Mathematical modelling and theoretical analysis of nonholonomic kinematic systems with a class of rheonomous affine constraints |
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Authors: | Tatsuya Kai |
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Institution: | Department of Electrical Engineering, Faculty of Information Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan |
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Abstract: | In this paper, we deal with kinematic control systems subject to a class of rheonomous affine constraints. We first define A-rheonomous affine constraints and explain a geometric representation method for them. Next, we derive a necessary and sufficient condition for complete nonholonomicity of the A-rheonomous affine constraints. Then, a mathematical model of nonholonomic kinematic systems with A-rheonomous affine constraints (NKSARAC), which is included in the class of nonlinear affine control systems, is introduced. Theoretical analysis on linearly-approximated systems and accessibility for the NKSARAC is also shown. Finally, we apply the results to some physical examples in order to confirm the effectiveness of them. |
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Keywords: | Rheonomous affine constraints Rheonomous bracket Complete nonholonomicity Nonholonomic kinematic systems Linearly-approximated systems Accessibility |
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