# Occupancy grid maps

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.

• So because the sensor is noisy so we need to take the measurements from sensor 9-10 times and then we estimate.Like if i take 10 mesurements and i obtain 7 times the grid cell to be occupied and remaining 3 times free.Then to capture this data.I use probability.Right? Commented Jun 23, 2020 at 17:30
• What is posterior probabilty of occupancy? Is it same as the probability of a grid cell being occupied ? Commented Jun 23, 2020 at 17:31
• You have your prior belief if it is occupied or not, you take a measurement and consider the probabilty of that measurement being faulty and use bayes’ rule to obtain the final or posterior probability of occupancy. Prior=before measurment, posterior=after measurement has been “combined” with the initial (or prior) belief
– 50k4
Commented Jun 23, 2020 at 17:34
• You can measure multiple times, you can track object where they are moving with a given probability, you can combine noisy measurements with other noisy measurements, there are a lot of options
– 50k4
Commented Jun 23, 2020 at 17:35

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)