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Solving time-varying inverse kinematics problem of wheeled mobile manipulators using Zhang neural network with exponential convergence

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Abstract

A mobile manipulator is a robotic device composed of a mobile platform and a stationary manipulator fixed to the platform. The forward kinematics problem for such mobile manipulators has a mathematical analytic solution; however, the inverse kinematics problem is mathematically intractable (especially for satisfying real-time requirements). To obtain the accurate solution of the time-varying inverse kinematics for mobile manipulators, a special class of recurrent neural network, named Zhang neural network (ZNN), is exploited and investigated in this article. It is theoretically proven that such a ZNN model globally and exponentially converges to the solution of the time-varying inverse kinematics for mobile manipulators. In addition, the kinematics equations of the mobile platform and the manipulator are integrated into one system, and thus the resultant solution can co-ordinate simultaneously the wheels and the manipulator to fulfill the end-effector task. For comparison purposes, a gradient neural network (GNN) is developed for solving time-varying inverse kinematics problem of wheeled mobile manipulators. Finally, we conduct extensive tracking-path simulations performed on a wheeled mobile manipulator using such a ZNN model. The results substantiate the efficacy and high accuracy of the ZNN model for solving time-varying inverse kinematics problem of mobile manipulators. Besides, by comparing the simulation results of the GNN and ZNN models, the superiority of the ZNN model is demonstrated clearly.

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Acknowledgments

This study is supported by the National Natural Science Foundation of China (under Grants 61075121 and 60935001), the Specialized Research Fund for the Doctoral Program of Institutions of Higher Education of China (under Project Number 20100171110045), and the Sun Yat-sen University Innovative Talents Cultivation Program for PhD students. Besides, both the authors of the article are the joint claimants of the first authorship.

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Authors and Affiliations

  1. College of Information Science and Engineering, Jishou University, Jishou , 416000, People’s Republic of China

    Lin Xiao

  2. School of Information Science and Technology, Sun Yat-sen University, Guangzhou , 510006, People’s Republic of China

    Lin Xiao & Yunong Zhang

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  1. Lin Xiao
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  2. Yunong Zhang
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Correspondence to Yunong Zhang.

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Xiao, L., Zhang, Y. Solving time-varying inverse kinematics problem of wheeled mobile manipulators using Zhang neural network with exponential convergence. Nonlinear Dyn 76, 1543–1559 (2014). https://doi.org/10.1007/s11071-013-1227-7

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  • DOI: https://doi.org/10.1007/s11071-013-1227-7

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