part ii chapter 9: topological path planning

Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 9: Topological Path Planning 1

9Part II

Chapter 9:Topological Path Planning


9 Objectives

• Define the difference between natural and artificial landmarks; give one example of each

• Given a description of an indoor office environment and a set of behaviors, build a relational graph representation labeling the distinctive places and local control strategies for gateways

• Describe in one or two sentences: gateway, image signature, visual homing, viewframe, orientation region

• Given a figure showing landmarks, create a topological map showing landmarks, landmark pair boundaries, and orientation regions


9 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?


9 Spatial Memory

• What’s the Best Way There? depends on the representation of the world

• A robot’s world representation and how it is maintained over time is its spatial memory– Attention

– Reasoning

– Path planning

– Information collection

• Two forms– Route (or qualitative)

– Layout (or metric)

• Layout leads to Route, but not the other way

Introduction to AI Robotics (MIT Press), copyright Robin Murphy 2000 Chapter 9: Topological Path Planning

9 Route, or Qualitative Navigation

• Two categories

• Relational– spatial memory is a relational graph, also known as a

topological map

– use graph theory to plan paths

• Associative– spatial memory is a series of remembered viewpoints,

where each viewpoint is labeled with a location

– good for retracing steps


9 Topological Maps Use Landmarks

• A landmark is one or more perceptually distinctive features of interest on an object or locale of interest

• Natural landmark: configuration of existing features that wasn’t put in the environment to aid with the robot’s navigation (ex. gas station on the corner)

• Artificial landmark: set of features added to the environment to support navigation (ex. highway sign)

• Roboticists avoid artificial landmarks!


9 Desirable Characteristics of Landmarks

• Recognizable (can see it when you need to)– Passive

– Perceivable over the entire range of where the robot might need to view it

– Distinctive features should be globally unique, or at least locally unique

• Perceivable for the task (can extract what you need from it)– ex. can extract relative orientation and depth

– ex. unambiguously points the way

• Be perceivable from many different viewpoints


9 Example Landmarks


9 floor plan

relational graph

Relational Methods

Nodes: landmarks, gateways,goal locations

Edges: navigable path

Gateway is an opportunityto change path heading


9 Problems with early relational graphs

• Not coupled with how the robot would get there

• Shaft encoder uncertainty accumulates


9 Kuipers and Byun: Spatial Hierarchy


9

Distinctive Places (recognizable, &at least locally unique)

Local control strategies (behaviorsto get robot between DPs)

Distinctive Place Approach


9neighborhoodboundary

distinctiveplace (withinthe corner)

path of robot as it moves into neighborhood and

to the distinctive place

Actually Getting to a Distinctive Place: Neighborhoods

Use one behavior until sees the DP (exteroceptivecueing) then swap to a landmark localization behavior


9 Class Exercise

• Create a relational graph for this floorplan

• Label each edge with the appropriate LCS: mtd, fh

• Label each node with the type of gateway: de, t, r

Room 1 Room 2

Room 3 Room 4

r1 r2

de1

de3

de2r3 r4

t1 t2 t3fh fh fh

fh

fh

mtd

mtd

mtd

mtd


9 Case Study

• Representation

• Sequencing of behaviors based on current perception (releasers) and subgoal

• Algorithm


9

R3->R7

Hd nodes becauseHave different perception


9 Transition Table

TO

FROM H F R Hd

H Navigate-Hall

Navigate-Hall

Undefined Navigate-Hall

F Navigate-Hall

Navigate-Foyer

Navigate-Door

Navigate-Door

R Undefined Navigate-door

Navigate-door

Navigate-door

Hd Navigate-hall

Navigate-hall

Navigate-door

Navigate-hall


9 Path Planning Algorithm

• Relational graph, so any single source shortest path algorithm will work (Dijkstra’s)

• If wanted to visit all rooms, what algorithm would you use?


9 Execution

Exception subscript


9 Associative Methods• Visual Homing

– bees navigate to their hive by a series of image signatures which are locally distinctive (neighborhood)

• QualNav– the world can be divided

into orientation regions (neighborhoods) based on perceptual events caused by landmark pair boundaries

• Assumes perceptual stability, perceptual distinguishability

RandalNelson,URochester

DarylLawton,AdvancedDecision Systems


9 Image Signatures

The world Tesselated (like faceted-eyes)

Resulting signaturefor home


9

Move to match thetemplate


9

tree

building

radiotower

mountain

OR1OR2

MetricMap

TopologicalRepresentationas OrientationRegions


9 Summary

• Route, qualitative, and topological navigation all refer to navigating by detecting and responding to landmarks.

• Landmarks may be natural or artificial; roboticists prefer natural but may have to use artificial to compensate for robot sensors

• There are two type of qualitative navigation: relational and associative


9 Summary (cont.)

• Relational methods use graphs (good for planning) and landmarks– The best known relational method is distinctive places

– Distinctive places are often gateways

– Local control strategies are behaviors

• Associative methods remember places as image signature or a viewframe extracted from a signature– can’t really plan a path, just retrace it

– direct stimulus-response coupling by matching signature to current perception

part ii chapter 9: topological path planning

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