Turns & Rotations

In NetLogo, it is very hard or rather impossible to visualize the proper rotations of the window cleaning robot during its motion and subsequently end up at exactly the right position. Therefore it was decided to not visualize the rotations, but instead, the turning movements are modeled by letting the robot ’teleport’ from the place before to the place after the turn. The time it takes to make a certain turn is then simply added to the time instance before the rotation. In this way, it is still possible to model the turns and rotations of the window cleaning robot in a realistic way. The question becomes then what will be the time that each specific turn takes? To give realistic values for this, the characteristic rotations and turns of the window cleaning robot are studied. In total there are six different turns or rotations which the window cleaning robot should be able to make. They are schematically shown in the figure below.

The first turn the robot should be able to perform is a pure rotation (Figure 2.a). This motion is very often needed during the robot’s cleaning job. To assign a time to the rotation, two parameters should be known: the angle to which the robot is currently heading, the angle to which the robot should head and the rotational speed of the robot when it is rotating. In reality, the robot knows how it is oriented by means of gravity sensors and thus knows the angle to which it is currently heading. Therefore it seems appropriate to use the angle at which the robot is heading in NetLogo as the current angle. The time it takes to perform a pure rotation can then be calculated by means of the following equation:

where t(rotation) is the time it takes to perform a pure rotation (s), w is the angular velocity of the robot (°/s) and Δa is the angle over which the robot should be rotated to face the upper edge of the window (°) (the angle to which the robot should head). The angular velocity of the robot is determined by using its speed and its dimensions:

where v is the speed of the window cleaning robot (m/s) and r(track) is the distance from the center of the robot to one of the crawler tracks. The value v equals 0.1 m/s which is determined by looking at a comparable window cleaning robot (WINDORO) while r(track) is estimated to be 0.09 m.
Another important motion of the window cleaning robot should be performed when it is for example in the upper left corner with its cleaning section headed to the window edge. The robot has to perform the motion that can be seen in Figure 2.b. First, it has to drive backwards to a position where it is able to turn. Since the robot has dimensions of 25 x 25 ""cm"" the distance from the upper edge that is needed to do a rotation can be simply calculated with use of the Pythagorean theorem: