Robotics Dual Quaternion Toolbox

This toolbox provides useful functions for creating and manipulating dual quaternions.

What are dual quaternions?

Dual quaternions are a convenient way of describing rigid body transformations (specifically unit dual quaternions, which are the focus of this toolbox). They carry the same information as other descriptions of pose, such as the commonly used homogeneous transformation matrix. However, they are more computationally efficient, and have some neat mathematical properties.

https://en.wikipedia.org/wiki/Dual_quaternion

What does this library contain?

This library contains a set of simple, elementary functions for manipulating dual quaternions:

• Transforming from rotation and translation quaternions, homogeneous matrices or angle-axis screw parameters
• Plotting on 3D axis
• Mutliplying, raising to power, normalising, conjugate, scalar part
• Calculating log and exponential maps (useful in kinematics)
• Combining using Screw Linear Interpolation (ScLerp), Dual Iterative Blending (DIB) and Dual Linear Blending (DLB) from https://users.cs.utah.edu/~ladislav/kavan06dual/kavan06dual.pdf
• Converting to and from twistor representation (https://arc.aiaa.org/doi/pdf/10.2514/1.G001522)

Requests

If you have any requests or recommendations for additional functions, please leave a comment or start a discussion.

Acknowledgement

If you use this toolbox for a project, please use the citation below.