Topological Simultaneous Mapping and Localization and Coverage

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Topological Simultaneous Mapping and Localization
(and Coverage)

• Howie Choset, George Kantor,
• Ercan Acar, Keiji Nagatani
• Carnegie Mellon University

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Roadmap-Based Path Planning

• Problem
• Start-goal
• Exploration
• Coverage
• Roadmap
• Accessibility
• Connectivity
• Departability
• Distance

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Point GVG

• Yap, Choset Burdick

GVG in R3 didjdk
No one-dimensional Retract in Punctured R3
HGVG in R3
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Control Laws

• where
• a and ß are scalar gains
• Null(?G(x)) is the null space of ?G(x)
• (?G(x)) is the Penrose pseudo inverse of ?G(x),
  i.e.,

D. Siler C. Kristoff SBP Class
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Topological Simultaneous Localization Mapping
Node Distance to nearby obstacles Number of
emanating edges Departure angles
Edge Path Length Correspondence
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Benefits Drawbacks of Topological Maps

• Cannot position in arbitrary locations
• Fails when environments is not topologically
  rich
• Hyper-symmetric
• Large open spaces

• Scale
• dimension
• geometric size
• Reduce planning problem
• Graph search
• Localization along a line
• Induces a hierarchy of maps for SLAM
• T Topological (Kuipers, Choset)
• F Feature-based (Leonard, Durrant-Whyte)
• L Local/Pixel-based (Morevac, Elfes, Thrun)
• D Dead-reckoning (Borenstein)
• Provides sensor space decomposition useful for
  control
• Brooks and other Behaviors sense/act
• Brockett Manikonda, Krishnaprasad, and Hendler
  Motion Description Languages
• Rizzi, Burridge, Koditschek Hybrid Controls
• Kuipers and Choset Topological Maps

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Hybrid T and F SLAM
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5
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Reduce planning problemGraph searchLocalization
along a line
4
5
Series of test increasing in complexity Pass
might be a match Fail not a match
Edge Length Relative distance between meet
points Number of landmarks Position and
covariance of landmarks
Node Distance to nearby obstacles Number of
emanating edges Departure angles
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Coverage

• Determine a path that passes the robot (or
  effector) over all points in a target region
  (volume)

Coordinated vs. Random
miketheheadlesschicken.org
Voronoi.sbp.ri.cmu.edu
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Sensor-based Complete Coverage
Goal Complete coverage of an unknown
environment Cell decomposition Incremental
construction
Time-exposure photo of a coverage experiment
Topological map
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Hierarchical Decomposition

• Topological (Kuipers, Choset)
• Feature-based (Leonard, Durrant-Whyte)
• Local/Pixel-based (Morevac, Elfes, Thrun)
• Dead-reckoning (Borenstein)

• Reduce dimension to
• One along an edge
• Zero at a node
• Can localize general area for
• localization

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Induce a Sequence of Control Laws

• Brooks and other Behaviors sense/act
• Brockett Manikonda, Krishnaprasad, and Hendler
  Motion Description Languages
• Rizzi, Burridge, Koditschek Hybrid Controls
• Kuipers and Choset Topological Maps
• Kantor, Choset, Rizzi, and Koditschek --
  Sensorium

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Sensorium (Sensor-space) Koditscheck

• No way points
• Sensory Driven
• Biological Evidence?
• Low-level

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Method Failure Modes
Hype-symmetric Environments
Large Open Spaces
Topological Information is not rich
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Benefits Drawbacks of Topological Maps

• Scale
• dimension
• geometric size
• Reduce planning problem
• Graph search
• Localization along a line
• Induces a hierarchy of maps
• Break-down SLAM into sub-problems T, F, L
• Select among different method
• Provides a useful sensor space decomposition
• topology resolves ambiguities

• Cannot position in arbitrary locations
• Fails when environments is not topologically
  rich
• Hyper-symmetric
• Large open spaces