Mapping

1
Lecture 8
Mapping 5 April, 2005
2
Quiz 5

• What is the most significant integration error in
  dead reckoning?
• State two requirements for a good landmark.
• Give two examples of navigation in nature. Are
  these examples using dead-reckoning, landmarks,
  or other techniques?
• What is perceptual aliasing? What are some
  methods to combat it?
• Name one issue each with single position, and
  multiple position, belief representations.

3
Overview

• Why do we map?
• Spatial decomposition
• Representing the robot
• Current challenges

4
Mapping

• Represent the environment around the robot
• Impacted by robot position representation
• Relationships
• Map precision must match application
• Precision of features on map must match precision
  of robots data (and hence sensor output)
• Map complexity directly affects computational
  complexity, and reasoning about localization and
  navigation
• Two basic approaches
• Continuous
• Decomposition (discretization)

5
Environment representation

• Continuous metric -gt x, y, theta
• Discrete metric -gt metric grid
• Discrete topological -gt topological grid
• Environmental modeling
• Raw sensor data
• Large volume, uses all acquired information
• Low level features (e.g. lines, etc)
• Medium volume, filters out useful information,
  still some ambiguities
• High level features (e.g. doors, car)
• Low volume, few ambiguities, not enough
  information

6
Continuous representation

• Exact decomposition of environment
• Closed-world assumption
• Map models all objects
• Any area of map without objects has no objects in
  corresponding environment
• Map storage proportional to density of objects in
  environment
• Map abstraction and selective capture of features
  to ease computational burden

7
Continuous representation

• Match map type with sensing device
• For laser ranger finder, may represent map as
  series of infinite lines
• Fairly easy to fit laser range data to series of
  lines

8
Continuous representation

• In conjunction with position representation
• Single hypothesis extremely high accuracy
  possible
• Multiple hypothesis
• Either, depict as geometric shape
• Or, as discrete set of possible positions
• Benefits of continuous
• High accuracy possible
• Dangers
• Can be computationally expensive
• Typically only 2D

9
Decomposition

• Capture only useful features of world
• Computationally better for reasoning,
  particularly if map is hierarchical

10
Exact cell decomposition

• Model empty areas with geometrical shapes
• Can be extremely compact (18 nodes in this
  figure)
• Assumption robot position within each area of
  free space does not matter

11
Fixed cell decomposition

• Tessellate world discrete approximation
• Each cell is either empty or full
• Inexact (note loss of narrow passageway on right)

12
Adaptive cell decomposition

• Multiple types of adaptation quadtree, BSP,
  exact
• Recursively decompose until a cell is completely
  free or completely an object
• Very space efficient compared to fixed cell
  approach

13
Occupancy grid

• Typically fixed decomposition
• Each cell is either filled or free
• Counter for cell 0 indicates free, above a
  certain threshold is considered to be filled with
  an object
• Particularly useful with range-based sensors
• If sensor strikes something in a cell, increase
  cell counter
• If sensor goes over cell and strikes something
  else, decrease cell counter (presuming is free
  space)
• By also discounting cell values over time, can
  deal with transient obstacles
• Disadvantages
• Map size a function of size of environment and
  size of cell
• Imposes a priori geometric grid on world

14
Occupancy grid

• Darkness of cell proportional to cell counter
  value

15
Topological decomposition

• Use environment features most useful to robots
• A graph specifying nodes and the connectivity
  between them
• Nodes not of fixed size nor specify free space
• A node is an area the robot can recognize its
  entry to and exit from

16
Topological example

• For this example, robot must be able to detect
  intersections between halls, and halls and rooms.

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Topological decomposition

• To robustly navigate with a topological map a
  robot
• Must be able to localize relative to nodes
• Must be able to travel between nodes
• These constraints require the robots sensors to
  be tuned to the particular topological
  decomposition
• Major advantage is ability to model non-geometric
  features (like artificial landmarks) that benefit
  localization

18
Map updates occupancy grids

• Occupancy grid
• Each cell indicates probability is free space and
  probability is occupied
• Need method to update cell probabilities given
  sensor readings at time t
• Update methods
• Sensor model
• Bayesian
• Dempster-Shafer

19
Representing the robot

• How represent the robot itself on a map?
• Point-robot assumption
• Represent the robot as a point
• Assume it is capable of omnidirectional motion
• Robot in reality is of nonzero size
• Dilation of obstacles by robots radius
• Resulting objects are approximations
• Leads to problems with obstacle avoidance

20
Current challenges

• Real world is dynamic
• Perception still very error prone
• Hard to extract useful information
• Occlusion
• Traversal of open space
• How to build up topology
• Sensor fusion

21
Summary

• Decomposition
• Continuous
• Discrete
• Map updating
• Bayes
• Dempster-Shafer
• Robot representation
• Current challenges

22
References

• Introduction to Autonomous Mobile Robots, R
  Siegwart and I Nourbaksh, Bradford
• Mobile Robotics A Practical Introduction, U
  Nehmzow, Springer
• Computational Principles of Mobile Robotics, G
  Dudek, M Jenkin, Cambridge University Press
• Introduction to AI Robotics, R Murphy, Bradford
• Rover Localizaton Results for the FIDO Rover, E
  Baumgartner, H Aghazarian, A Trebi-Ollennu, SPIE
  Photinics East Conference, October, 2001.