• No results found

The gyroscope, accelerometer and magnetometer signals of a typical trial of the first set of experiments are presented in Figure 3.3. The gyroscope signals show the angular velocities of the 3D rotations. The accelerometers show the three components of the gravitational acceleration and the acceleration of the sensor.

The components of the magnetic field vector and the disturbance as measured by the magnetometers are plotted in the lower graph.

42

3.3. Results

38 Figure 10

0 10 20 30 40 50 60 70

-8 -4 0 4 8

w (rad/s)

Gyroscopes

0 10 20 30 40 50 60 70

-20 0 20 40

a (m/s2)

Accelerometers

0 10 20 30 40 50 60 70

-2 -1 0 1

2 Magnetometers

H (normalized)

Time (s)

xy z

Figure 3.3 — Sensor signals of gyroscopes (upper), accelerometer (middle) and magnetometers (lowers) of combined 3D rotation near the ferromagnetic box.

39 Figure 11

0 10 20 30 40 50 60 70

0 10 20

30 Acceleration magnitude

|a| (m/s2)

0 10 20 30 40 50 60 70

0.5 1 1.5 2

2.5 Magnetic field magnitude

|H| (normalized)

0 10 20 30 40 50 60 70

-10 -5 0 5

10 Kalman filter errors

Error (deg)

Time (s)

Figure 3.4 — Results from the sensor signals as plotted in Figure 3.3. Upper: acceleration norm.

Middle: magnetic field magnitude. During the movements of the sensor, the magnetic norm is quite variable which is caused by the disturbed magnetic field. Lower: orientation difference between the filter with magnetic disturbance compensation and the optical reference system.

The gaps in the data are caused by missed markers from the optical reference system, so no reference orientation could be calculated.

43

Chapter 3. Evaluation of orientation measurements

In Figure 3.4, the norms of the accelerometer and magnetometer signals are given in the upper and middle graph, respectively. The effect of the magnetic dis-turbance is clearly noticeable in variability of the magnetic norm. The difference in orientation estimated with the inertial and magnetic sensor module compared to the optical reference system is given in the lower graph. The error was ex-pressed by the three components of the difference vector between both orientation estimates and was 2.7 root mean square (rms). When no magnetic disturbance compensation was applied the error was 11.9 rms.

Disturbances of the heading estimates due the metal case for a trial of the simulated assembly line experiment are shown in the upper graph of Figure 3.5.

In the first five seconds, the sensor module is in a non-disturbed area and the magnetic norm equals one. During the movements near the metal case, the norm is quite variable. After 50 seconds the arm is retreated from the disturbed area and the norm equals one again.

8 Figure 1

0 10 20 30 40 50 60

0 1

2 Norm magnetic field

Movement in vicinity of metal

0 10 20 30 40 50 60

-50 -250 25

50 Difference gyroscope integration

Error (deg)

0 10 20 30 40 50 60

-50 -250 25 50

Error (deg) Difference no disturbance compensation

0 10 20 30 40 50 60

-10 -505 10

Error (deg) Difference Kalman filter with disturbance compensation

Time (s)

XY Z

Figure 3.5 — Orientation estimation from the inertial and magnetic sensor measurements com-pared to the optical reference system in a simulated work task. Upper: normalized magnetic flux density. During the movements of the arm, the magnetic norm is quite variable which is caused by the disturbed magnetic field. Second: orientation angle difference in three axes when only gyroscopes are used. Third: Kalman-based filter orientation estimation with equal weight to accelerometer and magnetometer without disturbance model. Lower: Kalman-based filter with magnetic disturbance model.

44

3.3. Results

The subsequent graphs show the differences of the orientations obtained with the inertial and magnetic sensor module with respect to the optical reference sys-tem. In the second graph, it can be seen that the drift error becomes significant after only a few seconds when only gyroscopes are used. The third graph presents the output of the Kalman-based filter with an equal weight factor of the accelerom-eters and magnetomaccelerom-eters without magnetic disturbance compensation. When the arm enters the disturbed area, the orientation error around the Z-axis becomes quite large. After moving the arm away from the metal case the error converges back to zero. The disturbance is also noticeable in the other axes, since the mag-netic field also influences the inclination component (dip angle). The lower graph illustrates that the orientation estimates using the full Kalman-based filter with magnetic disturbance model is not disturbed and drift free. The difference in ori-entation between the filter and the optical reference system of the complete trial is 3.4 rms.

In total, 10 trials with arm ab/adduction and flexion/extension were recorded without magnetic disturbance, two for each of the five subjects. From the same set of movements, 9 trials were successfully captured in the vicinity of the metal case. The rms error when no metal was near the sensors was 2.6 (std. dev. 0.5).

With the metal case and no compensation applied, the rms error was 13.1 (std.

dev. 3.0). In the simulated assembly line experiments, the error was 19.8 (std.

dev. 3.6) with no compensation. Using the magnetic disturbance model and the described filter this rms error reduced significantly (paired t-test, p<0.01) to 3.6 (std. dev. 0.6).

3.3.1 Accuracy of the reference system

The accuracy of the reference system was considered by looking at the distances mx-y and mx-z between the markers x-y and x-z (Figure 3.1). Small variations in those distances were observed during the experiments (Figure 3.6).

Optical marker

m

a

b φ

To PC Optical

marker

Inertial and magnetic measurement unit

y x

z

Optical marker

m a

b φ

Figure 3.6 — Varying distances between markers cause errors in the orientation estimates of the optical reference frame.

45

Chapter 3. Evaluation of orientation measurements

Assuming fixed distances a and b between the markers and origin of the marker frame and the distance m delivered by the optical reference system (see Figure 3.7), the angle φ is calculated using the cosine rule:

cos φ = a2+ b2− m2

2ab (3.2)

With an initial orthogonal marker frame, the error φε becomes:

φε = 90− φ (3.3)

The total error φε was calculated by taking the norm of the error angles between markers x-y and x-z. The rms error related to the reference system was 0.9 (std.

dev. 0.3).

20 21 22 23 24 25 26 27 28 29 30

128

130 markers x - y 132

134 136

138 markers x - z

140 Distance between markers

Distance (mm)

20 21 22 23 24 25 26 27 28 29 30

-10 -5 0 5

10 Orientation difference Kalman filter - reference

Error (deg)

Time (s)

X Y Z

Figure 3.7 — Upper graph: distances in mm’s between x and y markers and x and z markers.

Lower graph: detail of orientation angle difference between Vicon system and the Kalman algo-rithm. Note the correlation between the error in the reference system and the difference between Vicon and Kalman filter.