Frontiers in Behavioral Neuroscience (Feb 2013)
3D kinematics using dual quaternions: theory and applications in neuroscience
Abstract
In behavioral neuroscience, many experiments are developed in 1 or 2 spatialdimensions, but when scientists tackle problems in 3-dimensions (3D), theyoften face problems or new challenges. Results obtained for lower dimensionsare not always extendable in 3D. In motor planning of eye, gaze or armmovements, or sensorimotor transformation problems, the 3D kinematics ofexternal (stimuli) or internal (body parts) must often be considered: howto describe the 3D position and orientation of these objects and link themtogether? We describe how motors (dual quaternions) provide a convenientway to describe the 3D kinematics for position only (point transformation) orfor combined position and orientation (through line transformation), easilymodeling rotations, translations or screw motions or combinations of these.We also derive expressions for the velocities of points and lines as well as thetransformation velocities. Then, we apply these tools to a motor planningtask for manual tracking and to the modeling of forward and inverse kinematicsof a 7dof 3-link arm to show the interest of dual quaternions as a toolto build models for these kinds of applications.
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