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A novel formation control scheme for mobile robots is introduced in the context of leader-follower framework with reduced communication exchange. The dynamical controller inputs for the robots are approximated from nonlinear optimal control techniques in order to track the designed control velocities generated by the kinematic controller. The proposed nonlinear optimal control technique, referred to as adaptive dynamic programming, uses neural networks (NNs) to solve the optimal formation control problem in discrete time in the presence of unknown internal dynamics and a known control coefficient matrix. A modification to the follower's kinematic controller is used to allow the desired formation to change in order to navigate around obstacles. The proposed obstacle avoidance technique modifies the desired separation and bearing of the follower to guide the follower around obstacles. Minimal wireless communication is utilized between the leader and the follower to allow the follower to approximate and compensate for the formation dynamics. All NNs are tuned online, and the stability of the entire formation is demonstrated using Lyapunov methods. Hardware results demonstrate the effectiveness of our approach.