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An adaptive formation control law for non-holonomic dynamic robots based on an artificial potential function method in the presence of lateral slip and parametric uncertainties is presented to organize multiple robots into formation. It is formulated to achieve the smooth control of the translational and rotational motion of a group of mobile robots while keeping a prescribed formation and avoiding inter-robot and obstacle collisions. In order to improve the formation control method effectively and reduce the distortion shape, the virtual leader-following method is proposed for every robot and an improved optimal assignment algorithm is used to solve multi-targets optimal assignment for the formation problem. Simulation results are provided to validate the theoretical results.