Abstract
Input disturbances and physical constraints are important issues in the kinematic control of redundant manipulators. In this chapter, we present a novel recurrent neural network to simultaneously address the periodic input disturbance, joint angle constraint, and joint velocity constraint, and optimize a general quadratic performance index. The presented recurrent neural network applies to both regulation and tracking tasks. Theoretical analysis shows that, with the presented neural network, the end-effector tracking and regulation errors asymptotically converge to zero in the presence of both input disturbance and the two constraints. Simulation examples and comparisons with an existing controller are also presented to validate the effectiveness and superiority of the presented controller.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Li, S., Zhang, Y., Jin, L.: Kinematic control of redundant manipulators using neural networks. IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2243–2254 (2017)
Klein, C.A., Huang, C.-H.: Review of pseudoinverse control for use with kinematically redundant manipulators. IEEE Trans. Syst. Man Cybern. SMC-13(2), 245–250 (1983)
Liao, B., Liu, W.: Pseudoinverse-type bi-criteria minimization scheme for redundancy resolution of robot manipulators. Robotica 33(10), 2100–2113 (2015)
Flacco, F., Luca, A.: Discrete-time redundancy resolution at the velocity level with acceleration/torque optimization properties. Robot. Auton. Syst. 70, 191–201 (2015)
Klein, C.A., Kee, K.B.: The nature of drift in pseudoinverse control of kinematically redundant manipulators. IEEE Trans. Robot. Autom. 5(2), 231–234 (1989)
Zhang, Y., Wang, J., Xia, Y.: A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits. IEEE Trans. Neural Netw. 14(3), 658–667 (2003)
Huang, S., Peng, Y., Wei, W., Xiang, J.: Clamping weighted least-norm method for the manipulator kinematic control with constraints. Int. J. Control 89(11), 2240–2249 (2016)
Cheng, F.T., Chen, T.H., Sun, Y.Y.: Resolving manipulator redundancy under inequality constraints. IEEE Trans. Robot. Autom. 10(1), 65–71 (1994)
Patchaikani, P.K., Behera, L., Prasad, G.: A single network adaptive critic-based redundancy resolution scheme for robot manipulators. IEEE Trans. Ind. Electron. 59(8), 3241–3253 (2012)
He, W., Huang, B., Dong, Y., Li, Z., Su, C.: Adaptive neural network control for robotic manipulators with unknown deadzone. IEEE Trans. Cybern. 48(9), 2670–2682 (2018)
Li, D., Liu, Y., Tong, S., Chen, C.L.P., Li, D.: Neural networks-based adaptive control for nonlinear state constrained systems with input delay. IEEE Trans. Cybern. 49(4), 1249–1258 (2019)
Guo, D., Yan, L., Nie, Z.: Design, analysis, and representation of novel five-step dtzd algorithm for time-varying nonlinear optimization. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4248–4260 (2018)
Yang, C., Li, Z., Cui, R., Xu, B.: Neural network-based motion control of underactuated wheeled inverted pendulum models. IEEE Trans. Neural Netw. Learn. Syst. 25(11), 2004–2016 (2014)
Jin, L., Li, S., Hu, B., Liu, M., Yu, J.: Noise-suppressing neural algorithm for solving time-varying system of linear equations: a control-based approach. IEEE Trans. Ind. Inform. 15(1), 236–246 (2019)
Jin, L., Li, S., Hu, B., Liu, M.: A survey on projection neural networks and their applications. Appl. Soft Comput. 76, 533–544 (2019)
Xiao, L., Li, K., Tan, Z., Zhang, Z., Liao, B., Chen, K., Jin, L., Li, S.: Nonlinear gradient neural network for solving system of linear equations. Inf. Process. Lett. 142, 35–40 (2019)
Xiang, Q., Liao, B., Xiao, L., Lin, L., Li, S.: Discrete-time noise-tolerant Zhang neural network for dynamic matrix pseudoinversion. Soft Comput. 23(3), 755–766 (2019)
Xiao, L., Li, S., Yang, J., Zhang, Z.: A new recurrent neural network with noise-tolerance and finite-time convergence for dynamic quadratic minimization. Neurocomputing 285, 125–132 (2018)
