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In this paper, an asymptotically stable (AS) combined kinematic/torque control law is developed for leader-follower-based formation control using backstepping in order to accommodate the complete dynamics of the robots and the formation, and a neural network (NN) is introduced along with robust integral of the sign of the error feedback to approximate the dynamics of the follower as well as its leader using online weight tuning. It is shown using Lyapunov theory that the errors for the entire formation are AS and that the NN weights are bounded as opposed to uniformly ultimately bounded stability which is typical with most NN controllers. Additionally, the stability of the formation in the presence of obstacles is examined using Lyapunov methods, and by treating other robots in the formation as obstacles, collisions within the formation do not occur. The asymptotic stability of the follower robots as well as the entire formation during an obstacle avoidance maneuver is demonstrated using Lyapunov methods, and numerical results are provided to verify the theoretical conjectures.