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This paper presents a model predictive control (MPC) approach for multivehicle formation taking into account collision avoidance and velocity limitation with reduced computational burden. The first part of the paper constructs a formation control law using feedback linearization with MPC in order to reduce the optimal control problem to a mixed-integer quadratic programming problem for a group of unicycles. The second part constructs a new branch-and-bound (B& B) -based algorithm for collision-avoidance problems. Numerical examples and experiments show that the proposed method significantly reduces computation time.