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Contents contributed and discussions participated by Filip Bártek

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Filip Bártek

Monte Carlo localization - Wikipedia, the free encyclopedia - 0 views

en.wikipedia.org/...Monte_Carlo_localization

shared by Filip Bártek on 18 May 15 - No Cached
  • particle filter localization
  • typically starts with a uniform random distribution of particles
  • hopefully most particles will converge to where the robot actually is.
  • ...19 more annotations...
  • environment is static and does not change with time
    • Filip Bártek
      Filip Bártek on 18 May 15
       
      We also need to capture the robot's velocity in the state (pose) in case the robot has some momentum, so the three parameters may be not enough for a 2D robot.
  • assumes the Markov property
  • position and orientation
  • particles are uniformly distributed over the configuration space
  • Given a map
  • every time
  • every time
  • motion_update
  • sensor_update
  • sensor_update
  • some noise is applied
  • It now believes it is at one of two locations.
  • The robot has successfully localized itself.
  • actuation command
  • no actuator is perfect: they may overshoot or undershoot the desired amount of motion
  • the motion model must be designed to include noise as necessary
  • Particles which were consistent with sensor readings are more likely to be chosen
  • possibly more than once
  • a robot becomes increasingly sure of its position as it senses its environment
Filip Bártek

Recursive Bayesian estimation - Wikipedia, the free encyclopedia - 0 views

en.wikipedia.org/...Recursive_Bayesian_estimation

shared by Filip Bártek on 18 May 15 - No Cached
  • is constant relative to
  • is constant relative to
  • is constant relative to
  • ...13 more annotations...
  • Markov assumption
  • conditionally independent of the other earlier states
  • measurement at the k-th timestep is dependent only upon the current state
  • proportional
    • Filip Bártek
      Filip Bártek on 18 May 15
       
      It is proportional with the factor \alpha. \alpha = 1 / p(z_k|z_{1:k-1}) A way to compute the value of \alpha is shown below. It is common to all the updated states x_k at a given time k and measurement z_k.
  • predicted
  • marginalising out the previous states
  • predicted state
    • Filip Bártek
      Filip Bártek on 18 May 15
       
      p(x_k|z_{1:k-1})
  • update
  • predict and update steps
  • measurement likelihood
    • Filip Bártek
      Filip Bártek on 18 May 15
       
      p(z_k|x_k)
  • is constant relative to
  • can usually be ignored in practice
    • Filip Bártek
      Filip Bártek on 18 May 15
       
      We are typically interested in relative probabilities of the states. Equivalently [?], the p(x_k|z_{1:k}) across all the estimated states x_k is a probability distribution: \Sum_{x_k}{p(x_k|z_{1:k})} = 1
  • simply normalized, since its integral must be unity
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