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7. SLAM

building a spatio-temporal memory for the robot

Probablilistic robotics

  • localisation with landmarks
  • localisation with edges

Uncertainty

  • measurement errors (sensors are not accurate)
  • actuation errors (actions never do excactly wht they are supposed to)

conditional probablility and bayes rule

P(E|O) = probablity that E is true given that we observe O

P(cold|cough) = P(cold) * P(cough|cold) i.e. . if we know the prior probability that I have a cold (without any evidence) and I know that a cold causes a cough, with some probability, then we can calculate the posterior probability

probablilistic inference

Bayes rule: P(H|E) = P(H) x P(E|H)

or bel(x_t) = bel(x_t-1) x prob(observation)

Updating State Estimate - Kalman filter

• The Kalman filter is commonly used to update the estimate of the robot’s state • Two phases:

  1. Prediction (Process Update) • predicts where the robot will be after performing an action
  2. Correction (Observation Update) • use observations to correct prediction • What follows is only a sketch of the Kalman filter • It’s nowhere near the complete algorithm

Robot determining if door is open

  • observsation 2 states: open or close
  • robot has two actions: push or nothing

Position tracking

Robot moves • Predict new position based on what motor actions are expected to do • Measure • Uses sensors to estimate motion • Update position estimate (often a Kalman Filter)

Particle filter 1 - rdm guess 2 .. 3 - weifht particle

Loop Closure

(Full SLAM) • Position tracking alone will accumulate errors • If the robot recognise a landmark that it has seen before • it can correct drift by updating estimate based on measurement of landmark • Error correction is back-propagated