Tabla 6 4 Resultados de autoevaluación de la maestra – Grupo 2º Infantil B
6.2 EVALUACIÓN POR OBJETIVOS
Although the IMU local axes were visually aligned to the wand axes, this did not account for the fact the IMU housing was not aligned with the internal sensors, and so a constant calibration matrix was used to map the IMU local axes to the wand local axes. The calibration matrix was defined by the mean angular separation between the FMC orientation and the VMA orientation over a 5-second trial, which resulted in a constant rotation of <2 that was applied to all results.
Experimental
Ten trials were completed ranging in duration from 5 to 120 seconds. Two test conditions were used:
1. The vendor supplied Kalman filter with recommend settings
2. The bi-directional fusion algorithm previously described (Chapter 2)
In each trial the wand was moved continuously through a volume measuring approximately 2m by 2m by 1m. Rapid direction changes such as might be experienced in slalom skiing were used.
4.1.2.
Results and discussion
The resulting root mean square (RMS) differences from ten trials are shown in Figure 4.3. The estimated RMS difference in orientation between the VMA and the IMU motion capture systems (test conditions #1 and #2) was between 1.8° and 12.9°. Neither the vendor‟s Kalman filter nor the bi-directional fusion algorithms were accurate for long duration measurements. Figure 4.3 shows the vendor‟s Kalman filter failed to report orientation accurately even for the short five-second trial (RMS difference approximately 6). The bi-directional fusion algorithm was robust, displaying a relatively constant error of less than 3 RMS for trials of up to 50 seconds in duration.
Orientation Error Analysis 5-120 seconds 0 2 4 6 8 10 12 14 0 20 40 60 80 100 120 Trial Length [s] R M S Er ro r [d eg] #1 Kalman Filter #2 Bidirectional
Figure 4.3: The difference between VMA and IMU motion capture over ten trials
An orientation accuracy of less than 3° RMS should be suitable for skiing because it is less than that reported for some optical motion capture systems in a laboratory situation, as discussed in Chapter 1 on page 7. Even though the on-snow measurements in this thesis will probably be less than 50 seconds duration the results are still unsatisfactory for two reasons:
1. Ski races last longer than 50 seconds.
2. The bi-directional algorithm maximum measurement time, while maintaining accuracy, may depend on the type of movement. For some body segments, especially the ski/boot/foot segment undergoing high vibrations, the actual robust measurement time may reduce.
A better fusion algorithm is therefore required.
4.2. Free movement algorithm and accuracy
In Section 4.1 it was established that neither the IMU vendor‟s Kalman filter nor the bi- directional fusion algorithms were accurate enough to measure orientation during a complete ski race. In Chapter
3 a prototype Fusion Motion Capture (FMC) system was developed that combined global positioning system (GPS) and IMU data in order to track a skier at Coronet Peak. Several problems with the prototype system accuracy were also reported. In this chapter the development of the FMC algorithm is therefore continued and the FMC algorithm is validated against VMA measurements using the wand described in the previous section. The main purpose of this section is to improve the accuracy and reliability of FMC; this is achieved by the implementation of a new free movement fusion algorithm that combines GPS and IMU data.Combining GPS and IMU data for accurate navigation is a well-established method (Brown, 2005; Broxmeyer, 1964), but its application to motion capture and biomechanical analysis of athletic performances was new and difficult to assess. A method was required to assess the quality of the FMC derived trajectory and orientation of an object undergoing free movement in a controlled laboratory environment.
Free movement is defined by 6 degrees of freedom (d-o-f); 3 d-o-f to describe the global X, Y, and Z-axes location of a body segment and 3 d-o-f to describe the orientation of the segment (eg roll, pitch, and yaw). Unfortunately, there appears to be no practical way to test the accuracy of the system for skiing directly because the spaces traversed are very large. Also, segment markers used for video tracking would not stay attached with an aggressive race strategy, and video auto-tracking algorithms do not work well under direct sunlight with a largely white background.
In order to objectively measure the accuracy of FMC the measurement of free movement in a laboratory setting is compared to a video motion analysis (VMA) system. The motion of a T- shaped wand, which represents the free motion of a single body segment, was tracked using both a video system and the FMC system. Because there was no GPS signal indoors, some additional data from the VMA system were substituted for GPS data that would normally be used in the fusion algorithm outdoors.
4.2.1.
FMC algorithm Version Two
The free movement of body segments in global space was obtained from the fusion algorithm outlined in Figure 4.4.
In Figure 4.4 the new fusion algorithm solves for the global trajectory and orientation of the IMU over extended periods of time. Figure 4.4 illustrates the process used when GPS data are available. Estimates of discrete orientation and continuous rotation are derived from the IMU gyroscopes, accelerometers and magnetometers. In Figure 4.4 the [Bi-directional Fusion 1] process is the bi-directional fusion algorithm used for the pendulum experiment in Chapter 2. In Figure 4.4 the [Orientation Fusion 2] process reduces the orientation error by minimising the residual between the continuous acceleration derived from the IMU data and the discrete acceleration derived by differentiation of the GPS velocity data. A rotational correction is applied to the IMU data over successive windows of data. The windows of data are long enough to ensure there is sufficient angular separation between the discrete GPS acceleration vectors, yet short enough so that a single orientation correction will account adequately for most of the changing accumulated integration errors.
Figure 4.4: The FMC algorithm Version Two
In Figure 4.4 the [Trajectory Fusion 3] process combines two independent estimates of trajectory to give a final global trajectory. Discrete estimates of velocity and location are obtained from the differentially corrected GPS receiver raw data. The resulting GPS measurements of location and velocity are noisy but should have long-term accuracy (over a long enough time period the mean value should coverage to the true mean location and velocity). Continuous global velocity and location estimates are obtained by integration of the IMU based global acceleration. They are subject to integration drift as a result of both orientation error and accelerometer gain and bias errors, but are accurate in the short term. The „fused‟ translation movement is derived by combining the long term accuracy of the GPS velocity and location with the short term accuracy of the continuous estimates of velocity and location. An example output for vertical velocity after the [Trajectory Fusion 3] process is illustrated in Figure 4.5, the circles are simulated GPS velocity, the green/grey line is the integrated IMU acceleration and the black line is the fused velocity estimate. The [Trajectory Fusion 3] process is similar to the fusion integration process used to determine centre-of-mass (CoM) from a force platform (Brodie, et al., 2007).