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Questions and Answers
Which of the following techniques are used to maximize log-likelihood in the context of approximation?
Which of the following techniques are used to maximize log-likelihood in the context of approximation?
In the approximation process, how many parameters are searched for?
In the approximation process, how many parameters are searched for?
What type of data is shown in the plots for "sonar-0", "sonar-1", "sonar-2", and "sonar-3"?
What type of data is shown in the plots for "sonar-0", "sonar-1", "sonar-2", and "sonar-3"?
What is the main difference between the "sonar" and "laser" data presented?
What is the main difference between the "sonar" and "laser" data presented?
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Considering the plots for "sonar-0", "sonar-1", "sonar-2", and "sonar-3", what can you conclude about the effect of angle on the probability distribution? (Select all that apply)
Considering the plots for "sonar-0", "sonar-1", "sonar-2", and "sonar-3", what can you conclude about the effect of angle on the probability distribution? (Select all that apply)
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Which of the following sensors is NOT classified as a proprioceptive sensor?
Which of the following sensors is NOT classified as a proprioceptive sensor?
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In probabilistic sensor models, what does P(z|x) represent?
In probabilistic sensor models, what does P(z|x) represent?
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What is the primary role of the map (m) in the beam-based sensor model equation?
What is the primary role of the map (m) in the beam-based sensor model equation?
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What is the significance of the independence assumption in the equation (P(z|x, m) = \prod_{k=1}^K P(z_k|x, m))?
What is the significance of the independence assumption in the equation (P(z|x, m) = \prod_{k=1}^K P(z_k|x, m))?
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Which of the following is NOT a factor contributing to uncertainty in proximity measurements?
Which of the following is NOT a factor contributing to uncertainty in proximity measurements?
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What is the key contribution of Bayes filters in probabilistic sensor models?
What is the key contribution of Bayes filters in probabilistic sensor models?
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Which of the following is an example of a typical measurement error in range measurements?
Which of the following is an example of a typical measurement error in range measurements?
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What are the four main types of measurement errors incorporated into the Beam-based Proximity Model?
What are the four main types of measurement errors incorporated into the Beam-based Proximity Model?
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Which of the following statements is true about the probability distribution for unexpected obstacles, $Punexp(z|x, m)$?
Which of the following statements is true about the probability distribution for unexpected obstacles, $Punexp(z|x, m)$?
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What does the equation for $Prand(z|x,m)$ represent?
What does the equation for $Prand(z|x,m)$ represent?
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What is the purpose of the parameters $\alpha_{hit}$, $\alpha_{unexp}$, $\alpha_{max}$, and $\alpha_{rand}$ in the equation for $P(z|x,m)?$
What is the purpose of the parameters $\alpha_{hit}$, $\alpha_{unexp}$, $\alpha_{max}$, and $\alpha_{rand}$ in the equation for $P(z|x,m)?$
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What is the main purpose of the Beam-based Proximity Model?
What is the main purpose of the Beam-based Proximity Model?
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What can be said about the shape of the probability density function, P(z|x, m), for the Beam-based Proximity Model?
What can be said about the shape of the probability density function, P(z|x, m), for the Beam-based Proximity Model?
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What is a likely reason for having the parameter $\eta$ in the equations for the probability distributions?
What is a likely reason for having the parameter $\eta$ in the equations for the probability distributions?
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Why are unexpected objects considered a source of error in the model?
Why are unexpected objects considered a source of error in the model?
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What is the significance of 'Raw Sensor Data' in relation to the Beam-based Proximity Model?
What is the significance of 'Raw Sensor Data' in relation to the Beam-based Proximity Model?
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Study Notes
Introduction to Mobile Robotics
- Probabilistic sensor models are used in mobile robotics.
- Bayesian filters are familiar tools, including Kalman filters, particle filters, hidden Markov models, dynamic Bayesian networks, and partially observable Markov decision processes (POMDPs).
