CS 326 A: Motion Planning

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CS 326 A Motion Planning

• http//robotics.stanford.edu/latombe/cs326/2002
• Motion Planning with Uncertainty

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Types of Uncertainty
W2

• Uncertainty in model
• Uncertainty in sensing
• Uncertainty in control

I
G
W1
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What is Uncertainty?

• Uncertainty Distribution of possible errors
• Ensemble distribution ? Optimize outcome in
  worst case (game against nature)? Guaranteed
  strategy (2nd paper)
• ? EDR strategy (1st paper)
• Probabilistic distribution? Optimize expected
  outcome? Probabilistic strategy

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Preimage

• The preimage of a goal G for a motion command
  (dir,term) is the largest subset P of C-space
  such that a motion starting from within P is
  guaranteed to end in G - dir is responsible for
  reaching G- term is responsible for recognizing
  that the goal has been attained
• dir direction of motion
• term termination condition

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Preimage Backchaining

• Problem goal G, initial region I
• Recursively compute preimages of G for multiple
  motion commands and preimages of these preimages,
  until a preimage contain I
• Lozano-Pérez, Mason, and Taylor, 1983

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What is the Issue?

• Goal reachability and recognizability are
  interdependent
• This means that a preimage depends on itself!!!
  (notion of fixed point)

See paper by Lozano-Pérez, Mason, and Taylor
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Example
Backprojectionfrom kernel
Kernel of goal
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Example
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Computational Approach

• Separate reachability and recognizability, e.g.
• ? kernel of goal backprojection from
  kernel? backprojection from landmark area in
  2nd paper
• ? Incomplete planning or task engineering