Toward Optimal Configuration Space Sampling

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Toward Optimal Configuration Space Sampling

• Presented by
• Yan Ke

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Sampling Problem

• Tool Sample points.
• Target Construct a roadmap representing the
  complete connectivity of the configuration space.

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More Points ? Better Sampling
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How to Sample Smartly?

• Complete knowledge of configuration Space
  (usually unavailable).
• Using information from past experience (our
  approach).

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Modeling Configuration Space

• Section 1

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Build a Model from Past Exp.

• Machine learning is concerned with how to
  automate learning from experience.
• An existing obstructed node indicates being his
  neighbors, you are also likely to be obstructed.
• And vise versa.

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Probability for a single node

• P(qi M)
• q newly sampled point
• i 1(free) or 0 (obstructed)
• M Model built from past experience
• We are learning P base on M.
• We want P(q1 M)?

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Basic Idea

• Model configuration space as binary
  classification C(p) (0,1)
• If q is ps neighbor,
• C(p) 1 P(q1 M)?
• C(p) 0 P(q1 M)?

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Approximation Function

• Denote C(q) P(q1 M)
• Obviously C(q) 0,1

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K-nearest Neighbors

• Q qi i 1,2n
• N(q,k) The function provides the k-nearest
  neighbors in Q.
• C(q)

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A Screen Shot from the Paper
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Probabilities

• P(q1 M) C(q)
• P(q0 M) 1 - C(q)

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Utility Function

• Section 2

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Utility Function

• Purpose Characterize the relevance of a
  configuration to successfully guide sampling.
• Relevance of a configuration
• Unexplored regions near to existing roadmap
  components?
• maximally distance from existing components in
  unexplored regions of configuration space?

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Utility Function

• U(qi , R)
• q newly sampled point
• i 1(free) or 0 (obstructed)
• R the roadmap

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Information Gain

• IG(S,K) H(S) H(SK)
• S some system
• K new knowledge
• H() entropy function
• As S getting more information, H(S)?

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Utility Function

• U(qi , R) IG (R,q) H(R) H(Rq)
• We claim that an obstructed sample doesnt
  provide us any IG
• i.e. U(qi , R) 0

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Another Screen Shot
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How to get around it?

• Return to our very basic goal Full Connectivity
• We restrict our current roadmap to be a set of
  disjoint component.
• The maximal IG is likely to appear near the
  middle point of two large disjoint components.

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Utility-Guided Sampling

• Section 3

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Utility-Guided Sampling
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Algorithm
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Experiment

• Environment Two workspaces with robots of
  varying degrees of freedom.

• Each robot 3-4 links.
• Each joint 3 degrees of freedom.
• Total 9 or 12 DOF

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Result Faster
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Conclusion

• Utility-Guided Sampling
• Guiding sampling to more relevant configurations.
• Experimentally proved to be efficient