We are interested in how the concept of affordances can affect our view to autonomous robot control, and how the results obtained from autonomous robotics can be reflected back upon the discussion and studies on the concept of affordances. In this paper, we studied how a mobile robot, equipped with a 3D laser scanner, can learn to perceive the traversability affordance and use it to wander in a room filled with spheres, cylinders and boxes. The results showed that after learning, the robot can wander around avoiding contact with non-traversable objects (i.e. boxes, upright cylinders, or lying cylinders in certain orientation), but moving over traversable objects (such as spheres, and lying cylinders in a rollable orientation with respect to the robot) rolling them out of its way. We have shown that for each action approximately 1% of the perceptual features were relevant to determine whether it is afforded or not and that these relevant features are positioned in certain regions of the range image. The experiments are conducted both using a physics-based simulator and on a real robot.