Bayesian Landmark Learning for Mobil Robot Localization

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Bayesian Landmark Learningfor Mobil Robot
Localization

• Journal of Machine learning
• Vol 33, pp4176 (1998)
• Author Sabastian Thrun

Presented ByYehia Kotb ykotb_at_csd.uwo.ca
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Introduction

• Mobile Robot Localization is the process of
  determining the Location of a mobile robot
  relative to its environment.

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Introduction

• Accurate Localization is a key prerequisite for
  successful navigation .

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Introduction

• All existing localization algorithms extract a
  small set of features from the robot sensor
  measurements.

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Model Matching approaches.
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Landmark approaches.
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Landmark Approaches

• Most of landmark approaches reply on static,
  hand-coded sets of features. disadvantages
• Lack of flexibility.
• Lack of Optimality.
• Lack of autonomy

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Questions to be asked

• What land marks are Best suited ?
• Can a robot learn its own set of features ?
• Can a robot learn optimal features?

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Beliefs, Acting, and Sensing
Sensing
Acting
Acting
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Robot Localization ?

• ? Robot (x, y,?).

Bel(?)
?
Which is the space of all locations

• This belief is described by a probability density
  function over all locations Bel(?)

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Prior and Posterior Believes

• The problem of localization is to approximate the
  true distribution which should be a peak in the
  robot location and zero elsewhere.

Belprior (?)
Belposterior (?).
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Location, Acting, an sensing
Current Location
Previous location
Action taken
Current Location
Sensor measurement
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Mapping Function s

• Computing meaningful estimates for the
  probability function above is difficult in most
  applications.
• It is essential to compute these estimates from
  data.

Mapping function
Sensor measurements
Features
s
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Position Tracking

• Position Tracking is when the robot knows It is
  initial location and goal of localization. In
  this case, Belprior (?(0)) is a point centered
  distribution that has a peak on the correct
  location.

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Self Localization
?

• If the initial location is not known in
  priori,The problem is known as self localization

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Sensing
Features
s
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Believe change by actions and sensing

• Sensor queries and actions change the robot
  internal belief.

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Robot Localization and Bayes

• According to Bayes Rule

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Robot Localization

• Markov assumption states that sensor readings are
  conditionally independent of previous sensor
  readings and actions given knowledge of the exact
  location.

Markov Assumption
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Robot Localization
To Summarize, the posterior belief after
observing the t-th feature vector f(t) is
proportional to the prior belief multiplied by
the likelihood of observing f(t) at ?(t)
BelPrior(?(t))
C Belposterior(?(t))
multiplication
P(f(t) ?(t))
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Robot Localization

• Actions also change the robot beliefs

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Robot Localization
According to the theorem of total probability
Since ?(t) does not depend on a(t)
Posterior Belief
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Localization
Verbally The probability of being at ?(t1) at
time t1 is the result of multiplying the
probability of previously having been at ?(t1)
with the probability that action a(t) carried the
robot to location ?(t1) .
P(?(t))
C Belprior(?(t1))
multiplication
P(?(t1))
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• From The two mathematically proven conclusions,
  It is convenient to have an incremental
  localization algorithm for localization.

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Incremental localization algorithm
END
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Incremental localization algorithm

• To apply the algorithm three probabilities must
  be known

• The initial estimate

2. The Transition probability
3. The map of the environment
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Incremental localization algorithm

• The Algorithm works as follows on the environment
  shown in the last figure

• The robot queries its sensors and finds out that
  its next to a door.
• As a result Bel(?) is large for door locations
  and small everywhere else.
• The robot moves forward, as a response, Bel(?) is
  shifted and slightly flattened out reflecting
  P(? ?,a) due to robot motion.
• The robot queries its sensors again to find out
  next door. The resulting density now has a peak
  and is fairly accurate.
• The robot knows with high accuracy where it is.

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Bayesian Landmark Learning(BaLL)

• General Description for BaLL

• Robot learn features along with routines for
  extracting them from sensory data.
• Features are computed by ANN that map sensor data
  to a lower dimensional feature space.
• A Bayesian analysis quantifies the average
  posterior error a robot is expected to make.
• The objective of ANN training is to minimize such
  error.
• The robot learns features that directly minimizes
  such error.

LEARNING s Is the Key of the algorithm
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Ball

• Advantages of Ball as claimed by the authors

• It is more flexible than static approaches to
  SLAM since it can adapt to the environment,
  sensor reading, and robot structure.
• It will often yield better results than static
  approaches. Since it directly chooses the optimal
  features.
• It increases the autonomy of the robot, since it
  requires not human to choose the appropriate
  features.

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The Bayesian Localization error

• Let ? denote the true location of the robot.
• Let e(?, ?) the error function between the true
  position and an arbitrary other position

Error for single location
Instantaneous error with respect to ?
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The Bayesian Localization error
Posterior Belief
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The Bayesian Localization error
Posterior Belief
Since fs(s)
Posterior Belief of sensing in location ?
The Error Eposterior is the exact localization
error after sensing
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ANN Preliminaries
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ANN Preliminaries
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4.2 BaLL - Neural network filters
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