An application of Lyapunov stability analysis to improve the performance of NARMAX models |
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| Authors: | Otar Akanyeti Iñaki Rañó Ulrich Nehmzow SA Billings |
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| Affiliation: | 1. School of Computer Science and Electronic Engineering, University of Essex, UK;2. Department of Computer Science and Systems Engineering, University of Zaragoza, Spain;3. School of Computing and Intelligent Systems, University of Ulster, UK;4. Department of Automatic Control and Systems Engineering, University of Sheffield, UK;1. College of Electrical and Information Engineering, Hunan University, Changsha, Hunan 410082, PR China;2. Department of Electrical Engineering, The City College of New York, 160 Convent Avenue, New York, NY 10031, USA;1. State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin, 150080, China;2. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta , Canada T6G 2V4;1. Department of Physics, Faculty of Science, Karadeniz Technical University, 61080 Trabzon, Turkey;2. Center of Excellence for Superconductivity Research, CESUR, Ankara University, 06830 Ankara, Turkey;3. Department of Elementary Science Education, Faculty of Education, Bayburt University, 69000 Bayburt, Turkey;4. Department of Energy Systems Engineering, Faculty of Engineering and Architecture, Sinop University, 57000 Sinop, Turkey;1. Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China;2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;3. Center for High-Energy Physics, Peking University, Beijing 100871, China;4. Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China |
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| Abstract: | Previously we presented a novel approach to program a robot controller based on system identification and robot training techniques. The proposed method works in two stages: first, the programmer demonstrates the desired behaviour to the robot by driving it manually in the target environment. During this run, the sensory perception and the desired velocity commands of the robot are logged. Having thus obtained training data we model the relationship between sensory readings and the motor commands of the robot using ARMAX/NARMAX models and system identification techniques. These produce linear or non-linear polynomials which can be formally analysed, as well as used in place of “traditional robot” control code.In this paper we focus our attention on how the mathematical analysis of NARMAX models can be used to understand the robot’s control actions, to formulate hypotheses and to improve the robot’s behaviour. One main objective behind this approach is to avoid trial-and-error refinement of robot code. Instead, we seek to obtain a reliable design process, where program design decisions are based on the mathematical analysis of the model describing how the robot interacts with its environment to achieve the desired behaviour. We demonstrate this procedure through the analysis of a particular task in mobile robotics: door traversal. |
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