Post on 20-Dec-2015
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Finding “Narrow Passages” withProbabilistic Roadmaps:
The Small-Step Retraction Method
Mitul Saha and Jean-Claude Latombe
Research supported byNSF, ABB and GM
Artificial Intelligence LabStanford University
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Probabilistic Roadmaps (PRM)
[Kavraki, Svetska, Latombe, Overmars, 1996]
startconfiguration
goalconfiguration
free-spacec-obstacleConfiguration-space
components
milestonelocal path
Roadmapcomponents
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PRM planners solve complicated problems
Complex geometries:obstacles: 43530 polygonsRobot: 4053 polygons
High dimensional
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Main Issue: “Narrow Passages”
free samples
colliding samples colliding local path
narrow passagelow density of free samples
high density of free samples
The efficiency of PRM planners drops dramatically in spaces with narrow passages
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• Problems with “narrow passages” are commonly encountered
Main Issue: “Narrow Passages”
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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. ‘99][Lien et al. ‘03] waste time moving many configurations out of collision
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Motivating Observation
decreasing width of the narrow passage
planningtime
easy narrow
passages
difficult narrow passages
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Roadmap constructio
nand repair
fattened free space
widened passage
Fattening
free spacec-obstacle
start
goal
Small-Step Retraction Method
1. Slightly fatten the robot’s free space2. Construct a roadmap in fattened free space3. Repair the roadmap into original free space
(1) (2 & 3)
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Small-Step Retraction Method
Roadmap constructio
nand repair
fattened free space
widened passage
Fattening
free spacec-obstacle
start
goal
-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 constructio
nand repair
fattened free space
widened passage
Fattening
free spacec-obstacle
start
goal
Repair during construction
Repair after construction
goal
PessimistStrategy
OptimistStrategy
fattenedfree space
startstart
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Small-Step Retraction Method
Roadmap constructio
nand repair
fattened free space
widened passage
Fattening
free spacec-obstacle
start
goal
Repair during Repair during constructionconstruction
Repair after Repair after constructionconstruction
fattenedfree space
goal
PessimistStrategy
OptimistStrategy
- Optimist may fail due to “false passages” but Pessimist is probabilistically complete
- Hence Optimist is less reliable, but much faster due to its lazy strategy
start
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Small-Step Retraction Method
Roadmap constructio
nand repair
fattened free space
widened passage
Fattening
free spacec-obstacle
start
goal
Repair during construction
Repair after construction
goal
PessimistStrategy
OptimistStrategy
Integrated planner:
1. Try Optimist for N time. 2. If Optimist fails,
then run Pessimist
fattenedfree space
start
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Quantitative Results• Fattening “preserves” topology/
connectivity of the free space• Fattening “alters” the topology/
connectivity of the free space
TimeSSRP(secs)
TimeSBL
(secs)
(a) 9.4 12295
(b) 32 5955
(c) 2.1 41
(d) 492 863
(e) 65 631
(f) 13588 >100000
TimeSSRP(secs)
TimeSBL
(secs)
(g) 386 572
(h) 3365 >100000
(a) (b) (c)
(d) (e)(f)
(g) (h)Alpha 1.0
Alpha 1.1
Upto 3 orders of magnitude improvement in the planning time
was observed
Our planner
A recent PRM planner
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Quantitative Results
• Test environments “without” narrow passages– SSRP and SBL have similar performance
TimeSSRP
TimeSBL
(i) 1.68 1.60
(j) 2.59 2.40
(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