Particle Filter for Robot Localization

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Particle Filter for Robot Localization

• Vuk Malbasa

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Problem

• Map is given as bitmap
• It is possible to measure distance to dark like
  from any position
• Robot needs to find out where on the map it is
  located
• Only available data is
• Odometry (noisy)
• Range finding (noisy)
• Robot is programmed to follow a particular route
  around the map and is allowed to measure at each
  time step

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Robot sensors

• The robot measures distance to wall from several
  directions
• I assumed that a gyroscope would always let the
  robot take measurements from the same angle
• Additive noise is simulated in the measurements
  as
• e N(0,1)
• The robot sees a vector of distances
• To localize the robot needs to find a spot on the
  map which has similar distances to what it sees
• The measure of similarity
• Given the current robot measurements as the mean
  of a normal distribution with a large standard
  deviation how likely are the measurements taken
  from different locations across the map?

R
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Measurements

• Sometimes the measurements can be ambiguous
• When there the robot is in a repetitive position
  on the map the distance function can be deceiving
• This is where odometry helps
• When in the features that the robot sees are
  unique to that position on the map then the
  distance function has one optimum

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Measurements

• When the map is complex and the measurements are
  noisy then the distance function shows multiple
  optima
• This leads to the importance of keeping track of
  previous positions of particles
• While a positions measurements may not be unique
  to a particular place on the map, the sequence of
  measurements is unique

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Algorithm

• initialize particles
• for i 1length(movement)
• take measurements from current position
• simulate measurements for particles
• calculate distance function
• assign weights
• resample
• move robot
• move particles
• end

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Practice
At the beginning of the movement there are many
possible positions because of noisy measurements
and the wide Gaussian distance function After a
few iterations there are only two major positions
left and the biggest one is wrong However once
the robot moves into a place on the map with
unique measurements there is only one position
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Parallel to evolutionary computation
Particle filters
Evolutionary Computation

• loop
• predict
• evaluate
• resample
• end

loop simulate evaluate reproduce end
Uncanny similarity