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In this paper, the problem of formation control with regard to leader–follower mobile robots in the presence of disturbances and model uncertainties, without needing to know the velocity of the leader robot, is presented. For this purpose, at first, a first-order kinematic model of leader–follower and leader–leader formations is obtained, and considering the absolute velocity of the leader robots as an uncertainty, a robust adaptive controller is designed to keep the desired formation. In this case, the upper bound of uncertainty is unknown and is obtained via stable adaptive laws. Afterwards, in order to deal with the accelerated robots and obstacles, second-order leader–follower and leader–leader formation models are obtained from the previous models. A robust adaptive controller is then designed to stabilize the entire system in the presence of disturbances and modeling uncertainties, without needing to know the parameters or matrices of the formation models. In addition, by considering one of the leaders in the leader–leader model as a virtual obstacle, the challenge of avoiding moving obstacles is also addressed in the presence of uncertainties. The simulation results show the effect of the presented controllers in effectively keeping the desired leader–follower formations. |
