dual_quaternions package from dual_quaternions repo

dual_quaternions

Package Summary

Tags No category tags.
Version 0.3.2
License MIT
Build type CATKIN
Use RECOMMENDED

Repository Summary

Checkout URI https://github.com/Achllle/dual_quaternions.git
VCS Type git
VCS Version 0.3.2
Last Updated 2020-06-12
Dev Status MAINTAINED
CI status No Continuous Integration
Released RELEASED
Package Tags No category tags.
Contributing Help Wanted (0)
Good First Issues (0)
Pull Requests to Review (0)

Package Description

dual quaternion operations

Additional Links

No additional links.

Maintainers

  • achille

Authors

  • achille

Dual Quaternions

travis GitHub tag (latest SemVer)

Dual quaternions are a way of representing rigid body transformations, just like homogeneous transformations do. Instead of using a 4 by 4 matrix, the transformation is represented as two quaternions. This has several advantages, which are listed under Why use dual quaternions? The term \'dual\' refers to dual number theory, which allows representing numbers (or in this case quaternions) very similar to complex numbers with the difference being that i{.sourceCode} or j{.sourceCode} becomes e{.sourceCode} (epsilon) and instead of i^2 = -1{.sourceCode} we have e^2 = 0{.sourceCode}. This allows e.g. multiplication of two dual quaternions to work in the same way as homogeneous matrix multiplication.

For more information on dual quaternions, take a look at the References. For conversion from and to common ROS messages, see dual_quaternions_ros.

image{.align-center}

Why use dual quaternions?

  • dual quaternions have all the advantages of quaternions including unambiguous representation, no gimbal lock, compact representation
  • direct and simple relation with screw theory. Simple and fast Screw Linear Interpolation (ScLERP) which is shortest path on the manifold
  • dual quaternions have an exact tangent / derivative due to dual number theory (higher order taylor series are exactly zero)
  • we want to use quaternions but they can only handle rotation. Dual quaternions are the correct extension to handle translations as well.
  • easy normalization. Homogeneous tranformation matrices are orthogonal and due to floating point errors operations on them often result in matrices that need to be renormalized. This can be done using the Gram-Schmidt method but that is a slow algorithm. Quaternion normalization is very fast.
  • mathematically pleasing

Installation

pip

pip install dual_quaternions

ROS package

Release into apt is on its way. Until then you\'ll have to build the catkin package from source.

cd ~/catkin_ws/src
git clone https://github.com/Achllle/dual_quaternions
cd ..
catkin_make

Usage

Import using:

from dual_quaternions import DualQuaternion

References

  • K. Daniilidis, E. Bayro-Corrochano, \"The dual quaternion approach to hand-eye calibration\", IEEE International Conference on Pattern Recognition, 1996
  • Kavan, Ladislav & Collins, Steven & Zara, Jiri & O\'Sullivan, Carol. (2007). Skinning with dual quaternions. I3D. 39-46. 10.1145/1230100.1230107.
  • Kenwright, B. (2012). A Beginners Guide to Dual-Quaternions What They Are, How They Work, and How to Use Them for 3D Character Hierarchies.
  • Furrer, Fadri & Fehr, Marius & Novkovic, Tonci & Sommer, Hannes & Gilitschenski, Igor & Siegwart, Roland. (2018). Evaluation of Combined Time-Offset Estimation and Hand-Eye Calibration on Robotic Datasets. 145-159. 10.1007/978-3-319-67361-5_10.
CHANGELOG

Changelog for package dual_quaternions

0.3.2 (2020-06-12)

  • Use distutils iso setuptools for running on buildfarm
  • Contributors: Achille

0.3.1 (2020-05-28)

  • Fix rst reference
  • Initial commit: copy dual_quaternions over from dual_quaternions_ros
  • Contributors: Achille

Wiki Tutorials

See ROS Wiki Tutorials for more details.

Source Tutorials

Not currently indexed.

Package Dependencies

System Dependencies

No direct system dependencies.

Launch files

No launch files found

Messages

No message files found.

Services

No service files found

Plugins

No plugins found.

