Ans(a)- We can determine the floor by the texture of it or the robot can guess that it is standing on the floor itself and the texture on the 
lowest most portion of the image which is uniformly decreasing in width along the edges to meet at some point. To find the walls we can use the
 texture as well as the long edge separating to continuous textures. Some idea of the floor can be estimated from sensing the dirt (or things) 
 as they will be very small in area and the edge of those will be touching the floor. Assumption: That the texture of the floor and walls is 
 continuous and we can find the edge between the floor and the things placed on it.

Ans(b)- After dividing it into grid of size 0.5m, we will assign the value of dirt to the grid by calculating the ratio of the surface area of 
the dirt on a particular to the surface area of the grid (0.25m^2). More the dirt covers the grid, more will be the value on that grid.

Ans(c)- As the above mapping clearly shows that the value of the dirt will be between 0 and 1 only. It seems to be a reasanoble range to use. 
In case, we also take into consideration the height or weight of the entity present on the floor, this might get change as well as the mapping.

Ans(d)- The robot can use the image and first determine the floor and then the walls by detecting the edges and the continuous texture of 
walls and floor.