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

11Chapter 11:

Localization and Map Making

a. Occupancy Gridsb. Evidential Methods

c. Exploration

OverivewOccupancy Grids-Sonar Models-Bayesian Updating-Dempster-Shafer-HIMMLocalization-ARIELExploration-Frontier-based-GVGSummary

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

11 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



11 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

MissionPlanner

Carto-grapher

BehaviorsBehaviorsBehaviorsBehaviors

deli

bera

tive

reac

tiveHow am I going to get

there?



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

– 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”



11 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

Localmap

Globalmap

Move

Integrate local map



11 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)

BlackIs groundTruth,Purple isMeasuredUsing shaftEncoders for



11 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



11 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



11 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

: half angle



11 Evidential Methods for Occupancy Grids

• Bayesian– Popularized by Hans Moravec

• Dempster-Shafer

• HIMM– Johan Borenstein



11 Bayesian

• Compute the value for each L for each sonar using sonar model– The value of L is a probability

• Compute the value for each L where sonars overlap uses Bayes’ rule for updating



11 Example: Value of L in Region II



11 Class Exercise:Value of L in Region I



11 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?



11 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”



11 Dempster-Shafer Theory & HIMM

• On board



11 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”

?



11 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”



11 Iconic Example: ARIEL



11 Results



11 Exploration

• Can explore reactively (move to open area as per Donath), but we’d like to create maps

• Two major methods– Frontier-based

– GVG



11 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)



11 GVG



11 Keeps moving, ignores areas hard to get too



11 Reaches deadend at 9, backtracks



11 Goes back and catches missing areas



11 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



11 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


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

Documents

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