The motion of the pendulum was also measured using two Sony DRV-940E camcorders shuttered at 1/500s. The digitising volume was calibrated using the static direct linear transformation procedure in the MaxTRAQ3D software (by Innovision Systems Ltd) that was used to manually digitise the motion of the pendulum. The MaxTRAQ software digitised individual fields giving a temporal resolution of 0.02s (50 pictures per second) and the digitised image was displayed at a resolution of 720x576 pixels.
2.2.2.
Method
A wooden pendulum was constructed which rotated about a good quality cylindrical bearing (Figure 2.3). The pendulum was 900 mm long with a 500 mm transverse arm oriented along the axis of rotation. Two IMUs were attached to the pendulum 350 mm and 700 mm from the centre of rotation with the local IMU x-axis oriented along the pendulum shaft. The motion of the pendulum was recorded using two shuttered video cameras and the output of the IMUs was sampled at 100Hz. Two different pendulum conditions were tested:
1. Normal motion in which the pendulum was set in motion by rotation about the X-axis and allowed to come to rest naturally.
2. Stopped motion in which the pendulum rotation about the X-axis was stopped and started abruptly.
Three points on the pendulum, the centre of rotation, the end of the pendulum arm and the end of the transverse arm were tracked in three dimensions using the MaxTRAQ software package. The projected angles of the pendulum motion were calculated from the three digitised points. Pendulum orientation was also determined from the output of the IMUs. Of the nine possible projected angles only three were required to completely define the pendulum orientation. The three projected angles chosen were equivalent to rotations about the X, Y and Z-axes as defined in the camera global coordinate system. The projected angle about the X-axis contained the majority of the pendulum motion. The projected angle about the Z-axis represented twists about the global vertical (or long axis of the pendulum when stationary) and should have been prevented by the pendulum design.
IMU accuracy was estimated by calculating the root mean square (RMS) difference between the three projected angles obtained from video motion analysis and the three projected angles obtained from the IMUs. The RMS difference between the projected angles of the two IMUs attached at different locations on the pendulum was calculated to estimate algorithm consistency. The Data from the IMUs were processed in two different ways:
1. Using the vendor‟s Kalman filter with the recommended settings; and 2. Using a custom bi-directional fusion integration algorithm.
2.2.3.
Results
An example of the normal pendulum motion derived from video analysis is shown below (Figure 2.7). The pendulum swings are expressed in projected angles and rotations about the X, Y and Z axis are represented by blue, green and red lines respectively. The pendulum oscillated about the X-axis with very little motion about the Y or Z-axes.
Figure 2.7: Video analysis of normal pendulum motion
Figure 2.8: Kalman filter algorithm estimation of normal pendulum motion
The same pendulum swing was measured by IMU using the vendor supplied Kalman filter algorithm (Figure 2.8) and the custom fusion algorithm (Figure 2.9). Figure 2.8 shows the output of the Kalman filter solution contained erroneous motion about the Z-axis, which corresponds to rotations about the long axis of the pendulum when it is hanging at rest. The accuracy of pendulum position orientation using video analysis was estimated by considering the length of the transverse arm. The RMS transverse arm length error was 4mm, which corresponds to an estimated orientation error of <0.5°.
The RMS differences between the IMU estimates of pendulum orientation and the video analysis estimate of orientation are shown below (Table 2.1). The tables illustrate the larger error in the Kalman filter estimate of orientation. Table 2.2 shows the difference in pendulum orientation obtained from IMU1 and IMU2 using both the fusion integration algorithm and the Kalman filter, the lower the RMS difference the better the reliability.
Table 2.1: Accuracy: The RMS error of IMU estimates of orientation. Projected angles obtained from the video analysis are used as a reference.
Test Condition Fusion IMU 1 Fusion IMU 2 Kalman IMU 1 Kalman IMU 2 Normal Pendulum 0.8º 0.9º 9.8º 11.7º Stopped Pendulum 0.9º 1.3º 8.5º 8.6º
Table 2.2: Reliability: The RMS difference between estimates of orientation obtained from two IMUs attached to the same pendulum at different locations
Test Condition Fusion IMU1vs IMU2 Kalman IMU1vs IMU2 Normal Pendulum 0.9º 4.0º Stopped Pendulum 0.7º 3.3º
2.2.4.
Discussion
A pendulum swing was used because it was repeatable and predictable. The cylindrical bearing substantially confined rotation to the X-axis, which was confirmed by the video analysis (Figure 2.7). There were however, small amounts of rotation about both the Y and Z-axes. The pendulum was also chosen because like skiing, it was a continuous movement and therefore, the attached IMU experienced both tangential and centripetal forces.
