [CrossRef]
Zhang, Z. C. , and Wu, Y. Q. , 2017, “ Fixed-Time Regulation Control of Uncertain Nonholonomic Systems and Its Applications,” Int. J. Control, 90(7), pp. 1327–1344. [CrossRef]
Spong, M. W. , Hutchinson, S. , and Vidyasagar, M. , 2006, Robot Modeling and Control, Wiley, Hoboken, NJ.
Slotine, J.-J. E. , and Li, W. , 1991, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ.

Figures

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Fig. 1

Plots of f(x)=Sig(x)α and f(x)=x

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Fig. 2

Position tracking error comparison with FTSMC

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Fig. 3

Velocity tracking error comparison with FTSMC

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Fig. 4

Requested inputs of the proposed fixed IDC

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Fig. 5

Requested inputs of FTSMC

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Fig. 6

Position tracking error comparison with large gains of FTSMC

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Fig. 7

Requested inputs of large gains of FTSMC

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Fig. 8

Position tracking errors with FTSMC under parametric uncertainties and disturbances

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Fig. 9

Velocity tracking errors with FTSMC under parametric uncertainties and disturbances

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Fig. 10

Requested inputs with FTSMC under parametric uncertainties and disturbances

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Fig. 11

Position tracking error comparison with finite IDC

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Fig. 12

Velocity tracking error comparison with finite IDC

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Fig. 13

Requested inputs of the finite IDC

Tables

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