Sensors for Mobile Robots
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Contact sensors: Bumpers
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Proprioceptive sensors: Accelerometers, Gyroscopes, laser light
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Proximity sensors: Sonar, Radar, Laser range-finders, Infrared
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Visual sensors: Cameras
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Satellite-based sensors: GPS
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Proprioceptive sensors measure internal system values.
Proximity Sensors
- The central task is to determine the probability of a measurement (z) given the robot's position (x).
- The question is where the probabilities originate.
- The approach is to explain a measurement.
Beam-based Sensor Model
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A scan (z) consists of K measurements (Z1, Z2, ..., Zk).
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Individual measurements are independent, given the robot position.
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The probability of a measurement (z) given the position (x) and map (m) is calculated.
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The map consists of details about objects and their locations in the environment.
Typical Measurement Errors of a Range Measurement
- Beams reflected by obstacles
- Beams reflected by people/caused by crosstalk
- Random measurements
- Maximum range measurements
Proximity Measurement
- Measurements can be caused by known obstacles, cross-talk, unexpected obstacles, or missing obstacles.
- Noise is related to uncertainty in measuring distances to known obstacles, the position of known obstacles, and positions of additional obstacles or whether obstacles are missed.
Beam-based Proximity Model
- The model incorporates four types of measurement errors.
- These errors are necessary for making the model work, including small measurement noise, unexpected objects, failures to detect objects, and random unexplained noise.
Measurement Noise in Beam-based Proximity Models
- A Gaussian distribution models measurement noise.
- The probability equation is given for the gaussian distribution, with variance and expected measurement.
Unexpected Obstacles in Beam-based Proximity Models
- The probability equation is given for unexpected obstacles, is a decaying function, dependent on the expected measurement and the maximum distance.
Random Measurements in Beam-based Proximity Models
- The probability of random measurements given a robot position and a map is a constant for all measurements within the range and 0 elsewhere.
Maximum Range in Beam-based Proximity Models
- The probability for maximum range is 1 if the measurement is at the maximum expected distance, zero otherwise.
Resulting Mixture Density
- The resulting probability of a measurement, given the robot's position and map is a mixture of various probabilities.
- The parameters of the model need to be determined.
Algorithm beam_range_finder_model
- Defines an algorithm for calculating the probability of a given measurement based on known parameters.
Raw Sensor Data
- Sonar and Laser data in the form of graphs for observed distances is shown.
Approximation
- Maximize log likelihood of the data.
- The search space is of n-1 parameters.
- Methods include: Hill climbing, Gradient descent, Genetic algorithms.
- The n-th parameter is computed to maintain normalization.
Approximation Results
- Approximation results using graphical representation for laser scans and sonar scans at distances of 300cm and 400cm are displayed.
Example- Model and Data
- Display of example output from the model and related data.
Influence of Angle to Obstacle
- Illustration of the influence of the angle to the obstacle.
- Diagrams for three different measurements (sonar-0, sonar-1, sonar-2, sonar-3).
Scan-based Model
- The beam-based model is not efficient for small, or edge obstacles.
- The idea is to check for the endpoint of the beam instead of following beam.
- The probability is a mixture of a Gaussian distribution centered at the distance to the nearest obstacle and a uniform distribution.
- Independent components are considered.
Example (Data for Scan Match)
- Illustrations of an example map with the calculated probability field.
San Jose Tech Museum (Data)
- Two images depicting the occupancy grid map and the likelihood field for the San Jose Tech Museum.
Scan Matching
- The likelihood field from a given scan is used to match scans.
Properties of Scan-based Model
- The model is highly efficient using 2D tables.
- The distance grid is smooth against changes in robot position.
- The approach facilitates scan matching and gradient descent techniques.
- Physical properties of beams are disregarded.
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Description
Test your knowledge on mobile robotics focusing on sensor models and Bayesian filters. This quiz covers various types of sensors used in mobile robotics, including proprioceptive and proximity sensors. Dive into the details of probabilistic approaches and their applications in robotic systems.
