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Stability Analysis of an Underactuated Autonomous Underwater Vehicle Using Extended-Routh’s Stability Method

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Abstract

In this paper, a new approach to stability analysis of nonlinear dynamics of an underactuated autonomous underwater vehicle (AUV) is presented. AUV is a highly nonlinear robotic system whose dynamic model includes coupled terms due to the hydrodynamic damping factors. It is difficult to analyze the stability of a nonlinear dynamical system through Routh’s stability approach because it contains nonlinear dynamic parameters owing to hydrodynamic damping coefficients. It is also difficult to analyze the stability of AUVs using Lyapunov’s criterion and LaSalle’s invariance principle. In this paper, we proposed the extended-Routh’s stability approach to verify the stability of such nonlinear dynamic systems. This extended-Routh’s stability approach is much easier as compared to the other existing methods. Numerical simulations are presented to demonstrate the efficacy of the proposed stability verification of the nonlinear dynamic systems, e.g., an AUV system dynamics.

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Acknowledgement

The authors wish to thank the editor and the reviewers for their suggestions to improve the quality of the paper.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, National Institute of Science and Technology, Berhampur, 761008, India

    Basant Kumar Sahu

  2. Department of Electrical Engineering, National Institute of Technology, Rourkela, 769008, India

    Bidyadhar Subudhi

  3. Intelligent Systems Research Laboratory, College of Engineering, University of Saskatchewan, Saskatoon, S7N 5A9, Canada

    Madan Mohan Gupta

Authors
  1. Basant Kumar Sahu
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  2. Bidyadhar Subudhi
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  3. Madan Mohan Gupta
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Corresponding author

Correspondence to Basant Kumar Sahu.

Additional information

This work was supported by Naval Research Board (NRB), Defense Research Development Organization (DRDO), Government of India (No. DNRD/05/4003/NRB/160).

Recommended by Associate Editor Min Cheol Lee

Basant Kumar Sahu received the M.Tech. degree in electronics design technology from Tezpur Central University, India in 2008. He was awarded the Canadian Commonwealth Scholarship by the Canadian Bureau for International Education for pursuing a short term research in the University of Saskatchewan, Canada in 2012, where he continued research work from 2012 to 2013. He received the Ph.D. degree at the Department of Electrical Engineering, National Institute of Technology (NIT) Rourkela, India in 2015. He is working as an associate professor in the Department of Electrical Engineering, National Institute of Science and Technology, India.

His research interests include nonlinear control, underwater vehicle control, robotics and intelligent control.

Bidyadhar Subudhi received the B.Eng. degree in electrical engineering, from NIT Rourkela, India in 1988, the M.Tech. degree in control and instrumentation from Indian Institute of Technology Delhi (IIT Delhi), India in 1993, and the Ph.D. degree in control system engineering from University of Sheffield, UK in 2003. He is a professor at the Department of Electrical Engineering, National Institute of Technology Rourkela, India. He has been a post-doctoral research fellow in the Department of electrical and computer engineering, National University of Singapore (NUS), Singapore during May to November of 2005. He was a visiting professor at University of Saskatchewan, Canada during May to June, 2009, and also at Asian Institute of Technology (AIT), Bangkok during January to May, 2013. He is currently the coordinator of Centre of Excellence, Renewable Energy System, Centre of Excellence, Industrial Electronics and Robotics and Dean (Alumni Relation) NIT Rourkela. He is also the principal investigator in several research projects funded by Defense Research Development Organization (DRDO), Council of Scientific and Industrial Research (CSIR) and Department of Science and Technology (DST), including the international cooperation projects under UK India Education Research Initiative (UKIERI) and Department of Science & Technology (DST)–Government of India and Ministry of Education and Science (RMES) schemes. He has published 83 journal papers in prestigious journals such as IEEE transactions, Institution of Engineering and Technology (IET): Control Theory and Applications and Elsevier, and presented 70 research papers in many international conferences both in India and abroad. He has edited one book and contributed 3 book chapters. He chaired a number of technical sessions at international conferences. He is a fellow of the IET (UK) and a senior member of IEEE (USA). He is a regular reviewer of IEEE Translations on Systems, Man and Cybernetics, Power Delivery, Control System Technology, Neural Networks and Automatic Control.

His research interests include system identification and adaptive control, networked control system, control of flexible and underwater robots, control of renewable energy systems, estimation and filtering with application to power system.

Madan Mohan Gupta received the B. Eng. (Hons.), and the M. Eng. degrees in electronics-communications engineering and control systems from the Birla Engineering College (now the Birla Institute of Technology & Science), India in 1961 and 1962, respectively. He received the Ph.D. degree in adaptive control systems from University of Warwick, UK in 1967. He is the fellow of the Institute of Electrical and Electronics Engineers (IEEE). He was also elected as a fellow of the International Society for Optical Engineering (SPIE) for his contributions to the field of neuro-control and neuro-fuzzy systems. He was also elected fellow of the International Fuzzy Systems Association (IFSA) for his contributions to the field of fuzzy-neural computing systems. He is the professor emeritus of mechanical engineering, director of Intelligent Systems Research Laboratory, College of Engineering, University of Saskatchewan, Canada. He has authored or co-authored over 900 published research papers. He has recently co-authored the seminal book Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory. He has previously co-authored Introduction to Fuzzy Arithmetic: Theory and Applications (the first book on fuzzy arithmetic) and Fuzzy Mathematical Models in Engineering and Management Science. Both of these books have Japanese translations. Also, he has edited or co-edited 19 other books as well as many Conference. proceedings and journals in the fields of his research interests such as adaptive control systems, fuzzy computing, neuro-computing, neuro-vision systems, and neurocontrol systems. He is also developing some new architecture of computational neural networks and computational fuzzy neural networks for application to advanced robotics, aerospace, medical, industrial, and business systems and law.

His research interests include nonlinear control, neuro-vision systems, neuro-control systems, integration of fuzzy-neural systems, neuronal morphology of biological vision systems, intelligent and cognitive robotic systems, cognitive information, new paradigms in information processing, chaos in neural systems, fuzzy-neural logic in law, signal and image processing with applications to medical systems.

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Sahu, B.K., Subudhi, B. & Gupta, M.M. Stability Analysis of an Underactuated Autonomous Underwater Vehicle Using Extended-Routh’s Stability Method. Int. J. Autom. Comput. 15, 299–309 (2018). https://doi.org/10.1007/s11633-016-0992-4

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