Abstract
Predefined-time stability contributes to constraining the tracking time of robotic manipulators, but the stringent judgment conditions restrict its practical application. This paper studies an adaptive practical predefined-time neural control scheme for uncertain multi-joint robotic manipulators with input saturation. First, a practical predefined-time stability criterion is established to ensure the closed-loop stability of uncertain systems. Then, the unknown robotic dynamic model can be approximated by radial basis function neural networks. Meanwhile, the input saturation of the robotic manipulator is compensated by introducing an adaptive term. Based on the constructed stability criterion, the proposed controller is proved to guarantee that the tracking error of the system converges to a small neighborhood of the origin within a predefined time and is independent of the initial state. Finally, the effectiveness of the proposed control scheme is emphasized by numerical simulations and experiments of a two-joint and a nine-joint robotic manipulator, respectively.
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References
Pan Y, Du P, Xue H, Lam HK (2020) Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance. IEEE Trans Fuzzy Syst 29(8):2388–2398
Wang H, Liu S, Yang X (2020) Adaptive neural control for non-strict-feedback nonlinear systems with input delay. Inf Sci 514:605–616
Sai H, Xu Z, Xu C, Wang X, Wang K, Zhu L (2022) Adaptive local approximation neural network control based on extraordinariness particle swarm optimization for robotic manipulators. J Mech Sci Technol 36(3):1469–1483
Haimo VT (1986) Finite time controllers. SIAM J Control Optim 24(4):760–770
Shao K, Zheng J, Huang K, Wang H, Man Z, Fu M (2019) Finite-time control of a linear motor positioner using adaptive recursive terminal sliding mode. IEEE Trans Industr Electron 67(8):6659–6668
Zhihong M, O’day M, Yu X (1999) A robust adaptive terminal sliding mode control for rigid robotic manipulators. J Intell Robot Syst 24(1):23–41
Yu X, Zhihong M (2002) Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Trans Circuits Syst I Fundam Theory Appl 49(2):261–264
Yang L, Yang J (2011) Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. Int J Robust Nonlinear Control 21(16):1865–1879
Polyakov A (2011) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110
Zuo Z (2015) Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl 9(4):545–552
Zuo Z (2015) Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica 54:305–309
Zuo Z, Han QL, Ning B, Ge X, Zhang XM (2018) An overview of recent advances in fixed-time cooperative control of multiagent systems. IEEE Trans Industr Inf 14(6):2322–2334
Ning B, Han QL, Zuo Z, Ding L, Lu Q, Ge X (2022) Fixed-time and prescribed-time consensus control of multi-agent systems and its applications: a survey of recent trends and methodologies. IEEE Trans Ind Inf
Su Y, Zheng C, Mercorelli P (2020) Robust approximate fixed-time tracking control for uncertain robot manipulators. Mech Syst Signal Process 135:106379
Sai H, Xu Z, Xia C, Sun X (2022) Approximate continuous fixed-time terminal sliding mode control with prescribed performance for uncertain robotic manipulators. Nonlinear Dyn 1–18
Yang P, Su Y (2021) Proximate fixed-time prescribed performance tracking control of uncertain robot manipulators. IEEE/ASME Trans Mechatron
Ba D, Li YX, Tong S (2019) Fixed-time adaptive neural tracking control for a class of uncertain nonstrict nonlinear systems. Neurocomputing 363:273–280
Wang F, Lai G (2020) Fixed-time control design for nonlinear uncertain systems via adaptive method. Syst Control Lett 140:104704
Hu Y, Yan H, Zhang H, Wang M, Zeng L (2022) Robust adaptive fixed-time sliding-mode control for uncertain robotic systems with input saturation. IEEE Trans Cybern 53(4):2636–2646
Chen M, Wang H, Liu X (2021) Adaptive practical fixed-time tracking control with prescribed boundary constraints. IEEE Trans Circuits Syst I Regul Pap 68(4):1716–1726
Sánchez-Torres JD, Gómez-Gutiérrez D, López E, Loukianov AG (2018) A class of predefined-time stable dynamical systems. IMA J Math Control Inf 35(Supplement_1):i1–i29
Muñoz-Vázquez AJ, Sánchez-Torres JD, Gutiérrez-Alcalá S, Jiménez-Rodríguez E, Loukianov AG (2019) Predefined-time robust contour tracking of robotic manipulators. J Franklin Inst 356(5):2709–2722
Munoz-Vazquez AJ, Sánchez-Torres JD, Jimenez-Rodriguez E, Loukianov AG (2019) Predefined-time robust stabilization of robotic manipulators. IEEE/ASME Trans Mechatron 24(3):1033–1040
Ni J, Liu L, Tang Y, Liu C (2019) Predefined-time consensus tracking of second-order multiagent systems. IEEE Trans Syst Man Cybern Syst 51(4):2550–2560
Sai H, Li Y, He S, Zhang E, Zhu M, Xu Z (2022) A nine-degree-of-freedom modular redundant robotic manipulator: development and experimentation. Proc Inst Mech Eng Part C J Mech Eng Sci 09544062221139968
Xie Z, Jin L (2022) Hybrid control of orientation and position for redundant manipulators using neural network. IEEE Trans Syst Man Cybern Syst
Muñoz-Vázquez AJ, Sánchez-Torres JD (2020) Predefined-time control of cooperative manipulators. Int J Robust Nonlinear Control 30(17):7295–7306
Shuzhi SG, Hang CC, Woon L (1997) Adaptive neural network control of robot manipulators in task space. IEEE Trans Ind Electron 44(6):746–752
Aldana-López R, Gómez-Gutiérrez D, Jiménez-Rodríguez E, Sánchez-Torres JD, Defoort M (2019) Enhancing the settling time estimation of a class of fixed-time stable systems. Int J Robust Nonlinear Control 29(12):4135–4148
