Mathematical modelling and theoretical analysis of nonholonomic kinematic systems with a class of rheonomous affine constraints

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...

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Bibliographic Details
Published inApplied mathematical modelling Vol. 36; no. 7; pp. 3189 - 3200
Main Author Kai, Tatsuya
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2012
Subjects
Accessibility
Complete nonholonomicity
Control systems
Kinematics
Linearly-approximated systems
Mathematical analysis
Mathematical models
Modelling
Nonholonomic kinematic systems
Nonlinearity
Representations
Rheonomous affine constraints
Rheonomous bracket
Linearly-approximated systems
Nonholonomic kinematic systems
Rheonomous bracket
Accessibility
Rheonomous affine constraints
Complete nonholonomicity
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Summary: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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ISSN:0307-904X
DOI:10.1016/j.apm.2011.10.015