Chapter 11: Localization and Map Making a. Occupancy Grids b. Evidential Methods c. Exploration

1. Chapter 11:Localization and Map Makinga. Occupancy Gridsb. Evidential Methodsc. Exploration Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

2. Objectives • Describe the difference between iconic and feature-based localization • Be able to update an occupancy grid using either Bayesian, DS, or HIMM • Describe the two types of formal exploration strategies Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

3. Behaviors Behaviors Behaviors Behaviors Navigation • Where am I going? Mission planning • What’s the best way there? Path planning • Where have I been? Map making • Where am I? Localization Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Carto- grapher Mission Planner deliberative How am I going to get there? reactive Chapter 11: Localization and Map Making

4. Motivation • Can make topological or metric maps, localize relative to landmark(s) or at any point • More desirable: metric maps, localize at any point • More readable by a human • GPS isn’t the answer • Localization error is on order of 1 meter • Reception difficult indoors • Want to know where features in environment are, not just robot (e.g., layout of walls, not just robot’s path) • Sensor measurements have some uncertainty that must be factored in • Formal methods called “evidential reasoning”, “theories of evidence” Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

5. Basic Idea • Sense and create a local map • Move a little • Record change in position, orientation • Sense and create a local map • Fuse/tile together Integrate local map Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Global map Local map Move D Chapter 11: Localization and Map Making

6. Observations about Process • Map is almost always a type of regular grid (because easier to visualize) • The “Move D” and “Integrate local map” are the hard part. • Integration requires accurate measurement of D (on order of inches and <=5 degrees) Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Black Is ground Truth, Purple is Measured Using shaft Encoders for D Chapter 11: Localization and Map Making

7. Iconic vs. Feature-Based • Issue is how to localize at each step to accurately measure D, then integrate local map • Iconic: use raw (or near raw) sensor readings • Match elements marked “empty” or “occupied” in a regular grid • OCCUPANCY GRID • Plug and chug, intense computations • Feature-based: use features extracted from raw data • Label and match corners, walls, whatever • Less features, so less computations Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

8. Occupancy Grids • Type of regular grid • L: eLement • Came out of sonar tradition • Each element is marked with belief that L is empty or occupied • Usually a number on a scale • [0,1] for probability and possibility theories • [0-15] for HIMM Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

9. Sonars and Occupancy Grids • Everything element L “under” the sonar beam gets marked with some value for empty, occupied • Exact value depends on • Sonar model • Evidential method • Generic sonar model • 3 regions • R: theoretical range, r: measured range • b: half angle Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

10. Evidential Methods for Occupancy Grids • Bayesian • Popularized by Hans Moravec • Dempster-Shafer • HIMM • Johan Borenstein Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

11. Bayesian • Compute the value for each L for each sonar using sonar model • The value of L is a probablility • Compute the value for each L where sonars overlap uses Bayes’ rule for updating Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

12. Example: Value of L in Region II Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

13. Class Exercise:Value of L in Region I Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

14. Other Issues • An element L may have multiple “hits” • Robot moves and senses subset of same area, Sonars overlap: what to do? • Use Bayes’ rule to update • If write a program to use Bayes’ rule, what’s the initialization of the occupancy grid? • P(Occupied)=P(Empty)=0.5 • Is this a good assumption? Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

15. Summary • Localization and map making are intertwined • Localization requires good maps • Map making requires good localization • Map making and localization techniques often use occupancy grids • Type of regular grid • Elements represent uncertainty of being empty, occupied • Multiple ways of combining uncertainty when an element has multiple “hits” Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

16. Dempster-Shafer Theory & HIMM • On board Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

17. Localization • Iconic: uses raw sensor data directly • Ex. Sonar and laser readings fused in an occupancy grid • Compare current and past reading • Feature-based: uses features extracted from sensor data • Ex. “corners”, “walls” Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary ? Chapter 11: Localization and Map Making

18. Iconic Example: ARIEL • Issues • k must be small to be tractable, but k must be large if noisy sensors • Doesn’t work with “just sonars” Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

19. Iconic Example: ARIEL Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

20. Results Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

21. Exploration • Can explore reactively (move to open area as per Donath), but we’d like to create maps • Two major methods • Frontier-based • GVG Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

22. Frontier Based Exploration • Robot senses environment • Borders of low certainty form frontiers • Rate the frontiers • Centroid • Utility of exploring (big? Close?) • Move robot to the centroid and repeat • (continuously localize and map as you go) Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

23. GVG Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

24. Keeps moving, ignores areas hard to get too Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

25. Reaches deadend at 9, backtracks Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

26. Goes back and catches missing areas Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

27. Discussion of Exploration • Both methods work OK indoors, not so clear on utility outdoors • GVG • Susceptible to noise, hard to recover nodes • Frontier • Have to rate the frontiers so don’t trash Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making

28. Summary • Map making requires • Localization and acurate measurements • Exploration • Localization and map making often use • Occupancy grids • Evidential methods for updating • Bayesian • DS • HIMM (quasi-evidential) • Two kinds of localization: iconic, feature-based • Two popular methods for exploration: frontier-based, GVG Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Chapter 11: Localization and Map Making