This paper develops an intelligent braking system (IBS) to navigate escaping motions of wheeled robots with variable center of gravity. The piecewise mapping in geometric space instead of the traditionally pointwise coordinate transformation in algebraic space is developed for quasi-nonholonomic systems in the topological point of view. The escaping dynamics of wheeled robots, not only onto the constrained space but also onto the unconstrained space, occurs when the vehicle escapes from the constraint manifold during braking or cornering. Traditionally, such slippage phenomenon is usually ignored because of strong nonlinear features. The proposed IBS consists of a traditional controller designed for the “rigid” subsystem and an IBS controller designed for the “softened” subsystem. This paper is primarily focused on modeling, analysis and control issues of intelligent braking problems for moving robots with variable center of gravity. Finally, computer simulations of wheeled robots are carefully made under the assumption of Coulomb’s viscous friction to justify the advantages of the proposed IBS algorithm.