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 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.