The critical angle is thus a function of the operating frequency chosen and the smoothness target. For the sensors used on RSSCy this angle is approximately 65 degrees for a flat target surface of unfinished plywood such as would be encountered for maze walls or for dividers in the wall following contests. Navigational planning involves determining the actual location of the robot and subsequently calculating the appropriate commands to move it to a new location and orientation. The simplest case reduces the problem to two dimensions with a priori knowledge of the surroundings in the form of a memory map, or world model. The task becomes one of trying to correlate a realworld, sensor-generated image to the model and extracting position and orientation accordingly.
Several factors complicate the problem.
For one, the real environment is three dimensional, and although the model represents each object as its projection on the X-Y plane, the sensor may see things differently, complicating the task of correlation. Second, large computational resources are required and the process is time consuming, requiring the robot to stop and think occasionally. Also, acquiring the data can take several seconds using ultrasonic ranging techniques, due to the relatively low velocity of sound waves in air. More important for the purposes of this discussion, however, are the effects of the various error sources previously described, which can act collectively to impede a solution. Figure 2a depicts the results of 30 range values taken by a single sensor mounted on an azimuth table, with the sensor approximately 5ft, from the wall.