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The trajectory-tracking problem for mobile robot is considered. A compound finite-time tracking control linearization algorithm base on feedback linearization and variable structure is proposed, and the reaching-control law is used to drive the steering angle trajectory with large inertial error exponentially toward the given switching surface neighborhood. When the steering angle trajectory is inside the neighborhood, the chattering-free control law based on continuous state-feedback drives the trajectory to the switching surface precisely while converting the original nonlinear system into a reduced system; state-feedback control law for the reduced system is then designed to stabilize the position error in finite time. Numerical simulations show the desired trajectory is attained fully in finite-time without chattering.