Xiao, L., Liao, B., Li, S., Chen, K.: Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations. Neural Netw. 98, 102–113 (2018)
Xiao, L., Zhang, Z., Zhang, Z., Li, W., Li, S.: Design, verification and robotic application of a novel recurrent neural network for computing dynamic Sylvester equation. Neural Netw. 105, 185–196 (2018)
Zhang, Z., Lu, Y., Zheng, L., Li, S., Yu, Z., Li, Y.: A new varying-parameter convergent-differential neural-network for solving time-varying convex QP problem constrained by linear-equality. IEEE Trans. Autom. Control 63(12), 4110–4125 (2018)
Jin, L., Li, S.: Nonconvex function activated zeroing neural network models for dynamic quadratic programming subject to equality and inequality constraints. Neurocomputing 267, 107–113 (2017)
Jin, L., Li, S., Liao, B., Zhang, Z.: Zeroing neural networks: a survey. Neurocomputing 267, 597–604 (2017)
Mao, M., Li, J., Jin, L., Li, S., Zhang, Y.: Enhanced discrete-time Zhang neural network for time-variant matrix inversion in the presence of bias noises. Neurocomputing 207, 220–230 (2016)
Jin, L., Zhang, Y., Li, S.: Integration-enhanced Zhang neural network for real-time-varying matrix inversion in the presence of various kinds of noises. IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2615–2627 (2016)
Li, S., Li, Y.: Nonlinearly activated neural network for solving time-varying complex sylvester equation. IEEE Trans. Cybern. 44(8), 1397–1407 (2014)
Li, S., Li, Y., Wang, Z.: A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application. Neural Netw. 39, 27–39 (2013)
Hopfield, J.J., Tank, D.W.: Neural’ computation of decisions in optimization problems. Biol. Cybern. 52(3), 141–152 (1985)
Zhang, Y., Chen, S., Li, S., Zhang, Z.: Adaptive projection neural network for kinematic control of redundant manipulators with unknown physical parameters. IEEE Trans. Ind. Electron. 65(6), 4909–4920 (2017)
Xia, Y., Feng, G., Wang, J.: A primal-dual neural network for online resolving constrained kinematic redundancy in robot motion control. IEEE Trans. Syst. Man Cybern. B Cybern. 35(1), 54–64 (2005)
Zhang, Y., Wang, J., Xu, Y.: A dual neural network for bi-criteria kinematic control of redundant manipulators. IEEE Trans. Robot. Autom. 18(6), 923–931 (2002)
Zhang, Y., Wang, J.: Obstacle avoidance for kinematically redundant manipulators using a dual neural network. IEEE Trans. Syst. Man Cybern. B Cybern. 34(1), 752–759 (2004)
Zhang, Y., Ge, S.S., Lee, T.H.: A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators. IEEE Trans. Syst. Man Cybern. B Cybern. 34(5), 2126–2132 (2004)
Jin, L., Li, S., La, H.M., Luo, X.: Manipulability optimization of redundant manipulators using dynamic neural networks. IEEE Trans. Ind. Electron. 64(6), 4710–4720 (2017)
Zhang, Y., Li, S., Gui, J., Luo, X.: Velocity-level control with compliance to acceleration-level constraints: a novel scheme for manipulator redundancy resolution. IEEE Trans. Ind. Inform. 14(3), 921–930 (2018)
Guo, D., Zhang, Y.: Acceleration-level inequality-based MAN scheme for obstacle avoidance of redundant robot manipulators. IEEE Trans. Ind. Electron. 61(12), 6903–6914 (2014)
Zhang, Z., et al.: A varying-parameter convergent-differential neural network for solving joint-angular-drift problems of redundant robot manipulators. IEEE/ASME Trans. Mechatron. 23(2), 679–689 (2018)
Xiao, L., et al.: Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator. IEEE Trans. Ind. Inform. 14(1), 98–105 (2018)
Zhang, Z., Beck, A., Magnenat-Thalmann, N.: Human-like behavior generation based on head-arms model for robot tracking external targets and body parts. IEEE Trans. Cybern. 45(8), 1390–1400 (2015)
Chen, D., Zhang, Y.: A hybrid multi-objective scheme applied to redundant robot manipulators. IEEE Trans. Autom. Sci. Eng. 14(3), 1337–1350 (2017)
Li, S., Chen, S., Liu, B., Li, Y., Liang, Y.: Decentralized kinematic control of a class of collaborative redundant manipulators via recurrent neural networks. Neurocomputing 91, 1–10 (2012)
