11 Overivew Occupancy Grids Sonar Models Bayesian Updating

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

11 Objectives • Describe the difference between iconic and featurebased localization Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary • Be able to update an occupancy grid using either Bayesian, DS, or HIMM • Describe the two types of formal exploration strategies Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 2

How am I going to get there? Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Cartographer Mission Planner Behaviors Chapter 11: Localization and Map Making deliberative -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Navigation reactive 11 • Where am I going? Mission planning • What’s the best way there? Path planning • Where have I been? Map making Overivew Occupancy Grids • Where am I? Localization -Sonar Models 3

11 Motivation • Can make topological or metric maps, localize relative to landmark(s) or at any point • More desirable: metric maps, localize at any point Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – 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” Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 4

11 Basic Idea Integrate local map Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Global map Move D Local map • Sense and create a local map • Move a little – Record change in position, orientation • Sense and create a local map – Fuse/tile together Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 5

11 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. Overivew Occupancy Grids – Integration requires -Sonar Models and <=5 degrees) -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration Black -Frontier-based Is ground -GVG Truth, Summary accurate measurement of D (on order of inches Purple is Measured Using shaft Encoders for D Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 6

11 Iconic vs. Feature-Based • Issue is how to localize at each step to accurately measure D, then integrate local map Overivew Occupancy Grids • Iconic: use raw (or near raw) sensor readings -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – 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 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 7

11 Occupancy Grids • Type of regular grid Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – L: e. Lement – 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 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 8

11 Sonars and Occupancy Grids • Everything element L “under” the sonar beam gets marked with some value for empty, occupied Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer • -HIMM Localization -ARIEL Exploration -Frontier-based -GVG • Summary Exact value depends on – Sonar model – Evidential method Generic sonar model – 3 regions – R: theoretical range, r: measured range – b: half angle Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 9

11 Evidential Methods for Occupancy Grids • Bayesian Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – Popularized by Hans Moravec • Dempster-Shafer • HIMM – Johan Borenstein Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 10

11 Bayesian • Compute the value for each L for each sonar using sonar model Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – The value of L is a probablility • Compute the value for each L where sonars overlap uses Bayes’ rule for updating Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 11

11 Example: Value of L in Region II Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 12

11 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 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 13

11 Other Issues • An element L may have multiple “hits” Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – 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? Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 14

11 Summary • Localization and map making are intertwined Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – 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” Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 15

11 Dempster-Shafer Theory & HIMM • On board Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 16

11 Localization • Iconic: uses raw sensor data directly Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – 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” Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 17

11 Iconic Example: ARIEL Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary • Issues – k must be small to be tractable, but k must be large if noisy sensors – Doesn’t work with “just sonars” Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 18

11 Iconic Example: ARIEL Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 19

11 Results Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 20

11 Exploration • Can explore reactively (move to open area as per Donath), but we’d like to create maps Overivew Occupancy Grids • Two major methods -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – Frontier-based – GVG Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 21

11 Frontier Based Exploration • Robot senses environment • Borders of low certainty form frontiers • Rate the frontiers Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL • Exploration -Frontier-based -GVG • Summary – Centroid – Utility of exploring (big? Close? ) Move robot to the centroid and repeat (continuously localize and map as you go) Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 22

11 GVG Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 23

11 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 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 24

11 Reaches deadend at 9, backtracks Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 25

11 Goes back and catches missing areas Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 26

11 Discussion of Exploration • Both methods work OK indoors, not so clear on utility outdoors Overivew Occupancy Grids • GVG -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – Susceptible to noise, hard to recover nodes • Frontier – Have to rate the frontiers so don’t trash Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 27

11 Summary • Map making requires Overivew Occupancy Grids -Sonar Models -Bayesian Updating -Dempster-Shafer -HIMM Localization -ARIEL Exploration -Frontier-based -GVG Summary – 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 Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 11: Localization and Map Making 28