Workspace-based Connectivity Oracle

1
Workspace-based Connectivity Oracle

• An Adaptive Sampling Strategy for PRM Planning
• Hanna Kurniawati and David Hsu
• Presented by Nicolas Lee and Stephen Russell

2
Outline

• Introduction/Motivation
• WCO Planner
• Constructing a component sampler
• Ensemble sampler
• Results

3
Introduction

• Standard Probabilistic Road Map (PRM)
• Two phases construction and query
• Construction creates map, R, that tries to
  accurately model connectivity of C
• Query tries to connect start/goal locations to R

4
Motivation

• Performance depends on quality of R
• Coverage and connectivity
• Algorithm struggles with narrow passages in C
• Other sampling strategies
• Dynamic Machine learning/adaptive hybrid
• Workspace information Identifying important
  regions in W
• e.g. Workspace Importance Sampling (WIS) focuses
  on regions with small local feature size

5
WCO Foundations

• Proposition
• If two configurations q, q ? C are connected by
  a path in Fc , then for any point f in a robot,
  Pf(q) and Pf(q), the projections of q and q in
  W, are connected by a path in Fw

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WCO

• Distinct components of R may in fact lie in the
  same connected component of Fc
• Examine workspace paths for multiple feature
  points and construct sampler for each f
• Search for channels in W and adapt distribution
  to sample more densely in regions covered by
  these channels

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Workspace Connectivity

• Decomposition T of Fw into non-overlapping cells
• Create adjacency grid GT of T
• Consider two milestones, m and m, and
  projections onto W, Pf(m) ? t and Pf(m) ? t
• Find workspace channel, ? set of nodes in GT
  connecting t and t
• Lf( ?) suggests a region of Fc for sampling

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Example

1. Milestones projected to decomposed workspace
2. Adjacency graph GT
3. Channel graph G

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Component Sampler Algorithm

1. Given f, sample configuration q based on sampling
   distribution over T
2. If q is collision free, then
3. Insert q into R as new milestone m
4. Nm, set of neighbors
5. for each m ? Nm do
6. if m ? Ri and m ? Rj, then
7. connect if possible
8. Project m to W
9. Update label sets for affected T
10. Delete paths in G connecting terminals with
    same label set
11. Let t ? T containing Pf(m). Perform
    breadth-first search and stop when reaching
    first terminal t ? t
12. Add path from t?t to G if they have different
    label sets
13. Update the sampling distribution

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Ensemble Sampler Algorithm

1. Initialize pi 1/K for i 0, 1, , K-1
2. for t 1, 2, do
3. Pick a component sampler si with probability pi
4. Sample a new configuration q using the component
   sampler picked
5. If a new milestone m is added to the roadmap R
   then
6. Update the distribution for each component
   sampler si
7. Update the probabilities pi

11
Probability Update

• Ensemble sampler performs almost as well as the
  best component sampler
• Kinematic constraints taken into account through
  higher probability in overlapping lifted channels

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Choosing Feature Points

• Must be representative of the robot
• Use vertices of convex hull and centroid for each
  rigid link of a robot

13
Test Configurations
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Comparison With Other Samplers

• WCO has better sampling in channel regions
  without too many samples elsewhere
• In many cases, run time is cut in half compared
  to the best of the other three samplers

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Limitations - 2 Bars Example
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Conclusion

• WCO is an adaptive sampling strategy for PRM
  planning
• Using AHS, combine information from workspace
  geometry and sampling history
• In trials, WCO outperformed strategies which only
  use workspace information OR dynamic sampling