Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 314–337 | Cite as

Adaptive robust control strategy for rhombus-type lunar exploration wheeled mobile robot using wavelet transform and probabilistic neural network

  • Yi ZuoEmail author
  • Yaonan Wang
  • Xinzhi Liu


In this paper, we propose a stable tracking control rule for rhombus-type lunar exploration wheeled mobile robot (RLEWMR) with completely unknown dynamics and unmodeled disturbance. The control system adopts a wavelet transform and probabilistic neural network (WTPNN) with accurate approximation capability to represent the unknown dynamics of the RLEWMR, and it also uses an adaptive robust compensator to confront the inevitable approximation errors due to the finite number of wavelet bases functions and to disturbances. Adaptive learning algorithms are proposed to learn the parameters of WTPNN weight and robust compensator on line. Based on the Lyapunov stability theorem, the tracking stability of the closed-loop system, the convergence of the WTPNN weight-updating process, and boundedness of WTPNN weight estimation errors are all guaranteed. The effectiveness and efficiency of the proposed controller is demonstrated by simulation and experiment studies.


Adaptive wavelet transform and probabilistic neural network Robust tracking control Lyapunov stability theorem Nonholonomic mobile robot 

Mathematics Subject Classification



Compliance with ethical standards

Conflict of interest

All the authors declare that they have no conflict of interest.


This study was funded by National Natural Science Foundation of China (61304019, 51674042), Education Department of Hunan Province Science and Technology Program (15C0037, 16C0041), Key Laboratory Foundation for power technology of renewable energy sources of Hunan Province (2011KFJJ004), State grid corporation of science and technology innovation project (5216AB150003, 5216AB14003D), and China Institute of Electrical Engineering Power Youth Science and Technology Innovation Projects (201014).


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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.School of Energy and Power EngineeringChangsha University of Science and TechnologyChangshaPeople’s Republic of China
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  3. 3.College of Electric and Information TechnologyHunan UniversityChangshaPeople’s Republic of China
  4. 4.Collaborative Innovation Center of Clean Energy and Smart GridChangshaChina

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