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We apply a novel motion planning and control methodology, which is based on a non-smooth navigation function, to a point mobile robot moving amongst moving obstacles. The chattering introduced by the discontinuous potential field is suppressed using non-smooth backstepping. The combined controller guarantees global asymptotic convergence and collision avoidance. This controller is particularly suitable for real time implementation on systems with limited computational resources. The effectiveness of the proposed scheme is verified through computer simulations.