Simultaneous Localization and Mapping

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Simultaneous Localization and Mapping
Presented by Lihan He Apr. 21, 2006
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Outline

• Introduction
• SLAM using Kalman filter
• SLAM using particle filter
• Particle filter
• SLAM by particle filter
• My work searching problem

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Introduction SLAM
SLAM Simultaneous Localization and Mapping
A robot is exploring an unknown, static
environment.

• Given
• The robots controls
• Observations of nearby features

The controls and observations are both noisy.

• Estimate
• Location of the robot -- localization
• where I am ?
• Detail map of the environment mapping
• What does the world look like?

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Introduction SLAM
Markov assumption
State transition Observation function
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Introduction SLAM
Method Sequentially estimate the probability
distribution p(xt) and update the map.
Prior p(x0)
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Introduction SLAM
Map representations
1. Landmark-based map representation
Track the positions of a fixed number of
predetermined sparse landmarks. Observation
estimated distance from each landmark.
2. Grid-based map representation
Map is represented by a fine spatial grid, each
grid square is either occupied or empty.
Observation estimated distance from an
obstacle using a laser range finder.
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Introduction SLAM
Methods
The robots trajectory estimate is a tracking
problem
1. Parametric method Kalman filter
Sequentially update µt and St
2. Sample-based method particle filter
Represent the distribution of robot location xt
(and map mt) by a large amount of simulated
samples.
Resample xt (and mt) at each time step
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Introduction SLAM
Why is SLAM a hard problem?
Robot location and map are both unknown.

• The small error will quickly accumulated over
  time steps.
• The errors come from inaccurate measurement of
  actual robot motion (noisy action) and the
  distance from obstacle/landmark (noisy
  observation).

When the robot closes a physical loop in the
environment, serious misalignment errors could
happen.
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SLAM Kalman filter
Update equation
Assume Prior p(x0) is a normal
distribution Observation function p(ox) is a
normal distribution
Then Posterior p(x1), , p(xt) are all normally
distributed. Mean µt and covariance matrix St
can be derived analytically. Sequentially update
µt and St for each time step t
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SLAM Kalman filter
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SLAM Kalman filter
The hidden state for landmark-based SLAM
Map with N landmarks (32N)-dimentional Gaussian
State vector xt can be grown as new landmarks are
discovered.
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SLAM particle filter
Update equation
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SLAM particle filter
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SLAM particle filter
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SLAM particle filter
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SLAM particle filter
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SLAM particle filter
State transition probability
Observation probability
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SLAM particle filter

• Lots of work on SLAM using particle filter are
  focused on
• Reducing the cumulative error
• Fast SLAM (online)
• Way to organize the data structure (saving robot
  path and map).
• Maintain single map cumulative error
• Multiple maps memory and computation time

• In Parrs paper
• Use ancestry tree to record particle history
• Each particle has its own map (multiple maps)
• Use observation tree for each grid square (cell)
  to record the map corresponding to each particle.
• Update ancestry tree and observation tree at each
  iteration.
• Cell occupancy is represented by a probabilistic
  approach.

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SLAM particle filter
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Searching problem
Assumption

• The agent doesnt have map, doesnt know the
  underlying model, doesnt know where the target
  is.
• Agent has 2 sensors
• Camera tell agent occupied or empty cells in
  4 orientations, noisy sensor.
• Acoustic sensor find the orientation of the
  target, effective only within certain distance.
• Noisy observation, noisy action.

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Searching problem

• Similar to SLAM
• To find the target, agent need build map and
  estimate its location.

• Differences from SLAM
• Rough map is enough an accurate map is not
  necessary.
• Objective is to find the target. Robot need to
  actively select actions to find the target as
  soon as possible.

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Searching problem

• Model
• Environment is represented by a rough grid
• Each grid square (state) is either occupied or
  empty.
• The agent moves between the empty grid squares.
• Actions walk to any one of the 4 directions, or
  stay. Could fail in walking with certain
  probability.
• Observations observe 4 orientations of its
  neighbor grid squares occupied or empty.
  Could make a wrong observation with certain
  probability.
• State, action and observation are all discrete.

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Searching problem
In each step, the agent updates its location and
map

• Belief state the agent believes which state it
  is currently in. It is a distribution over all
  the states in the current map.
• The map The agent thinks what the environment
  is .
• For each state (grid square), a 2-dimentional
  Dirichlet distribution is used to represent the
  probability of empty and occupied.
• The hyperparameters of Dirichlet distribution are
  updated based on current observation and belief
  state.

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Searching problem
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Searching problem
Map update (Dirichlet distribution)
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Searching problem
Belief state update
aup
aright
Map representation update
aright
aup
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Searching problem
Choose actions
Each state is assigned a reward R(s) according to
following rules
Less explored grids have higher reward.
Try to walk to the empty grid square.
Consider neighbor of s with priority.
x
x