In a ski race the athlete experiences continuously changing forces while passing through consecutive course gates. Fortuitously, the gates are often spaced symmetrically and so part of
the athlete‟s motion, rotation about his anterioposterior axis, could be simply modelled by the motion of an inverted pendulum. The inverted pendulum is a commonly used model for some types of human motion.
The fusion algorithm performed very well. For test condition 1, the normal pendulum swing, the fusion algorithm output (Figure 2.9) was almost identical to the video output (Figure 2.7). The RMS error in orientation for the fusion algorithm was between 0.8º and 1.3º, which would be good enough for the analysis of alpine ski racing. The vendor‟s Kalman filter did not perform well; the RMS error was between 8.5° and 11.7º, and the peak orientation error was of the order of 30° about the Z-axis, which was significantly larger than the RMS error of 3º specified by the manufacturer. This type of motion capture equipment is relatively new and therefore, no agreed accuracy standard exists.
The fusion algorithm produced very similar results independent of the location of the IMU on the pendulum. The RMS difference was between 0.7º and 0.9º for the two locations on the pendulum (Table 2.2). The Kalman filter solution was less reliable for the two positions on the pendulum, producing significantly different estimations of orientation. The RMS error was between 3.3º and 4.0º.
The vendor‟s algorithm performed poorly for one of two reasons. The first possibility is that, during the periods of motion, the static estimate (Equation 2.1) was used to correct for the low frequency drift of the gyroscopes. The static estimate was biased during the pendulum swings because the centripetal acceleration was always measured along the same local axis of the IMU.
The second possibility is that the vendor‟s algorithm estimated the global acceleration using the method suggested by Luinge (Luinge & Veltink, 2005). This method requires that the orientation is accurately known. If the orientation error accumulates beyond a small threshold the global acceleration may be projected into the wrong axes and error may grow exponentially. Consequently, the threshold for stability may depend on the magnitude of acceleration experienced by the IMU. This would explain why the error decreased over the second half of the motion as the pendulum amplitude decreased (Figure 2.8).
In either case, if the calculation of orientation from the accelerometers and magnetometers data (Equation 2.1) was based on multiple cross products it might have given non-linear results as discussed elsewhere (Brodie, et al., 2008d). Consequently, even if the accelerometer and magnetometer data required to form the static orientation estimate were normally distributed about the true values, the resulting orientation estimate might be biased. The bias would appear worse in parts of the world where the magnetic dip angle was greater and when high accelerations were present. The magnetic dip in the lab is high (60º).
The fusion algorithm was good for short periods of motion (up to 30 seconds) provided there were short stationary periods before and after the action. The algorithm worked because the
orientation of the IMUs in the start and finish positions was the same and hence the magnetic field measured by the IMUs in both positions contained the same bias. In particular, this could be achieved for human motion in the laboratory by making the subject start and finish in the same calibrated position. The algorithm should work for all types of short motion provided the linear range of the sensors is not exceeded. The gyroscopes used in the IMUs have a linear range of 900ºs-1, which seems adequate for most human movements.
The results show it is possible to use small, light-weight and relatively inexpensive IMUs to accurately measure the orientation of body segments during dynamic motion. With such a system it may be possible to measure the biomechanics of alpine skiing with an acceptable degree of accuracy, but further development work is required.
2.3. Static accuracy
The previous pendulum experiment showed it was possible to obtain accurate dynamic measurements of orientation from an IMU. The vendor‟s data processing needs to be stripped away however, and the new system should, if possible, use the raw binary sensor data.
The purpose of the following research was to determine if it is possible to obtain accurate calibrated data from the XSens MT9 IMU raw binary data. Further information is provided on the accompanying CD (Brodie, et al., 2008d).
Raw data from the sensors within the IMUs are converted from binary representation to calibrated data by applying bias, gain, and temperature compensation. The calibrated data contain the acceleration, rate of rotation and magnetic field as measured in each of the three local axes of the IMU. The conversion process minimises any errors due to misalignment of the sensors within the IMU and any temperature effects.
Of particular interest is the performance specification of the unit as a whole. The static accuracy of orientation was reported to be <1.0º, the dynamic accuracy was reported to be 3º RMS, and orthogonality was reported to be 0.1º (XSens, 2004a). These specifications come with the caveat that data must be captured in a homogeneous magnetic environment and accuracy may depend on the type of motion measured. No detail were given about what is an acceptable „type of motion‟ and so it appears that the manufacturer, at the time the manual was written, was unsure of what „type of motion‟ could be measured accurately.
2.3.1.
Method
The experiments were designed to determine the absolute and relative orientation accuracy of an IMU based on the accelerometer and magnetometer channels. The experiments tested:
1. The accuracy of the static orientation measurements.
2. Whether a custom calibration procedure would improve accuracy. 3. The stability of the custom calibration over twenty-two days.