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We present a leader-follower-based adaptive formation control method for electrically driven nonholonomic mobile robots with limited information. First, an adaptive observer is developed under the condition that the velocity measurement is not available. With the proposed adaptive observer, the formation control part is designed to achieve the desired formation and guarantee the collision avoidance. In addition, neural network is employed to compensate the actuator saturation, and the projection algorithm is used to estimate the velocity information of the leader. It is shown, by using the Lyapunov theory, that all errors of the closed-loop system are uniformly ultimately bounded. Simulation results are presented to illustrate the performance of the proposed control system.