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This paper investigates a nonlinear-model-predictive-control (NMPC)-strategy-based distributed leader-follower consensus multi-robot formation system. The control objective of this system is to design a group of nonholonomic robots to converge into the desired geometric pattern and to track a designed path. A directed graph that specifies communication topology for the formation is given. A leader-follower consensus formation problem based on the mobile robot kinematic model is obtained, which is further reformulated into a constrained nonlinear minimization problem through the NMPC strategy. A general projection neural network (GPNN) is implemented to efficiently derive the optimal control inputs for the robots. The simulation results verify the effectiveness of the proposed formation algorithm.