Recent questions tagged dual_quaternions at answers.ros.org

dual_quaternions package from dual_quaternions repo

dual_quaternions

Package Summary

Tags No category tags.
Version 0.3.2
License MIT
Build type CATKIN
Use RECOMMENDED

Repository Summary

Checkout URI https://github.com/Achllle/dual_quaternions.git
VCS Type git
VCS Version 0.3.2
Last Updated 2020-06-12
Dev Status MAINTAINED
CI status No Continuous Integration
Released RELEASED
Package Tags No category tags.
Contributing Help Wanted (0)
Good First Issues (0)
Pull Requests to Review (0)

Package Description

dual quaternion operations

Additional Links

No additional links.

Maintainers

  • achille

Authors

  • achille

Dual Quaternions

travis GitHub tag (latest SemVer)

Dual quaternions are a way of representing rigid body transformations, just like homogeneous transformations do. Instead of using a 4 by 4 matrix, the transformation is represented as two quaternions. This has several advantages, which are listed under Why use dual quaternions? The term \'dual\' refers to dual number theory, which allows representing numbers (or in this case quaternions) very similar to complex numbers with the difference being that i{.sourceCode} or j{.sourceCode} becomes e{.sourceCode} (epsilon) and instead of i^2 = -1{.sourceCode} we have e^2 = 0{.sourceCode}. This allows e.g. multiplication of two dual quaternions to work in the same way as homogeneous matrix multiplication.

For more information on dual quaternions, take a look at the References. For conversion from and to common ROS messages, see dual_quaternions_ros.

image{.align-center}

Why use dual quaternions?

  • dual quaternions have all the advantages of quaternions including unambiguous representation, no gimbal lock, compact representation
  • direct and simple relation with screw theory. Simple and fast Screw Linear Interpolation (ScLERP) which is shortest path on the manifold
  • dual quaternions have an exact tangent / derivative due to dual number theory (higher order taylor series are exactly zero)
  • we want to use quaternions but they can only handle rotation. Dual quaternions are the correct extension to handle translations as well.
  • easy normalization. Homogeneous tranformation matrices are orthogonal and due to floating point errors operations on them often result in matrices that need to be renormalized. This can be done using the Gram-Schmidt method but that is a slow algorithm. Quaternion normalization is very fast.
  • mathematically pleasing

Installation

pip

pip install dual_quaternions

ROS package

Release into apt is on its way. Until then you\'ll have to build the catkin package from source.

cd ~/catkin_ws/src
git clone https://github.com/Achllle/dual_quaternions
cd ..
catkin_make

Usage

Import using:

from dual_quaternions import DualQuaternion

References

  • K. Daniilidis, E. Bayro-Corrochano, \"The dual quaternion approach to hand-eye calibration\", IEEE International Conference on Pattern Recognition, 1996
  • Kavan, Ladislav & Collins, Steven & Zara, Jiri & O\'Sullivan, Carol. (2007). Skinning with dual quaternions. I3D. 39-46. 10.1145/1230100.1230107.
  • Kenwright, B. (2012). A Beginners Guide to Dual-Quaternions What They Are, How They Work, and How to Use Them for 3D Character Hierarchies.
  • Furrer, Fadri & Fehr, Marius & Novkovic, Tonci & Sommer, Hannes & Gilitschenski, Igor & Siegwart, Roland. (2018). Evaluation of Combined Time-Offset Estimation and Hand-Eye Calibration on Robotic Datasets. 145-159. 10.1007/978-3-319-67361-5_10.
CHANGELOG

Changelog for package dual_quaternions

0.3.2 (2020-06-12)

  • Use distutils iso setuptools for running on buildfarm
  • Contributors: Achille

0.3.1 (2020-05-28)

  • Fix rst reference
  • Initial commit: copy dual_quaternions over from dual_quaternions_ros
  • Contributors: Achille

Wiki Tutorials

See ROS Wiki Tutorials for more details.

Source Tutorials

Not currently indexed.

Package Dependencies

System Dependencies

No direct system dependencies.

Launch files

No launch files found

Messages

No message files found.

Services

No service files found

Plugins

No plugins found.

