Finding Narrow Passages with Probabilistic Roadmaps: The SmallStep Retraction Method

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Finding Narrow Passages withProbabilistic
Roadmaps The Small-Step Retraction Method
Mitul Saha and Jean-Claude Latombe
Research supported by NSF, ABB and GM
Artificial Intelligence Lab Stanford University
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Probabilistic Roadmaps (PRM)
goal configuration
start configuration
free-space
c-obstacle
Configuration-space components
Kavraki, Svetska, Latombe, Overmars, 1996
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PRM planners solve complicated problems
Complex geometries obstacles 43530
polygons Robot 4053 polygons
High dimensional
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Main Issue Narrow Passages
narrow passage
free samples
colliding local path
colliding samples
The efficiency of PRM planners drops
dramatically in spaces with narrow passages
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Main Issue Narrow Passages

• Problems with narrow passages are commonly
  encountered

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Main Issue Narrow Passages

• Proposed strategies
• Filtering strategies,
• e.g., Gaussian sampling Boor et al. 99
• and bridge test Hsu et al. 03
• ? rely heavily on rejection sampling
• Retraction strategies,
• e.g., Wilmart et al. 99Lien et al. 03
• ? waste time moving many
  configurations out of collision

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Motivating Observation
planning time
decreasing width of the narrow passage
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Small-Step Retraction Method
Roadmap construction and repair
(2 3)
(1)

• Slightly fatten the robots free space
• Construct a roadmap in fattened free space
• Repair the roadmap into original free space

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Small-Step Retraction Method
Roadmap construction and repair
Fattening
widened passage
fattened free space

• Free space can be indirectly fattened by
• reducing the scale of the geometries (usually of
  
• the robot) in the 3D workcell with respect to
• their medial axis
• -This can be pushed into the pre-processing
• phase

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Small-Step Retraction Method
Roadmap construction and repair
Fattening
start
Repair during construction
Pessimist Strategy
Optimist Strategy
Repair after construction
goal
fattened free space
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Small-Step Retraction Method
Roadmap construction and repair
Fattening
start
Repair during construction
Pessimist Strategy
Optimist Strategy
Repair after construction
goal
fattened free space
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Small-Step Retraction Method
Roadmap construction and repair
Fattening
start
Pessimist Strategy
Repair during construction
?Integrated planner 1. Try Optimist for N
time. 2. If Optimist fails, then run
Pessimist
Optimist Strategy
Repair after construction
goal
fattened free space
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Quantitative Results

• Fattening preserves topology/ connectivity of
  the free space

• Fattening alters the topology/ connectivity of
  the free space

(c)
(a)
(b)
Alpha 1.1
(g)
Alpha 1.0
(f)
(d)
(e)
Upto 3 orders of magnitude improvement in the
planning time was observed
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Quantitative Results

• Test environments without narrow passages
• SSRP and SBL have similar performance

(i)
(j)
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Conclusion

• SSRP is very efficient at finding narrow passages
  and still works well when there is none
• The main drawback is that there is an additional
  pre-computation step

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Finding Narrow Passages withProbabilistic
Roadmaps The Small-Step Retraction Method