Skip to main content

Dual quaternion implementation

Project description

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 or j becomes e (epsilon) and instead of i^2 = -1 we have e^2 = 0. 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.

viz.gif

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.

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Files for dual-quaternions, version 0.3.1
Filename, size File type Python version Upload date Hashes
Filename, size dual_quaternions-0.3.1-py2-none-any.whl (8.3 kB) File type Wheel Python version py2 Upload date Hashes View
Filename, size dual_quaternions-0.3.1-py3-none-any.whl (8.3 kB) File type Wheel Python version py3 Upload date Hashes View
Filename, size dual_quaternions-0.3.1.tar.gz (7.1 kB) File type Source Python version None Upload date Hashes View

Supported by

AWS AWS Cloud computing Datadog Datadog Monitoring DigiCert DigiCert EV certificate Facebook / Instagram Facebook / Instagram PSF Sponsor Fastly Fastly CDN Google Google Object Storage and Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Salesforce Salesforce PSF Sponsor Sentry Sentry Error logging StatusPage StatusPage Status page