First published online June 16, 2005
Journal of Experimental Biology 208, 2503-2514 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01658
A method for deriving displacement data during cyclical movement using an inertial sensor
Thilo Pfau1,*,
Thomas H. Witte1 and
Alan M. Wilson1,2
1 Structure and Motion Laboratory, The Royal Veterinary College, Hawkshead
Lane, Hatfield, Hertfordshire, AL9 7TA, UK
2 Structure and Motion Laboratory, Royal National Orthopaedic Hospital,
Brockley Hill, Stanmore, Middlesex, HA7 4LP, UK

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Fig. 1. Schematic drawing of the data collection set-up. The inertial sensor is
mounted over the thoracic spinous processes (the withers) of the horse with
the motion analysis marker wand attached. Cables are run from the inertial
sensor to a laptop computer (via the safety harness mast) as well as
from the optical motion capture cameras to a second laptop computer.
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Fig. 2. The harness employed for attachment of the inertial sensor to the thoracic
spinous processes of the subject animal. The wands and markers for 3D optical
motion capture are also shown.
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Fig. 3. Schematic drawing of the coordinate systems used. Orientation of the
inertial sensor is expressed as a sequence of roll, pitch and heading from the
`sensor' into the `earth' system. In order to compare optical motion capture
and inertial sensor output, the `global' coordinate system is used.
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Fig. 4. Displacement data for x (craniocaudal), y (lateral) and
z (dorsoventral) movement for optical motion capture (blue) and
inertial sensor (red) for a series of strides at canter (9 m s-1).
In the integration process, a context window of one stride to each side of the
current stride has been used for the mean subtraction.
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Fig. 5. Optical motion capture (blue) and inertial sensor (red) outputs for x,
y and z displacements and roll, pitch and heading angles of the
sensor mounted over the thoracic spinous processes of a horse during treadmill
locomotion (mean ± S.D.). Data are shown for the mean gait
cycle (stride) at (A,B) walk (1.4 m s-1), (C,D) trot (3.5 m
s-1) and (E,F) left lead canter (9.0 m s-1). For the
x, y and z displacements and for the heading angle, the
stride-to-stride differences, as indicated by the standard deviations, are
bigger than the differences between the two methods (difference between the
mean traces). For roll and pitch orientation, however, there is a small offset
between the mean traces of the two methods, which increases from walk to trot
and canter. The biggest inter-stride variability can be found in the
y direction for both methods and across all gaits. This demonstrates
the tendency of the horse to drift from side to side while performing on the
treadmill.
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Fig. 6. Motion analysis (blue) and inertial sensor (red) outputs for x, y
and z displacements after high-pass filtering (mean ±
S.D.). Data are shown for a stride at (A) walk (1.4 m
s-1), (B) trot (3.5 m s-1) and (C) left lead canter (9.0
m s-1). Smaller standard deviations (compared with the unfiltered
displacements in Fig. 5),
especially in the y direction, show that high-pass filtering is a
valid means of eliminating non-cyclical inter-stride differences of the
displacements.
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Fig. 7. Histograms of frame-wise difference between motion analysis and inertial
sensor for roll, pitch and heading angles and x, y and z
displacements for the whole data set. Histograms are shown for (A) walk (1.4 m
s-1), (B) trot (3.5 m s-1) and (C) left lead canter (9.0
m s-1). The spread of the histograms is generally increasing from
walk to trot and canter. In addition, there is an offset in roll and pitch
orientation, which increased with speed.
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Fig. 8. Histograms of frame-wise difference between motion analysis and inertial
sensor x, y and z displacements after high-pass filtering.
Histograms are shown for (A) walk (1.4 m s-1), (B) trot (3.5 m
s-1) and (C) left lead canter (9.0 m s-1). The reduced
spread of the histograms (compared with the unfiltered displacement error
histograms in Fig. 7)
demonstrates the ability of the inertial sensor integration process to capture
the cyclical components of the displacements.
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Fig. 9. Ranges of x, y and z displacements are shown as a
function of speed and gait for a horse exercising on a treadmill. Ranges are
calculated as the difference between maximum and minimum values within the
mean stride. Error bars represent ±1 S.D., and the number of
strides in each category is given. Walk is represented by open circles, trot
by triangles and canter by diamonds.
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© The Company of Biologists Ltd 2005