1. 11 Chapter 11: Localization and Map Making a. Occupancy Grids b. Evidential Methods c. Exploration Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

2. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making2 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

3. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making3 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 Mission Planner Carto- grapher Behaviors deliberative reactive How am I going to get there? Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

4. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making4 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

5. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making5 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 Local map Global map Move  Integrate local map Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

6. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making6 Observations about Process Map is almost always a type of regular grid (because easier to visualize) The “Move  ” and “Integrate local map” are the hard part. –Integration requires accurate measurement of  (on order of inches and <=5 degrees) Black Is ground Truth, Purple is Measured Using shaft Encoders for  Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

7. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making7 Iconic vs. Feature-Based Localization Algorithms Issue is how to localize at each step to accurately measure , 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

8. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making8 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

9. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making9 Sensor models Empirical methods - by testing a sensor and collecting data about correctness of a result - set of beliefs from all possible observations form the model; Analytical methods - generating a model from the physical properties of the sensor subjective methods rely on a designer’s experience

10. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making10 Sonars and Occupancy Grids Every 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, s: measured range –r: range of grid element –  : half angle Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

11. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making11 Sonar model Region I - grid elements are probably occupied Region II - grid elements are probably empty Region III - condition of grid elements is unknown sensor readings are more likely to be correct along the acoustic axis than towards the edges

12. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making12 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

13. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making13 Example 1: Value of L in Region II Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

14. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making14 Example 2: Value of L in Region I Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

15. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making15 Bayesian Compute the value for each L for each sonar using sonar model –The value of L is a probability –Bayes’ formula for conditional probabilty P(Occupied | s) = _____P(s |Occupied) P(Occupied)______________ P(s |Occupied) P(Occupied) + P(s |Empty) P(Empty) –Simplyfing assumption P(Occupied) = P(Empty) = 0.5 –with this assumption P(Occupied | s) = P(s |Occupied) 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

16. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making16 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 one writes 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

17. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making17 Dempster-Shafer Theory Deals with the distinction between uncertainty and ignorance computes the probability that the evidence supports the proposition - belief function Bel(X) example with flipping a coin which may not be fair Bel(Headup) = 0 and Bel(Headdown) = 0 with an expert stating that the coin is fair at 90%, I.e. that P(Headup) = 0.5 the belief is computed as Bel(Headup) = 0.5 x 0.9 = 0.45 Bel(Headdown) = 0.5 x 0.9 = 0.45 the gap is Bel(dontknow) = 0.1 Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

18. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making18 Dempster-Shafer Theory In case of occupancy grid the possible subsets are {Occupied}, {Empty}, {Dontknow} assigns an initial value of belief Bel(dontknow) = 1 to a grid element Provides results similar to Bayes method - but not always, Disadvantages - 1. does not helps to make a decision in many cases where Bayes method does; 2. Semantics of Belief function is not defined precisely with respect to decision making

19. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making19 HIMM - Histogrammic Motion Mapping quasi-evidential technique scores certainty in a highly specialized way suitable for sonars uses simply sonar model - only elements along the acoustic axis are updated - the uncertainty score is expressed as an integer from 0 to 15 updating rule - if element is empty decrement its occupancy by 1 - if element is occupied increment its occupancy by 3 - believes that a region is occupied more than it believes that it is empty (opposite to evidential methods)

20. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making20 HIMM - Histogrammic Motion executes much faster than the true evidential methods works best when the robot moves fast may suffer in performance or even give wrong results when the robot moves slowly very narrow field of view limited to sonars uses integer numbers only more parameters to tune

21. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making21 Comparison Bayesian and Dempster-Shafer produce essentially the same results - the major difference is the weight of conflict metric HIMM executes much faster but tends to be less accurate ways to improve performance of the Bayesian and Dempster-Shafer - to use integer numbers - to adapt sensor model (area of coverage) to the robot velocity - to use adaptive learning of the parameters - to adjust the sensor to the environment - to change the update rules - to use asymetric priors

22. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making22 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

23. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making23 Comparison Iconic methods more accurate with fewer data points, Iconic methods impose fewer restrictions on the environment, feature-based methods faster during localization (but require feature extraction) feature-based methods better in handling poor initial location estimates, no technique handles a dynamic environment.

24. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making24 Continuous localization and mapping uses exteroception, match current perception with past observations current perception added using registration tradeoff between 1) localizing after every sensor update and 2) localizing after n sensor updates which have been fused

25. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making25 Continuous localization and mapping 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

26. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making26 Iconic Example: ARIEL Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

27. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making27 Results Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

28. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making28 Feature-based localization extracting features such as a wall, opening and corner, finding the feature in the next sensor update. Finding good set of features is difficult extension of topological navigation - once the robot constructed a topological map, it can localize itself

29. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making29 Exploration Question: where have I not been? Can explore reactively (move to open area as per Donath), but we’d like to create maps could be done with a random walk - but not efficient could be done with repulsive potential fields and “avoid past” behavior, could be done with occupancy grid and a behavior “move to unknown area”, Two major methods –Frontier-based –GVG Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

30. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making30 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

31. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making31 GVG Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

32. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making32 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

33. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making33 Reaches deadend at 9, backtracks Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

34. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making34 Goes back and catches missing areas Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary

35. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making35 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

36. 11 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making36 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