13-09-2012, 10:38 AM
Mobile Robot Localization and Mapping using the Kalman Filter
[attachment=33659]
Mobile Robot Localization
Where am I?
Given a map, determine the robot’s location
Landmark locations are known, but the robot’s position is not
From sensor readings, the robot must be able to infer its most likely position on the field
Example : where are the AIBOs on the soccer field?
Mobile Robot Mapping
What does the world look like?
Robot is unaware of its environment
The robot must explore the world and determine its structure
Most often, this is combined with localization
Robot must update its location wrt the landmarks
Known in the literature as Simultaneous Localization and Mapping, or Concurrent Localization and Mapping : SLAM (CLM)
Example : AIBOs are placed in an unknown environment and must learn the locations of the landmarks (An interesting project idea?)
Bayesian Filter
Why should you care?
Robot and environmental state estimation is a fundamental problem!
Nearly all algorithms that exist for spatial reasoning make use of this approach
If you’re working in mobile robotics, you’ll see it over and over!
Very important to understand and appreciate
Efficient state estimator
Recursively compute the robot’s current state based on the previous state of the robot
The Kalman Filter
Motion model is Gaussian…
Sensor model is Gaussian…
Each belief function is uniquely characterized by its mean m and covariance matrix
Computing the posterior means computing a new mean m and covariance from old data using actions and sensor readings
What are the key limitations?
Problems with the Linear Model Assumption
Many systems of interest are highly non-linear, such as mobile robots
In order to model such systems, a linear process model must be generated out of the non-linear system dynamics
The Extended Kalman filter is a method by which the state propagation equations and the sensor models can be linearized about the current state estimate
Linearization will increase the state error residual because it is not the best estimate
Enhancements to the EKF
Multiple hypothesis tracking
Multiple Kalman filters are used to track the data
Multi-Gaussian approach allows for representation of arbitrary probability densities
Consistent hypothesis are tracked while highly inconsistent hypotheses are dropped
Similar in spirit to particle filter, but orders of magnitude fewer filters are tracked as compared to the particle filter
[attachment=33659]
Mobile Robot Localization
Where am I?
Given a map, determine the robot’s location
Landmark locations are known, but the robot’s position is not
From sensor readings, the robot must be able to infer its most likely position on the field
Example : where are the AIBOs on the soccer field?
Mobile Robot Mapping
What does the world look like?
Robot is unaware of its environment
The robot must explore the world and determine its structure
Most often, this is combined with localization
Robot must update its location wrt the landmarks
Known in the literature as Simultaneous Localization and Mapping, or Concurrent Localization and Mapping : SLAM (CLM)
Example : AIBOs are placed in an unknown environment and must learn the locations of the landmarks (An interesting project idea?)
Bayesian Filter
Why should you care?
Robot and environmental state estimation is a fundamental problem!
Nearly all algorithms that exist for spatial reasoning make use of this approach
If you’re working in mobile robotics, you’ll see it over and over!
Very important to understand and appreciate
Efficient state estimator
Recursively compute the robot’s current state based on the previous state of the robot
The Kalman Filter
Motion model is Gaussian…
Sensor model is Gaussian…
Each belief function is uniquely characterized by its mean m and covariance matrix
Computing the posterior means computing a new mean m and covariance from old data using actions and sensor readings
What are the key limitations?
Problems with the Linear Model Assumption
Many systems of interest are highly non-linear, such as mobile robots
In order to model such systems, a linear process model must be generated out of the non-linear system dynamics
The Extended Kalman filter is a method by which the state propagation equations and the sensor models can be linearized about the current state estimate
Linearization will increase the state error residual because it is not the best estimate
Enhancements to the EKF
Multiple hypothesis tracking
Multiple Kalman filters are used to track the data
Multi-Gaussian approach allows for representation of arbitrary probability densities
Consistent hypothesis are tracked while highly inconsistent hypotheses are dropped
Similar in spirit to particle filter, but orders of magnitude fewer filters are tracked as compared to the particle filter