Recent questions tagged dual_quaternions at answers.ros.org

dual_quaternions package from dual_quaternions repo

dual_quaternions

Package Summary

Tags No category tags.
Version 0.3.2
License MIT
Build type CATKIN
Use RECOMMENDED

Repository Summary

Checkout URI https://github.com/Achllle/dual_quaternions.git
VCS Type git
VCS Version master
Last Updated 2020-08-14
Dev Status MAINTAINED
CI status Continuous Integration
Released RELEASED
Package Tags No category tags.
Contributing Help Wanted (0)
Good First Issues (0)
Pull Requests to Review (0)

Package Description

dual quaternion operations

Additional Links

No additional links.

Maintainers

  • achille

Authors

  • achille

Dual Quaternions

travis GitHub tag (latest SemVer)

Dual quaternions are a way of representing rigid body transformations, just like homogeneous transformations do. Instead of using a 4 by 4 matrix, the transformation is represented as two quaternions. This has several advantages, which are listed under Why use dual quaternions? The term \'dual\' refers to dual number theory, which allows representing numbers (or in this case quaternions) very similar to complex numbers with the difference being that i{.sourceCode} or j{.sourceCode} becomes e{.sourceCode} (epsilon) and instead of i^2 = -1{.sourceCode} we have e^2 = 0{.sourceCode}. This allows e.g. multiplication of two dual quaternions to work in the same way as homogeneous matrix multiplication.

For more information on dual quaternions, take a look at the References. For conversion from and to common ROS messages, see dual_quaternions_ros.

image{.align-center}

Why use dual quaternions?

  • dual quaternions have all the advantages of quaternions including unambiguous representation, no gimbal lock, compact representation
  • direct and simple relation with screw theory. Simple and fast Screw Linear Interpolation (ScLERP) which is shortest path on the manifold
  • dual quaternions have an exact tangent / derivative due to dual number theory (higher order taylor series are exactly zero)
  • we want to use quaternions but they can only handle rotation. Dual quaternions are the correct extension to handle translations as well.
  • easy normalization. Homogeneous tranformation matrices are orthogonal and due to floating point errors operations on them often result in matrices that need to be renormalized. This can be done using the Gram-Schmidt method but that is a slow algorithm. Quaternion normalization is very fast.
  • mathematically pleasing

Installation

pip

pip install dual_quaternions

ROS1 package ~~~~~~~~~~~

apt install ros-$ROSDISTRO-dual-quaternions

Usage

Import using:

from dual_quaternions import DualQuaternion

References

  • K. Daniilidis, E. Bayro-Corrochano, \"The dual quaternion approach to hand-eye calibration\", IEEE International Conference on Pattern Recognition, 1996
  • Kavan, Ladislav & Collins, Steven & Zara, Jiri & O\'Sullivan, Carol. (2007). Skinning with dual quaternions. I3D. 39-46. 10.1145/1230100.1230107.
  • Kenwright, B. (2012). A Beginners Guide to Dual-Quaternions What They Are, How They Work, and How to Use Them for 3D Character Hierarchies.
  • Furrer, Fadri & Fehr, Marius & Novkovic, Tonci & Sommer, Hannes & Gilitschenski, Igor & Siegwart, Roland. (2018). Evaluation of Combined Time-Offset Estimation and Hand-Eye Calibration on Robotic Datasets. 145-159. 10.1007/978-3-319-67361-5_10.
CHANGELOG

Changelog for package dual_quaternions

0.3.2 (2020-06-12)

  • Use distutils iso setuptools for running on buildfarm
  • Contributors: Achille

0.3.1 (2020-05-28)

  • Fix rst reference
  • Initial commit: copy dual_quaternions over from dual_quaternions_ros
  • Contributors: Achille

Wiki Tutorials

See ROS Wiki Tutorials for more details.

Source Tutorials

Not currently indexed.

Package Dependencies

System Dependencies

No direct system dependencies.

Launch files

No launch files found

Messages

No message files found.

Services

No service files found

Plugins

No plugins found.

Recent questions tagged dual_quaternions at answers.ros.org