Title: Finding Narrow Passages with Probabilistic Roadmaps: The SmallStep Retraction Method
1Finding 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
2Probabilistic Roadmaps (PRM)
goal configuration
start configuration
free-space
c-obstacle
Configuration-space components
Kavraki, Svetska, Latombe, Overmars, 1996
3PRM planners solve complicated problems
Complex geometries obstacles 43530
polygons Robot 4053 polygons
High dimensional
4Main Issue Narrow Passages
narrow passage
free samples
colliding local path
colliding samples
The efficiency of PRM planners drops
dramatically in spaces with narrow passages
5Main Issue Narrow Passages
- Problems with narrow passages are commonly
encountered
6Main 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
7Motivating Observation
planning time
decreasing width of the narrow passage
8Small-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
9Small-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
10Small-Step Retraction Method
Roadmap construction and repair
Fattening
start
Repair during construction
Pessimist Strategy
Optimist Strategy
Repair after construction
goal
fattened free space
11Small-Step Retraction Method
Roadmap construction and repair
Fattening
start
Repair during construction
Pessimist Strategy
Optimist Strategy
Repair after construction
goal
fattened free space
12Small-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
13Quantitative 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
14Quantitative Results
- Test environments without narrow passages
- SSRP and SBL have similar performance
(i)
(j)
15Conclusion
- 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
16Finding Narrow Passages withProbabilistic
Roadmaps The Small-Step Retraction Method