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1
Navigation

• Jeremy Wyatt
• School of Computer Science
• University of Birmingham

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Where am I?

• Knowing where you are is a key problem in
  robotics
• Also hard because
• Low bandwidth sensing was noisy (e.g sonar)
• High bandwidth sensing (vision) is very expensive
  to process
• Problem is now partially solved
• Better low bandwidth sensing
• More robust interpretation methods

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Particle Filtering

• State of the art method
• A randomised algorithm
• IDEA track position using many randomised points
  (particles)
• Unlikely particles discard
• Likely particles keep and replicate

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The kidnapped robot problem
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Actions and observations

• Action model what happens when you take an
  action?
• Observation model how likely was your
  observation?

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Particle Filtering a sketch

• Generate n particles randomly
• Repeat
• Take an action
• Move particles according to the action model
• Make an observation
• Weight particles according to the observation
  model
• Generate n new particles according to the
  normalised weights
• Throw away the old particles

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Moving particles action model

• Particles are points in 3D space
• Action
• Add noise, so we
• sample from

Dq
Dx
Dy
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Action model
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Weighting particles observation model

• The observation at time t1 is
• Model says how likely is given
• This likelihood becomes the
  particles weight

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Resampling

• Old particles
• with weights
• New particles
• We normalise the weights and sample new particles
  by treating the weights as a probability
  distribution

2 particles here
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Particle Filtering the algorithm

• Time
• Generate n particles randomly
• Repeat
• Take an action
• Move each particle by sampling from
• Make an observation
• Weight each particle according to the observation
  model
• Generate n new particles by treating the
  normalised weights as a probability distribution
• Throw away the old particles

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Applied to multiple robots
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Applied to vision
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Summary

• Problem of locating myself within a known map
• Particle filtering
• Observation Action model
• Extensions and Problems