Sonar Measurements

1. Improving MCL

To improve monte carlo localisation we could:

• Take measaurements, then filter possible positions on the map based on the measurements, then resample from the remaining positions. (e.g. filter distance from sonar, filter orientation from compass).
• Use recognition: learn characteristics of many chosen locations on the map, then use the measurements to recognize which location we are at. This is more robust to noise, but requires more computation and training data.

2. Recognition

To do recognition:

1. Place robot in each target location, taking raw measurements (called a signature).
2. Afterward, to decide on the location it must compare histograms with a correlation test. The square difference between new measurement histogram and saved signature histogram is: . The location with the smallest is the most likely location. A threshold is used to decide if the recognition is good enough to be used as a measurement update in MCL.

If the test histogram can be brought into close agreement by only a shift, then the robot is in the same place but rotated. To save computation, we can build a signature invariant to robot's rotation.

3. Grid Mapping

Probablistic Occupancy Grid Mapping infers which parts of the environment are navigable free space, and which contain obstacles. An occupancy grid accumulates uncertain information from sensors into precise maps. For each cell :

• fis the probability that cell is occupied.
• is the probability that cell is free.
• .
• Initialize probabilities to 0.5 (unknown).

On sonar measurement (reporting depth ), we get evidence for cells distance in front of the root are more likely to be occupied, and cells closer than are more likely to be free. We can update the probabilities using Bayes Rule:

We dont need to calculate as we could calculate and then normalize the probabilities.

If we take the ratio of the probabilities, and use odds notation , we get:

In this form, each cell stores , and is updated additively. Cells with probability will have log odds a positive log means probability , and a negative log means probability .

3.1 Likelihood Model

To model the sensor's likelihood function, we consider the ratio of likelihoods we need to update log odds:

• The log odds update .
• For cells within the sonar beam but closer than the measured depth , so we can choose a constant negative value for .
• For cells within the sonar around , so we can choose a constant positive value for .