1. SA-1 Mapping with Known Poses Ch 4.2 and Ch 9

2. 2 Why Mapping? Learning maps is one of the fundamental problems in mobile robotics Maps allow robots to efficiently carry out their tasks, allow localization … Successful robot systems rely on maps for localization, path planning, activity planning etc.

3. 3 The General Problem of Mapping What does the environment look like?

4. 4 The General Problem of Mapping Formally, mapping involves, given the sensor data, to calculate the most likely map

5. 5 Mapping as a Chicken and Egg Problem So far we learned how to estimate the pose of the robot given the data and the map. Mapping, however, involves to simultaneously estimate the pose of the vehicle and the map. The general problem is therefore denoted as the simultaneous localization and mapping problem (SLAM). We will first describe how to calculate a map given we know the pose of the robot.

6. 6 Problems in Mapping Sensor interpretation How do we extract relevant information from raw sensor data? How do we represent and integrate this information over time? Robot locations have to be estimated How can we identify that we are at a previously visited place? This problem is the so-called data association problem.

7. 7 Occupancy Grid Maps Introduced by Moravec and Elfes in 1985 Represent environment by a grid. Estimate the probability that a location is occupied by an obstacle. Key assumptions Occupancy of individual cells (m[xy]) is independent Remember that Robot positions are known in current discussion!

8. 8 Updating Occupancy Grid Maps Idea: Update each individual cell using a binary Bayes filter (ch4.2, P94). Additional assumption: Map is static. Let’s look at the binary Bayes filter first.

9. 9 Binary Bayes Filter

10. 10 Binary Bayes Filter

11. 11 Binary Bayes Filter This binary Bayes filter uses an inverse measurement model p(x|z t ), instead of the familiar forward model p(z t |x). The inverse measurement model specifies a distribution over the (binary) state variable as a function of the measurement z t. Inverse models are often used in situations where measurements are more complex than the binary state. An example of such a situation is the problem of estimating whether or not a door is closed, from camera images.

12. 12 Binary Bayes Filter

13. 13 Binary Bayes Filter

14. 14 Binary Bayes Filter

15. 15 Binary Bayes Filter

16. 16 Updating Occupancy Grid Maps

17. 17 Updating Occupancy Grid Maps

18. 18 Updating Occupancy Grid Maps

19. 19 Updating Occupancy Grid Maps Inverse Sensor Model (inverse measurement model)

20. 20 Updating Occupancy Grid Maps

21. 21 Incremental Updating of Occupancy Grids (Example)

22. 22 Resulting Map Obtained with Ultrasound Sensors

23. 23 Occupancy Grids: From scans to maps

24. 24 Tech Museum, San Jose CAD map occupancy grid map

25. 25 Summary Occupancy grid maps are a popular approach to represent the environment of a mobile robot given known poses. In this approach each cell is considered independently from all others. It stores the posterior probability that the corresponding area in the environment is occupied. Occupancy grid maps can be learned efficiently using a probabilistic approach.