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This paper presents a switching controller for positioning a unicycle-like mobile robot at a desired point with final orientation avoiding obstacles in completely unknown environments. To this aim two complementary algorithms are included: the first decides whether to avoid an obstacle around its right or left side, and the second is intended to detect when an obstacle was successfully avoided. The obstacle avoidance is performed using a laser-based reactive contour-following controller. The switching controllers include the stability analysis at the switching times, using common and multiple Lyapunov functions. Finally, experimental results in a typical unicycle-like mobile robot show the performance of the proposed hybrid control system.