The first estimation of orientation [Bi-directional Fusion 1] was based on the magnetic coordinate system described in Chapter 2. In the magnetic coordinate system, the global Z- axis is vertical while the X-axis points to magnetic north. The video system used the same global Z-axis but an arbitrary X-axis convenient for the laboratory layout. The substitute GPS
measurements (from the VMA system) were already in the VMA coordinate system and so the second part of the FMC algorithm [Orientation Fusion 2] rotated the IMU measurements into the VMA coordinate system automatically. The average angle between magnetic north and the VMA global X-axis was 14.5, but the magnetic field appeared to be quite variable in our laboratory.
Figure 4.5: Fusion Integration estimation of vertical velocity
4.2.2.
Method
The free movement of a wand was tracked using FMC and a MaxTRAQ two-camera VMA system. The same wand from Section 4.1 was used, but in addition the IMU was also tracked directly by the VMA system.
The FMC algorithm was implemented in MATLAB. The mean location and velocity of the wand T-intersection over each second (calculated from the MaxTRAQ VMA system data) was used as a substitute for the GPS data normally used outdoors. Suitably scaled Gaussian noise was added to the VMA location and velocity data. Because ski racers travel over 200m at about 20m.s-1, compared with the wand moving 2m at speeds of about 2m.s-1 in the laboratory experiment, the standard deviation of the noise was scaled from <0.1m.s-1 and 15m, for velocity and location (from the GPS specifications of our receiver), to 0.01m.s-1 and 0.15m respectively. The scaling ensured the effect of the noise on the laboratory motion was similar to the effect of noise on skiing motion.
Experimental
Ten trials were completed ranging in duration from 5 to 120 seconds. Data from three conditions are presented in the results:
1. Video Internal Error - The estimated internal error of the VMA system based on the known distance between the marker balls of the wand.
2. FMC+VMA - The calculated the difference between VMA and FMC orientation and location. The mean location and velocity of the IMU over each second derived from the VMA system was input into the FMC algorithm as substitute GPS data.
3. „FMC+VMA+Noise - The calculated the difference between VMA and FMC orientation and location. Noise was added to the VMA data before being input into the FMC algorithm, which ensured it was a good substitute for GPS data.
In each trial the wand was moved continuously through a volume measuring approximately 2m by 2m by 1m. The movement exhibited rapid direction and orientation changes such as might be experienced in slalom skiing. The example trial in Figure 4.6 shows the wand location and orientation at 0.5s intervals from both VMA (blue) and FMC (red); there is no discernable difference between them. The example trial is also available as a video (Video 4.1).
Video 4.1: Appendices\FMC Video\Wand.avi
Figure 4.6: Experimental set up, the wand was moved through free space.
VMA system error
The internal location error in the VMA system was estimated by comparing the known distances between the black marker balls with the measured distances. Two location errors in the local orthogonal axes in the plane of the wand were calculated, Equation 4.4 and Equation 4.5. The third orthogonal axis error (E3) was assumed to be the mean of the two
calculated errors, (E1 andE2). The location error was obtained from the error in each axis of movement using Equation 4.6.
Equation 4.4 Equation 4.5 Equation 4.6
The internal orientation error of the VMA system was estimated from the arctangent of the ratio between the marker separation and location error, Equation 4.7 and Equation 4.8. The third orthogonal error (Eθ3) was assumed to be the mean of the two calculated errors, (Eθ1 andEθ2). The orientation error was obtained from the orientation error about each axis of movement using Equation 4.9.
Equation 4.7
Equation 4.8
Equation 4.9
4.2.3.
Results and discussion
The internal error of the VMA system, estimated from the known geometry of the wand and the RMS differences between VMA and FMC estimates of orientation and location for the ten trials are shown in Figure 4.7 and Figure 4.8.
The estimated root mean square (RMS) difference in orientation between the VMA and FMC systems was between 1.8° and 2.6°, which was similar to the estimated error range for the VMA system of 1.2º to 3.1º (Figure 4.7). The FMC measurement of wand orientation appeared robust because neither the addition of noise to the substituted GPS inputs nor increased measurement duration increased the RMS difference.
Figure 4.7: VMA Orientation Error and difference between VMA and FMC over trials
Figure 4.8: VMA Location Error and difference between VMA and FMC over trials
The RMS difference in location between the VMA and FMC systems ranged from 1.1cm to 2.5cm but was much more susceptible to noise in the substituted GPS data. In the presence of scaled Gaussian noise the RMS difference in location between the VMA and FMC systems ranged between 3.9cm and 8.6cm over the ten trials with a trend for difference in location to reduce as measurement duration increased (Figure 4.8). This was expected because, when discrete location measurements (such as GPS) contain noise, more points are required to obtain an accurate location.
The FMC algorithm performed at a similar level of accuracy to the VMA system, for both orientation and location. FMC has additional advantages, it may be used in motion capture tasks where camera based systems are not practical. FMC also has other advantages in some situations where, as part of a biomechanical analysis of movement, joint forces and torques
are important. Forces and torques are often derived from linear and angular segment acceleration and our IMUs contain accelerometers and gyroscopes that measure acceleration and angular velocity directly. The direct IMU measurement of acceleration and angular velocity removes the need for numerical differentiation processes that introduce noise. In contrast, body segment angular velocity from VMA systems is derived from successive estimates of orientation, which in turn are derived from location measurements of three or more markers attached to body segments. As a result, the VMA measurement of angular velocity is likely to contain higher levels of noise compared with the IMU measurement of angular velocity
In Figure 4.9 the differences between VMA and FMC measurements of angular velocity are clearly visible. The VMA estimate of angular velocity contained more noise. The VMA estimate of angular velocity contained an estimated 13°.s-1 RMS of noise, which was 26% of the measured RMS angular velocity (50°.s-1) during the trial.
Figure 4.9: Local y-axis angular velocity of the wand (VMA) and the IMU gyroscope
Figure 4.9 shows a high level of noise in the VMA measurement of angular velocity. It is standard practise to use a low pass filter to reduce this type of VMA noise, but if this is done, then the high frequency components of the movement, especially during impacts, might be lost. A much better measurement of angular velocity is obtained directly from the IMU without additional filtering. As a consequence, estimates of angular acceleration from FMC measurements of angular velocity preserve more of the high frequency components of the motion because only a single numerical differentiation with minimal smoothing is required. In addition, because IMUs measure local linear acceleration directly, most of the high frequency components of linear motion are preserved when calculating net joint forces and torques.
So how might the fusion algorithm perform on the ski slope? The VMA and FMC spatial trajectory errors (around 0.04m) for the wand were made semi independent by the addition of scaled Gaussian distributed noise (0.15m for location). On the snow, if the GPS has a specified RMS error of 15m, FMC might locate the skier on the slope with a RMS error of 4m. If this level of error is unacceptable, it might be reduced further by starting the athlete from a known surveyed point on the slope, or using more accurate GPS modules.
On snow, errors in FMC measurements of orientation and heading should not increase significantly relative to the wand results because the accurate GPS velocity (calculated from the Doppler shift) is used as an input to the FMC algorithm. However because the wand movements in the laboratory were smooth, the effects of impacts or high frequency vibrations experienced while skiing are unknown. It is possible that the low frequency components of ski orientation measurements taken while chattering over an icy course will be less accurate than the low frequency components of the athlete‟s helmet orientation. FMC should however measure the high frequency components, within the linear range of the internal sensors, equally well in both cases.