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This paper considers the formation control of multiple skid-steered mobile robots with nonholonomic constraint in each robot dynamics. We propose a switching control method based on local sensor-based information for the group of robots. If the distance between leader and follower robots is larger than the switching threshold, a nonlinear control law is employed to make the followers move effectively toward the leader robot; otherwise, finite-time control based on feedback linearization is used to quickly stabilize the relative distance and orientation of the follower robots. Both stability analysis and simulations are provided and moreover, the formation control of Pioneer 3-AT mobile robots by the proposed method is shown.