Li, S., He, J., Li, Y., Rafique, U.: Distributed recurrent neural networks for cooperative control of manipulators: a game-theoretic perspective. IEEE Trans. Neural Netw. Learn. Syst. 28(2), 415–426 (2017)
Jin, L., Zhang, Y.: G2-type SRMPC scheme for synchronous manipulation of two redundant robot arms. IEEE Trans. Cybern. 45(2), 153–164 (2015)
Hou, Z.G., Cheng, L., Tan, M.: Multicriteria optimization for coordination of redundant robots using a dual neural network. IEEE Trans. Syst. Man Cybern. B Cybern. 40(4) 1075–1087 (2010)
Jin, L., Li, S., Luo, X., Li, Y., Qin, B.: Neural dynamics for cooperative control of redundant robot manipulators. IEEE Trans. Ind. Inform. 14(9), 3812–3821 (2018)
Zhang, Y., Li, S.: A neural controller for image-based visual servoing of manipulators with physical constraints. IEEE Trans. Neural Netw. Learn. Syst. 29(11), 5419–5429 (2018)
Jin, L., Li, S.: Distributed task allocation of multiple robots: a control perspective. IEEE Trans. Syst. Man Cybern. Syst. 48(5), 693–701 (2018)
Wang, Z., et al.: Neural network learning adaptive robust control of an industrial linear motor-driven stage with disturbance rejection ability. IEEE Trans. Ind. Inform. 13(5), 2172–2183 (2017)
Chen, W., Yang, J., Guo, L., Li, S.: Disturbance-observer-based control and related methods-an overview. IEEE Trans. Ind. Electron. 63(2), 1083–1095 (2016)
Liu, F., Li, Y., Cao, Y., She, J., Wu, M.: A two-layer active disturbance rejection controller design for load frequency control of interconnected power system. IEEE Trans. Power Electorn. 31(4), 3320–3321 (2016)
Fedele, G., Ferrise, A.: On the uncertainty on the phase of a stable linear system in the periodic disturbance cancellation problem. IEEE Trans. Autom. Control 61(9), 2720–2726 (2016)
Muramatsu, H., Katsura, S.: An Adaptive periodic-disturbance observer for periodic-disturbance suppression. IEEE Trans. Ind. Inform. 14(10), 4446–4456 (2018)
Li, S., Zhou, M., Luo, X.: Modified primal-dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises. IEEE Trans. Neural Netw. Learn. Syst. 29(10), 4791–4801 (2018)
Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. Wiley, New York (2006)
Guo, D., Zhang, Y.: A new inequality-based obstacle-avoidance MVN scheme and its application to redundant robot manipulators. IEEE Trans. Syst. Man Cybern. C Appl. Rev. 42(6), 1326–1340 (2012)
Zhang, Z., Zheng, L., Yu, J., Li, Y., Yu, Z.: Three recurrent neural networks and three numerical methods for solving a repetitive motion planning scheme of redundant robot manipulators. IEEE/ASME Trans. Mechatron. 22(3), 1423–1434 (2017)
Assal, S.F.M.: Learning from hint for the conservative motion of the constrained industrial redundant manipulators. Neural Comput. App. 23(6), 1649–6660 (2013)
Kong, Y., Lu, H., Xue, Y., Xia, H.: Terminal neural computing: finite-time convergence and its applications. Neurocomputing 217, 133–141 (2016)
Dosiek, L., Pillay, P.: Cogging torque reduction in permanent magnet machines. IEEE Trans. Ind. Appl. 43(6), 1565–1571 (2007)
Zhang, Y., Ge, S.S.: Design and analysis of a general recurrent neural network model for time-varying matrix inversion. IEEE Trans. Neural Netw. 16(6), 1477–1490 (2005)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)
Gao, X.B.: Exponential stability of globally projected dynamic systems. IEEE Trans. Neural Netw. 14(2), 426–431 (2003)
Oppenheim, A.V., Willsky, A.S.: Signals & Systems. Prentice-Hall, Englewood Cliffs (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zhang, Y., Li, S., Zhou, X. (2020). Redundancy Resolution with Periodic Input Disturbance. In: Deep Reinforcement Learning with Guaranteed Performance. Studies in Systems, Decision and Control, vol 265. Springer, Cham. https://doi.org/10.1007/978-3-030-33384-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-33384-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-33383-6
Online ISBN: 978-3-030-33384-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)