# The Window

In the model created with NetLogo, the window is modeled as a grid of patches. This means that the shape of the window is assumed to be rectangular, which is appropriate for the domain of the considered window cleaning robots. In the model, a single patch represents an area of 50 x 50 mm in reality. The height and width of the window is however restricted to a multiple of 250 mm (the same dimension as the robot). This is done because modeling a multiple of 50 mm is quite complex and would take too long to program. For the height of the window, this has to do with the fact that the robot then has to consider incomplete rows. Since both the standard motion planning algorithm and the developed algorithms have these simplifications and would both have the same problems in real life, they and their results can still reasonably be compared.

It is assumed that each of the above-mentioned patches of the window will get a certain dirtiness value in the model. Patches with a higher dirtiness value will ask for more wiping motions of the window cleaning robot. To model realistic dirt, clusters of persistent dirt (thus with a higher value of dirtiness) are created, together with a more or less even distribution of dirt with a lower value of dirtiness on the rest of the window surface. In reality, the former type of dirt is comparable with for example bird droppings, while the latter can represent dust particles on the window. Besides that, all patches get a number that denotes how hard it is to clean each of them. This number will be taken into account when the dirt reduction that the robot causes when it moves over the patch is calculated. This hard to clean number is chosen from an exponential distribution for each patch. For a small number of patches, this will have the result that the dirtiness value is much harder to reduce than for the others. They thus require a huge amount of wiping motions before they are entirely clean. These little spots are comparable with a situation, in reality, were a dirty spot on the window could not be cleaned at all or is very hard to clean, for example, stickers or scratches on the window. How the algorithms cope with these hard to clean spots will be discussed in section 'Cleaning'. More precise information about how the dirt distribution was eventually exactly modeled can be found in the section about modeling.