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In this paper, we deal with nonholonomic dynamical system based on the Lagrangian formulation. In modeling nonholonomic control systems, we especially focus on vakonomic mechanics, which is one of the constrained variation methods to derive the equations of motions of constrained systems. Using vakonomic mechanics, we introduce the vakonomic affine system (VAS) and analyze it theoretically in the context of nonlinear control theory. Then we consider control problems of the VAS and show simulation results to demonstrate the effectiveness of our theory.