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The aim of this paper is to introduce a nonlinear error framework for nonholonomic mobile robots for which a robust tracking controller is synthesized such that the overall feedback error system is globally asymptotically stable (GAS); this, in turn, accomplishes the desired trajectory tracking of the control, since the errors are driven to the equilibrium. In contrast to locally asymptotically stability or globally uniformly ultimately boundedness, which discusses the asymptotic stability in the region around the initial states and equilibrium or the states being in the small vicinity of equilibrium for sufficiently large time, GAS assures, for any initial error, the error trajectory approaches the origin, no matter how large the error is. It is shown in this paper that the time-varying inertia matrix of the nonholonomic mobile robots is chosen to be a quadratic Lyapunov candidate for its symmetric positive definiteness nature, which plays a key role of successfully synthesizing a norm-based sliding-mode controller. It is this particular designed controller that fulfills GAS of the nonholonomic mobile robots. A robustness issue with respect to parametric uncertainties and disturbances is also considered.