Two mental transformations were carried out: a simulated rotation around the robots axis, and a simulated translation toward the barrier of obstacles. In the first, the robot has to estimate whether it is standing in the center of the circle. In the second, the robot has to estimate the distance to the obstacle in front.
In figure 7.3, the robot is roughly in the middle of the circle, but apparently this cannot be decided from the image representation (figure 7.4). The reason for this asymmetry is that the center of the robot differs from the optical axis of the camera. However, the location can be estimated by simulating a turn around the rotational axis of the robot and by predicting the distance in the frontal sector.
After observing the current image, the robot simulated a left and a right turn (around its rotational axis, i.e., vL = - vR), and anticipated the effect of these movements on the image representation. From the current position the robot simulated five rotational steps (2 sec each) to the left with the velocity vL = - 40 mm/sec and vR = 40 mm/sec, and, also from the current position, five steps to the right at the opposite velocity. Five steps at this speed corresponded to a rotation of 72o. Since the obstacles were standing in a circle, it was not necessary to cover the entire 360o in the mental simulation. Then, the values of the frontal sector for the different representations were compared (altogether 11 values). If they had a variance of less than one pixel squared it was concluded that they were the same, and thus the robot centered in the circle (which is the only point having same distance to the circle boundary in all directions). 20 trials were evaluated, with the robot placed at 20 arbitrary positions (in the vicinity of the center) with random orientation.
In the second task, the robot simulated a forward movement at speed v = 40 mm/sec. The frontal sector value was predicted. If it dropped below a threshold, the simulation stopped. The threshold was chosen such that the bottom part of the obstacle was still just visible and not occluded by the robot body. The robot was placed at 15 arbitrary positions on a line through the center of the circle. The distance between the forefront of the robot and the forefront of the obstacle in front was measured. The results of these two tasks are in section 7.3.5.