Transcript Coverage Planning - University of North Carolina at Chapel

Coverage Planning
Jamie Snape
The University of North Carolina at Chapel Hill
Covering salesman problem
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Identify the shortest possible
tour of a subset of n given
cities such that every city not
on the tour is within some
predetermined neighborhood
of a city that is on the tour
Current and Schilling (1989)
Coverage Planning
• Determine the path for a robot to pass over all
points in its free space
• Must pass over all points in the target environment,
not just through all the neighborhoods
Applications
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Floor cleaning
Lawn mowing
Mine hunting
Harvesting
Painting
Oceanographic mapping
Fiorini and Prassler (2000)
Heuristics
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Simple rules of thumb that may
work well
No provable guarantees
ensuring success of coverage
iRobot Corporation
Completeness
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Guarantees a path that
completely covers free space
Break the target region into
cells that are simple to cover
Attain provably complete
coverage by visiting each cell
in the decomposition
AB Electrolux
Cost-per-quality of coverage
• Complete approaches require more sensory and
computational power
• Randomized searches negate need for costly
localization hardware
• May be more cost efficient to use heuristics and
multiple robots
Time-to-completion
• Consider area-per-unit path length travelled
• Turning occupies more time than traveling in a
straight line
• Minimizing the number of turns improves
completion time
Layout of environment
• Many motion planning algorithms assume the
layout of the environment is known in advance
• Often not a realistic assumption in coverage
planning
• May have to use onboard sensors to acquire this
information and perform coverage at the same time
Heuristic algorithms
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Simple set of behaviors such
as spiraling, room crossing, or
wall following
Hierarchy of cooperating
heuristics form more
complicated actions
iRobot Corporation (2007)
Multiple robot heuristic
algorithms
• Repulsion heuristic to ensure even spread out of
robots to allow more uniform coverage
• Combine with other heuristics like avoiding
obstacles to provide overall behaviors
• Individual paths not planned but chosen at random
Imperfect sensors
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Probability that an area is
sensed when covered is less
than 1.0
As probability decreases,
advantages of complete
algorithms decrease
Eventually a random search
becomes as effective and less
expensive robots may be used
Gage (1993)
Approximate cellular
decomposition
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Fine-grid-based representation
of free space
Cells all same size and shape,
but the union of the cells only
approximates the entire area
Normally assume once a robot
has entered a cell it has been
covered
Moravec and Elfes (1985)
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When each cell has been
visited, coverage is complete
Conventional wavefront
algorithm
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Assign a goal cell 0 and then 1
to all surrounding cells
All unmarked cells neighboring
those marked 1 are labeled
with a 2 and so on
Wavefront propagation does
not terminate until a value is
given to all cells in free space
Zelinsky et al (1993)
Conventional wavefront
algorithm
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Determine coverage path by
moving towards a cell that has
highest value neighboring the
cell that has not been visited
Reduces to following the
equipotential curves from top
to bottom when no obstacles
are present
Specifying of both start and
goal is unusual for coverage
planning algorithms
Zelinsky et al (1993)
Conventional wavefront
algorithm
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Wavefront potential function
can be defined to encode cost
functions to optimize coverage
algorithm
Compute distance of each cell
to the nearest obstacle and
then use the weighted sum of
these with the original potential
to compute the path
Results in fewer turns
Zelinsky et al (1993)
Planar terain-covering
algorithm
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Cells fixed in width, but top
and bottom can have any
shape
Start at an arbitrary point and
zigzag up and down straight
lines to cover the given area
Does not assume prior
knowledge of the environment
Hert et al (1996)
Planar terain-covering
algorithm
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Areas that would not be
covered or covered twice are
detected and covered
immediately
Recursive zigzagging causes
these inlets to be covered in
depth first order
Robot must remember the
doorways through which it
enters and exits an inlet
Hert et al (1996)
Planar terain-covering
algorithm
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When the area is not simply
connected minor modifications
are made to represent areas
around islands that would not
be covered as an artificial bay
Hert et al (1996)
Exact cellular decomposition
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Set of non-intersecting regions
whose union fills the entire
area
Each cell can be covered
using simple motions
Problem is reduced to planning
movements from one cell to
the next
LaValle (2006)
Boustrophedon decomposition
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Individual cells covered in back
and forth motions like an ox
plowing a field
An optimization of vertical
decomposition to eliminate cell
boundaries that unnecessarily
interrupt this boustrophedon
motions
LaValle (2006)
Boustrophedon decomposition
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A line segment is swept
through the environment
Whenever there is a change in
connectivity of this slice a new
cell is formed
Choset (2001)
Optimal line sweep
decomposition
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A further optimization to
reduce robot turns
Number of turns to cover a
boustrophedron cell
approximately proportional to
the width of region
perpendicular to the motion
Choose a slice direction to
minimize the sum of widths of
all cells in the decomposition
Huang (2001)
Multi-robot complete
algorithms
• Divide the time to complete coverage
• Can use other robots as beacons to minimize
errors
• Enhances robustness to ensure successful
coverage
Summary
• Heuristics and randomized or complete algorithms
• Approximate and exact cellular decompositions
• Each method has benefits and drawbacks
• Availability and effectiveness of sensors an issue
References
• Choset (2001): Coverage for robotics - a survey of
recent results
• Choset and Pignon (1997): Coverage path
planning - the boustrophedon decomposition
• Current and Schilling (1989): The covering
salesman problem
• Fiorini and Prassler (2000): Cleaning and
household robots - a technology survey
References
• Gage (1993): Randomized search strategies with
imperfect sensors
• Hert, Tiwari, and Lumelsky (1996):
A terrain-
covering algorithm for an AUV
• Huang (2001): Optimal line-sweep decompositions
for coverage algorithms
• Moravec and Elfes (1985): High resolution maps
from wide angle sonar
References
• iRobot Corporation (2007): iRobot Roomba 500
Series Owner’s Guide
• LaValle (2006): Planning Algorithms
• Zelinsky, Jarvis, Byrne, and Yuta (1993): Planning
paths of complete coverage of an unstructured
environment by a mobile robot