Sánchez-Torres JD, Defoort M, Munoz-Vázquez AJA (2018) Second order sliding mode controller with predefined-time convergence. In: 15th International conference on electrical engineering, computing science and automatic control (CCE). IEEE 2018:1–4
Wu C, Yan J, Shen J, Wu X, Xiao B (2021) Predefined-time attitude stabilization of receiver aircraft in aerial refueling. IEEE Trans Circuits Syst II Express Briefs 68(10):3321–3325
Wang Z, Liang B, Sun Y, Zhang T (2019) Adaptive fault-tolerant prescribed-time control for teleoperation systems with position error constraints. IEEE Trans Ind Inf 16(7):4889–4899
Liu B, Hou M, Wu C, Wang W, Wu Z, Huang B (2021) Predefined-time backstepping control for a nonlinear strict-feedback system. Int J Robust Nonlinear Control 31(8):3354–3372
Sai H, Xu Z, He S, Zhang E, Zhu L (2022) Adaptive nonsingular fixed-time sliding mode control for uncertain robotic manipulators under actuator saturation. ISA Trans 123:46–60
Zhu G, Du J (2020) Robust adaptive neural practical fixed-time tracking control for uncertain Euler–Lagrange systems under input saturations. Neurocomputing 412:502–513
Jia S, Shan J (2019) Finite-time trajectory tracking control of space manipulator under actuator saturation. IEEE Trans Ind Electron 67(3):2086–2096
Jiménez-Rodríguez E, Loukianov AG, Sánchez-Torres JD (2017) A second order predefined-time control algorithm. In: 2017 14th international conference on electrical engineering, computing science and automatic control (CCE). IEEE, pp 1–6
Zhang N, Wang S, Hou Y, Zhang L (2020) A robust predefined-time stable tracking control for uncertain robot manipulators. IEEE Access 8:188600–188610
Wu Y, Li G, Zuo Z, Liu X, Xu P (2020) Practical fixed-time position tracking control of permanent magnet DC torque motor systems. IEEE/ASME Trans Mechatron 26(1):563–573
Bateman H (1953) Higher transcendental functions [volumes i-iii]. vol. 1. McGraw-Hill Book Company
Jin X (2018) Adaptive fixed-time control for MIMO nonlinear systems with asymmetric output constraints using universal barrier functions. IEEE Trans Autom Control 64(7):3046–3053
Qian C, Lin W (2001) Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst Control Lett 42(3):185–200
Sciavicco L, Siciliano B (2001) Modelling and control of robot manipulators. Springer
Jing C, Xu H, Niu X (2019) Adaptive sliding mode disturbance rejection control with prescribed performance for robotic manipulators. ISA Trans 91:41–51
Sai H, Xu Z, Han T, Wang X, Li H (2022) Observer-based free-will arbitrary time sliding mode control for uncertain robotic manipulators. J Vib Control 10775463221138327
Ge SS, Hang CC, Lee TH, Zhang T (2013) Stable adaptive neural network control, vol 13. Springer
Wen C, Zhou J, Liu Z, Su H (2011) Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Trans Autom Control 56(7):1672–1678
Sai H, Xu Z, Xu C, Wang X, Wang K, Zhu L (2022) Adaptive local approximation neural network control based on extraordinariness particle swarm optimization for robotic manipulators. J Mech Sci Technol 36(3):1469–1483
Chang W, Li Y, Tong S (2018) Adaptive fuzzy backstepping tracking control for flexible robotic manipulator. IEEE/CAA J Autom Sin 8(12):1923–1930
Chen B, Liu X, Liu K, Lin C (2009) Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6):1530–1535
Zhang L, Wang Y, Hou Y, Li H (2019) Fixed-time sliding mode control for uncertain robot manipulators. IEEE Access 7:149750–149763
Jin L, Zhang F, Liu M, Xu SSD (2022) Finite-time model predictive tracking control of position and orientation for redundant manipulators. IEEE Trans Ind Electron
Li R, Qiao H (2019) A survey of methods and strategies for high-precision robotic grasping and assembly tasks-some new trends. IEEE/ASME Trans Mechatron 24(6):2718–2732
Sun W, Diao S, Su SF, Sun ZY (2021) Fixed-time adaptive neural network control for nonlinear systems with input saturation. IEEE Trans Neural Netw Learn Syst
Van M (2019) An enhanced tracking control of marine surface vessels based on adaptive integral sliding mode control and disturbance observer. ISA Trans 90:30–40
Santos JC, Gouttefarde M, Chemori A (2022) A nonlinear model predictive control for the position tracking of cable-driven parallel robots. IEEE Trans Robot 38(4):2597–2616
Wu Y, Wang Y (2020) Asymptotic tracking control of uncertain nonholonomic wheeled mobile robot with actuator saturation and external disturbances. Neural Comput Appl 32:8735–8745
Wang Y, Zhu K, Chen B, Jin M (2020) Model-free continuous nonsingular fast terminal sliding mode control for cable-driven manipulators. ISA Trans 98:483–495
Kong L, He W, Yang W, Li Q, Kaynak O (2020) Fuzzy approximation-based finite-time control for a robot with actuator saturation under time-varying constraints of work space. IEEE Trans Cybern 51(10):4873–4884
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This work is partially supported by the National Natural Science Foundation of China (11972343).
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Sai, H., Xu, Z. & Zhang, E. Adaptive practical predefined-time neural tracking control for multi-joint uncertain robotic manipulators with input saturation. Neural Comput & Applic 35, 20423–20440 (2023). https://doi.org/10.1007/s00521-023-08797-2
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DOI: https://doi.org/10.1007/s00521-023-08797-2