Abstract
This paper presents a modeling technique and analysis based on nonlinear control theory for kinematic systems subject affine constraints. Affine constraints are more general constraints as linear constraints that many researchers have been studied. We have already modeled and investigated kinematic systems subject affine constraints in, however, we introduce a new analysis method for the systems in this paper. We first define affine constraints and affine/non-affine variables, and explain a condition for nonholonomicity of affine constraints. Next, nonholonomic kinematic systems with affine constraints (NKSAC) are derived from affine constriants and control inputs. We then analyze the NKSAC from the view point of nonlinear control theory. Especially, we focus on the most basic issues of nonlinear contro systems, local accessibility, small-time local controllability and local asymptotic stabilizability. By using the analysis method we propose in this paper, we can derive simpler conditions for the NKSAC in comparison with. Finally, some physical examples are illustrated in order to confirm our results.
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