Why do we take probabilistic approch to model the environment for robots in occupancy grid maps.The assumption is always taken that each cell on the grid map is either free or occupied.So why have probabilitic approch?
As the wikipedia page of Occupancy grid mapping explains, the result of the mapping process is a binary 1 or 0, occupied or not, the decision itself may be based on noisy data, which involves the probabilistic assessment of prior information to infer the posterior probability of the occupancy.
Cause of the intrinsic noise in sensory data, we have to consider a probabilistic model (mostly Gaussian) for the sensor measurements. As a matter of fact, the description and definition of the mapping problem will be probabilistic. The goal is to compute the most likely map given the sensor data and commands given to the robot:
In occupancy grid mapping as the most simple method, each cell (grid) is a binary random variable:
If you want to incoorporate our sensors properly you first need to build a sensor model. This model tells you whenever your sensor measured something, what is the probability that this is the real value. You will get a distribution.
So when you measure 1m there is a prob. of .5 that thus measurement is true and a prob of .3 that the real distance ist actually 1.2m. To process this information you will not just modify one cell in you map but all adjacent cells. You need to to merge the distribution into the map.
HP Moravec - Sensor devices and systems for robotics, 1989 - Springer (original certainty map paper)
Probabilistic Sensor Models (lecture on this topic)