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COMP 150: Probabilistic Robotics for Human-Robot Interaction - - PowerPoint PPT Presentation

Sep 26, 2022 955 likes •1.87k views

COMP 150: Probabilistic Robotics for Human-Robot Interaction Instructor: Jivko Sinapov www.cs.tufts.edu/~jsinapov Today Homework 1 hints Introduction for Particle Filters for localization Localization and Mapping Robot Maps

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COMP 150: Probabilistic Robotics for Human-Robot Interaction

Instructor: Jivko Sinapov www.cs.tufts.edu/~jsinapov

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Today

  • Homework 1 hints
  • Introduction for Particle Filters for localization
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Localization and Mapping

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Robot Maps

[https://www.pirobot.org/blog/0015/map-1b.png]

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Robot Maps

[http://www.openrobots.org/morse/doc/1.2/user/advanced_tutorials/ros_nav_tutorial.html]

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Robot Maps

[https://raw.githubusercontent.com/wiki/introlab/rtabmap/doc/IROS-Kinect-Challenge/combined.png]

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Robot Maps

[http://rrt.fh-wels.at/images/sites/fancybox/3d_mapping.jpg]

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Robot Maps

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A Simple 1-D Map

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A Simple 1-D Map

How would we represent this map using math?

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A Simple 1-D Map

At t = 1, our robot receives an observation:

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A Simple 1-D Map

At t = 1, our robot receives an observation:

x bel(x)

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A Simple 1-D Map

At t = 1, our robot receives an observation:

x bel(x)

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A Simple 1-D Map

At t = 1, our robot receives an observation:

x bel(x)

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A Simple 1-D Map

At t = 1, our robot receives an observation:

x bel(x)

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A Simple 1-D Map

At t = 1, our robot receives an observation:

x bel(x)

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A Simple 1-D Map

At t = 1, our robot receives an observation:

x bel(x) Clearly, a single Gaussian is insufficient to represent our belief that we may be at either of the 3 doors with equal probability

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A Simple 1-D Map

At t = 1, our robot receives an observation:

x bel(x) Clearly, a single Gaussian is insufficient to represent our belief that we may be at either of the 3 doors with equal probability What if we had an initial estimate of the robot’s location prior to

  • bserving and moving?
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But what if we don’t know where we are at the start?

Or, what if somebody moves the robot manually after it started its operation?

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Odometry

“Odometry is the use of data from motion sensors to estimate change in position over time. It is used in robotics by some legged or wheeled robots to estimate their position relative to a starting location. This method is sensitive to errors due to the integration of velocity measurements over time to give position estimates. “

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Odometry Errors

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Basic idea behind Particle Filters

x

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Now, in 2-D

[http://www.ite.uni-karlsruhe.de/METZGER/DIPLOMARBEITEN/dipl2.html]

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Robot Pose

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Odometry Motion Model

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Sampling from the Model

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Motion Model

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Velocity Models with Different Parameters

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Velocity Models with Different Parameters

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Example

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Initially, we do not know the location of the robot, so the particles are everywhere

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Next, the robot sees a door

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Therefore, we inflate particles next to a door and shrink the rest

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Therefore, we inflate particles next to a door and shrink the rest

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Computing the weights

x1 x1 p(z1|x1) x1 Before After

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Before, we continue we re-sample our particles to make them all the same size

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Before, we continue we re-sample our particles to make them all the same size

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Resampling Rules

= = =

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Resampling

  • Given: Set S of weighted samples.
  • Wanted : Random sample, where the probability
  • f drawing xi is given by wi.
  • Typically done n times with replacement to

generate new sample set S’.

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w2 w3 w1 wn Wn-1

Roulette wheel Resampling

w2 w3 w1 wn Wn-1

  • Roulette wheel
  • Binary search, n log n
  • Stochastic universal sampling
  • Systematic resampling
  • Linear time complexity
  • Easy to implement, low variance

[From Thrun’s book “Probabilistic Robotics”]

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Next, the robot moves to the right...

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Therefore, we have to shift the particles to the right as well

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Therefore, we have to shift the particles to the right as well

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...and add some position noise

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...and add some position noise

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Next, the robot senses that is next to a door

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Next, the robot senses that is next to a door

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…we resample again

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The robot keeps going to the right...

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...we shift the particles again

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...and we add noise.

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And so on...

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Now, let’s compare that to some of the other methods

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Grid Localization

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Markov Localization

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KF

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Particle Filter

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Examples

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Localizing using Sonar

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Using Ceiling Maps

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Vision-Based Localization

P(z|x) h(x) z

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Under a light

Measurement z: P(z|x):

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Close to a light

Measurement z: P(z|x):

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Far from a light

Measurement z: P(z|x):

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Could the robot use both vision and sonar to localize? How?

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Summary

Particle filters are an implementation of recursive Bayesian filtering They represent the posterior by a set of weighted samples. In the context of localization, the particles are propagated according to the motion model. They are then weighted according to the likelihood of the

  • bservations.

In a re-sampling step, new particles are drawn with a probability proportional to the likelihood of the observation.

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Localization and Mapping Project Ideas

  • Build maps and localize using vision
  • 2D and/or 3D vision
  • Ceiling Maps
  • Incorporate multiple sources of observations for

computing p(z1,z2,…,zk|x)

  • Integrate existing mapping and localization

algorithms into the turtlebot2 code-base

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Credits

  • Some slides adapted / borrowed from:

Alexander Stoytchev Sebastian Thrun

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THE END

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