Abstract
An equation can be transformed into an equivalent equation at a different level, which is termed equation equivalence or even generalized to be equation equivalency. In recent years, Zhang equivalency, more specifically, Zhang equation equivalency, i.e., a new equation equivalency originated from Zhang neurodynamics, has been proposed and investigated. Referring to Zhang equivalency and doing a careful investigation, we similarly find that an inequation can also be transformed into an equivalent inequation at a different level. The novel inequation equivalency named Zhang inequation equivalency (ZIE) is investigated in this paper. Then, ZIE is applied to acceleration-level redundant manipulator motion control. The configuration adjustment and cyclic motion generation of two types of redundant manipulators are investigated and simulated. Comparative experimental results verify the validity of the proposed ZIE. In fact, ZIE can also be applied in different actual projects according to practical requirements.
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References
Zhang, Y., Yang, M., Qiu, B., Li, J., Zhu, M.: From mathematical equivalence such as Ma equivalence to generalized Zhang equivalency including gradient equivalency. Theor. Comput. Sci. 817, 44–54 (2020)
Zhang, Y., Yang, M., Huang, H., Xiao, M., Hu, H.: New discrete-solution model for solving future different-level linear inequality and equality with robot manipulator control. IEEE Trans. Ind. Inform. 15(4), 1975–1984 (2019)
Li, J., Mao, M., Zhang, Y., Qiu, B.: Different-level algorithms for control of robotic systems. Appl. Math. Model. 77, 922–933 (2020)
Zhang, Y., Li, Z., Yang, M., Ming, L., Guo, J.: Jerk-level Zhang Neurodynamics equivalency of bound constraints, equation constraints, and objective indices for cyclic motion of robot-arm systems. IEEE Trans. Neural Netw. Learn. Syst. 34(6), 3005–3018 (2021)
Tang, Z., Tan, N., Zhang, Y.: Velocity-layer Zhang equivalency for time-varying joint limits avoidance of redundant robot manipulator. IET Control Theor. Appl. 16(18), 1909–1921 (2022)
Zhang, Y., Chou, Y., Chen, J., Zhang, Z., Xiao, L.: Presentation, error analysis and numerical experiments on a group of 1-step-ahead numerical differentiation formulas. J. Comput. Appl. Math. 239(1), 406–414 (2013)
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., He, L., Hu, C., Guo, J.: General four-step discrete-time zeroing and derivative dynamics applied to time-varying nonlinear optimization. J. Comput. Appl. Math. 347, 314–329 (2019)
Zhang, Y., Li, S., Kadry, S., Liao, B.: Recurrent neural network for kinematic control of redundant manipulators with periodic input disturbance and physical constraints. IEEE Trans. Cybern. 49(12), 4194–4205 (2019)
Xiao, L., Zhang, Z., Li, S.: Solving time-varying system of nonlinear equations by finite-time recurrent neural networks with application to motion tracking of robot manipulators. IEEE Trans. Syst. Man Cybern. Syst. 49(11), 2210–2220 (2019)
Guo, D., Xu, F., Li, Z., Nie, Z., Shao, H.: Design, verification, and application of new discrete-time recurrent neural network for dynamic nonlinear equations solving. IEEE Trans. Ind. Inform. 14(9), 3936–3945 (2018)
Xiao, L., Li, K., Duan, M.: Computing time-varying quadratic optimization with finite-time convergence and noise tolerance: a unified framework for zeroing neural network. IEEE Trans. Neural Netw. Learn. Syst. 30(11), 3360–3369 (2019)
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)
Oppenheim, A.V., Willsky, A.S., Nawab, S.H.: Signals and Systems. Prentice Hall, New Jersey (1998)
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)
Jin, L., Li, S.: Distributed task allocation of multiple robots: a control perspective. IEEE Trans. Syst. Man Cybern. Syst. 48(5), 693–701 (2018)
Zhang, Y., Zhang, Z.: Repetitive motion planning and control of redundant robot manipulators. Spinger-Verlag, Berlin (2013). https://doi.org/10.1007/978-3-642-37518-7
Mathews, J.H., Fink, K.D., Nawab, S.H.: Numerical Methods Using MATLAB, 4th edn. Prentice Hall, New Jersey (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, Z., Zhang, Y.: Acceleration-level cyclic-motion generation of constrained redundant robots tracking different paths. IEEE Trans. Syst. Man Cybern. B, Cybern. 42(4), 1257–1269 (2012)
Acknowledgements
This work is aided by the National Natural Science Foundation of China under Grant 61976230, the Project Supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme under Grant 2018, and also the Key-Area Research and Development Program of Guangzhou under Grant 202007030004.
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Lu, J., Yang, M., Tan, N., Hu, H., Zhang, Y. (2024). Computer Simulations of Applying Zhang Inequation Equivalency and Solver of Neurodynamics to Redundant Manipulators at Acceleration Level. In: Luo, B., Cheng, L., Wu, ZG., Li, H., Li, C. (eds) Neural Information Processing. ICONIP 2023. Lecture Notes in Computer Science, vol 14447. Springer, Singapore. https://doi.org/10.1007/978-981-99-8079-6_19
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