Statistical Modelling 9 (2009), 5168
Modelling orientation trajectories
Julia J Faraway
Department of Mathematical Sciences,
University of Bath,
Bath, BA2 7AY
UK
eMail:
jjf23@bath.ac.uk
Su Bang Choe
University of Michigan
U.S.A.
eMail:
sbchoe@gmail.com
Abstract:
We describe a modelling approach for orientation trajectories. The
initial and final orientations of the object are taken as known and
the problem of how the object will transition between the endpoints
is considered. Orientations are represented as quaternions and
mapped to a tangent space. The deviation from the geodesic
connecting the endpoints is introduced and called the slerp residual.
Modelling the slerp residuals substantially reduces the distortion
caused by mapping to the tangent space. Bézier curves are used to
compactly model the trajectories and provide a linkage to potential
predictors. Data from an experiment to study human motion while
reaching to perform a wide variety of grasps are considered. The
orientation trajectories of the hand are modelled in several ways
resulting in a simple yet interpretable model.
Keywords:
Bézier curves; functional data analysis; quaternions
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