Lecture 8
Mapping
5 April, 2005
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
Quiz 5
1.What is the most significant integration error in dead
reckoning?
2.State two requirements for a good landmark.
3.Give two examples of navigation in nature. Are these
examples using dead-reckoning, landmarks, or other
techniques?
4.What is perceptual aliasing? What are some methods to
combat it?
5.Name one issue each with single position, and multiple
position, belief representations.
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
Overview
• Why do we map?
• Spatial decomposition
• Representing the robot
• Current challenges
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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)
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
Environment representation
• Continuous metric
-> x, y, theta
• Discrete metric
• Discrete topological
• Environmental modeling
-> metric grid
-> topological grid
– 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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
Decomposition
• Capture only useful features of world
• Computationally better for reasoning, particularly if map
is hierarchical
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
Fixed cell decomposition
• Tessellate world: discrete approximation
• Each cell is either empty or full
• Inexact (note loss of narrow passageway on right)
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
Occupancy grid
• Darkness of cell proportional to cell counter value
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
Topological example
• For this example, robot must be able to detect
intersections between halls, and halls and rooms.
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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 robot’s sensors to be tuned to
the particular topological decomposition
• Major advantage is ability to model non-geometric
features (like artificial landmarks) that benefit
localization
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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 robot’s radius
– Resulting objects are approximations
– Leads to problems with obstacle avoidance
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
Summary
• Decomposition
– Continuous
– Discrete
• Map updating
– Bayes
– Dempster-Shafer
• Robot representation
• Current challenges
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005
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.
UNIVERS ITY OF
MARYLAND
Planetary Surface Robotics
ENAE 788U, Spring 2005