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The quasi-constrained dynamics is composed of motions not only onto the constraint space but also onto the unconstraint or the "freedom" space, which may occur when the system escapes or slips away from its constraint manifold during high-speed motion. Traditionally, slippage phenomenon, which has been an issue in the automobile industry, is usually ignored because of its high frequency and strong nonlinear features. Conventional Frobenius theorem is focused on the holonomic dynamics, which are integrable on the freedom space. On the other hand, a complementary Frobenius theorem (CFT) is proposed to release conventional constraints from "hard" to "soft' models. In this paper, we derive a geometric formulation instead of its algebraic counterpart for acatastatically nonholonomic systems in the viewpoint of topology. Besides, we propose a mixed fuzzy controller (MFC) for the nonholonomic system with escaping motions, which includes a traditional controller for the hard subsystem and a non-tradtional controller with fuzzy rules for another soft subsystem on the constraint manifold. The closedloop stability of'the nonholonomic system with an MFC scheme will be proved under admissible condtions. Finally, th proposed algorithm is applied to a wheeled vehicle with an anti-lock braking system (ABS) under the assumption of Coulomb's viscous friction. Computer simulation is used to jus* the results.