Mapping with Known Poses

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Mapping with Known Poses
CS5391 AI Robotics
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Some Information

• Course website and office hours will remain the
  same.
• Contact info
• Mohan Sridharan mohan.sridharan_at_ttu.edu
• www.cs.ttu.edu/smohan
• Interests learning, adaptation with visual
  information on mobile robots, cognitive systems,
  multiagent systems.
• Topics covered Bayesian principles,
  localization.
• Topics to be covered Mapping SLAM, Planning.

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Agenda

• Introduction to mapping
• Motivate SLAM.
• Mapping with known poses.
• Some examples.
• Simple counting-based mapping.
• MAP estimation.

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Why Mapping?

• Maps are a fundamental requirement
• Provides a frame of reference to humans and
  robots!
• Maps used for localization, path-planning,
  activity-planning, active-sensing
• Autonomous behavior requires Simultaneous
  Localization And Mapping (SLAM).

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The General Problem of Mapping
What does the environment look like?
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Mathematical Formulation

• Formally, given the sensor data
• mapping involves finding the most likely map
  (mode)
• Finding full posterior is easier with
  independence assumption

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Mapping is a Chicken and Egg Problem

• Localization estimate robot pose given sensor
  data and map.
• Goal Autonomous mobile robots that require
  little/no human supervision.
• Challenge simultaneously estimate robot pose and
  the map (SLAM).
• Bootstrap off of localization and map-building
  with known pose.

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Problems in Mapping

• Noise in sensing and actuation
• Extract information from noisy sensory data?
• Model and account for motion error accumulation?
• Ambiguity in perception
• Establish correspondence between sensor readings?
• Data association
• Identify that robot is at a previously visited
  place?
• Close the loop?
• Large continuous search space
• Binary map with N grid-cells represents 2N maps!!

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Types of SLAM-Problems

• Grid maps or scans
• Lu Milios, 97 Gutmann, 98 Thrun 98
  Burgard, 99 Konolige Gutmann, 00 Thrun, 00
  Arras, 99 Haehnel, 01
• Landmark-based
• Leonard et al., 98 Castelanos et al.,
  99 Dissanayake et al., 2001 Montemerlo et al.,
  2002

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Occupancy Grid Maps (Moravec and Elfes, 1985)

• Environment a collection of grid cells.
• Estimate the probability that a cell is occupied.
• Key assumptions
• Occupancy of individual cells (mij) is
  independent!
• Robot poses are known!
• Post-processing tool

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Updating Occupancy Grid Maps

• Idea Update each individual cell within
  field-of-view using a binary Bayes filter.
• Additional assumption Map is static i.e. control
  commands can be neglected!!

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Binary Bayes Filter (revisited)

• Elegant, avoids truncation errors
• Chapter 4 Table 4.2 in textbook.

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Updating Occupancy Grid Maps

• Use the log-odds representation.
• Cross-check with equation 4.19, Chapter 4

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Updating Occupancy Grid Maps

• Update the map cells using the inverse sensor
  model
• Log-odds of occupancy of grid cell, given the
  current measurement and known pose.
• Information about the world conditioned on
  measurements caused by the world.
• Table 9.2 for an ad-hoc example, Section 9.3 for
  principled function-approximation.

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Adhoc Inverse Sensor Model

• Incorporate factors involved in the computation
  of
• Factors
• Relative distance of robot from cells
  center-of-mass.
• Relative orientation of robot from cells
  center-of-mass.
• Width of obstacle and sensor beams.
• Cells outside field-of-view
• Cells within suitable range
• Other cells

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Function Approx. Inv. Sensor Model

• Sampling-based approach.
• Approach
• Sample a map from a set of feasible maps.
• Sample a robot pose
• Sample a measurement
• Get ground-truth occupancy value from map
• Learn predictor that minimizes error over data
  samples.
• Use relative pose, model sensor characteristics.

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Incremental Updating of Occupancy Grids (Example)
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Agenda

• Introduction to mapping
• Motivate SLAM.
• Mapping with known poses.
• Some examples.
• Simple counting-based mapping.
• MAP estimation.

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The General Problem of Mapping
What does the environment look like?
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Recap

• Goal simultaneously localize and mapping (SLAM).
• Occupancy Grid mapping assume known pose and
  independence
• Binary Bayes filter and inverse sensor models for
  updating individual cells.
• Adhoc and Sampling-based approaches for the
  inverse sensor model.

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Incremental Updating of Occupancy Grids (Example)
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Resulting Map Obtained with Ultrasound Sensors
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Resulting Occupancy and Maximum Likelihood Map
The maximum likelihood map is obtained by
clipping the occupancy grid map at a threshold of
0.5
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Occupancy Grids From scans to maps
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Tech Museum, San Jose
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Agenda

• Introduction to mapping
• Motivate SLAM.
• Mapping with known poses.
• Some examples.
• Simple counting-based mapping.
• MAP estimation.

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Alternative Simple Counting

• For every cell count
• hits(i, j) no. of times a beam ended at lti, jgt.
• misses(i, j) no. of times a beam passed through
  lti, jgt
• Value of interest P(reflects(i, j))
• Count how often a cell has reflected a beam and
  how often it was intercepted.

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The Measurement Model
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Maximum A Posteriori (MAP) Mapping

• Relax independence assumption
• Output mode of posterior instead of full
  posterior
• Use measurement models instead of inverse models.

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Computing the Most Likely Map

• Compute value for m that maximizes
• Assuming a uniform prior probability for p(m),
  this is equivalent to maximizing (Section 9.4.2)

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Difference between Occupancy Grid Maps and
Counting

• The counting model (with MAP) determines how
  often a cell reflects a beam
• No inverse sensor model ?
• Store all data i.e. incremental updates not
  possible ?
• The occupancy model represents whether or not a
  cell is occupied by an object.
• Incremental updates possible ?
• Inverse sensor models, independence assumption ?
• Although a cell might be occupied by an object,
  it says nothing about the reflection probability.

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Example Occupancy Map
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Example Reflection Map
glass panes
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Summary

• Occupancy grid maps are a popular approach to
  represent the environment of a mobile robot given
  known poses.
• It stores the posterior probability that the
  corresponding area in the environment is
  occupied.
• Occupancy grid maps can be learned efficiently
  considering each cell independently from all
  others.
• Reflection maps are an alternative
  representation, each cell stores the probability
  that a beam is reflected by this cell.
• Reflection maps are more optimal.
• MAP approach relaxes independence constraint.
• Sensor model for computing the likelihood of
  measurements.