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: