Development and validation of a wearable inertial measurement ...
2011 11th IEEE-RAS International Conference on Humanoid Robots Bled, Slovenia, October 26-28, 2011
Development and validation of a wearable inertial measurement system for use with lower limb exoskeletons Tadej Beravs, Peter Reberšek, Domen Novak, Janez Podobnik, Marko Munih Laboratory of Robotics University of Ljubljana Ljubljana, Slovenia [email protected] sensors is required. Among them are sensors that measure human body kinematics. For instance, the MIT leg exoskeleton [3] measures hip and knee angles using rotary potentiometers. Similarly, the HAL [2] uses accelerometers and gyroscopes in addition to potentiometers to measure joint angles. Since upper and lower body movement are strongly coordinated during walking [4], it would be useful for exoskeletons to also measure upper body movement using separate sensors.
Abstract—This paper presents a system of inertial measurement units, each consisting of an accelerometer, gyroscope and magnetometer. They are characterized by a small size, wireless transmission, and open architecture, with the purpose of either integration into lower limb exoskeletons or general human movement analysis. Kalman filtering and the factored quaternion algorithm are used to track the orientation of each unit, and angles of the human joints are calculated from multiple units. After calibration, the system was tested with a wooden leg mockup and an actual human. The Optotrak optical measurement system was used as a reference. Differences between the inertial measurement system and the Optotrak were less than 2 degrees for the wooden leg and less than 5 degrees for the human leg, suggesting that the system represents a promising possibility for wearable movement tracking and analysis. Keywords-inertial measurement analysis; exoskeleton; sensor fusion
I.
unit;
human
In our own research, we aim for a wearable sensor system for the upper and lower body that can be either integrated in an exoskeleton or used for general human movement analysis. An optimal solution are so-called inertial measurement units (IMUs), which combine an accelerometer, a gyroscope and optionally a magnetometer [5, 6]. For exoskeletons, IMUs would be superior to potentiometers since they can be attached directly to the human body and thus detect small movements earlier than potentiometers. They have been previously used in commercially available systems such as the Xsens MVN (Xsens Technologies B. V.). However, since no commercial solutions with adequate real-time capabilities can be found for our own applications, we sought to develop our own IMU system that would have advantages over existing systems.
movement
INTRODUCTION
Exoskeletons for the lower limbs are generally designed either for human performance augmentation or to provide assistance to physically impaired persons. Exoskeletons purely meant for clinical therapy purposes are currently non-portable, treadmill-based devices (e.g. the Lokomat (Hocoma A. G.) and the LOPES [1]). However, there is a great interest in developing wearable robots (autonomous orthoses) that can provide assistance in everyday life. One example is the Hybrid Assistive Leg (HAL) exoskeleton [2], which is also targeted at assistive and rehabilitative applications. A second example is the eLEGS (Berkeley Bionics), primarily aimed at paraplegics.
First, by using novel 3-axis integrated electronic sensor components, we wish to minimize the size and weight of the sensor. The implemented sensor is only 30 mm in width and a few millimeters in height (for comparison, the Xsens MTX is 58x50 mm with a height of 23 mm). This also removes the need to position the different sensors (e.g. one accelerometer for each axis) perpendicularly to each other since an integrated electronic sensor component already has perpendicularly positioned sensors inside the circuit. Second, each sensor needs to be connected to a central unit wirelessly so as not to impede the wearer. Additionally, to allow easy integration into larger systems such as an exoskeleton, the new system needs to have a modular design, open-source architecture, high-frequency real-time capability and the possibility of full customization. The development and validation of this system is presented in the following sections.
From a sensory viewpoint, a lower limb exoskeleton can be treated as an intelligent robot that requires inputs from several sensors to properly interact with the human body and the environment. Such an intelligent robot faces several challenges. First, it needs to combine information from different sensors to form a complete representation of the environment – both internal and external. Second, it needs to make intelligent decisions to, for example, respond to events such as the wearer's desire to change his/her walking pattern or even potentially dangerous events such as unstable gait. In order to address these challenges, a complex network of This work was supported by the EU within the EVRYON Collaborative Project STREP (FP7-ICT-2007-3-231451) and additionally supported by the Slovenian Research Agency.
978-1-61284-868-6/11/$26.00 ©2011 IEEE
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II.
MATERIALS AND METHODS
A. Hardware design Our wearable system for body movement measurement is based on inertial measurement units (IMUs) placed on the human body (section A.1). However, data transmission from the IMUs over classic wire connections is unfeasible since these wires would impede the subject during walking. Thus, it is necessary to implement a wireless transmission system, (section A.2). Finally, the IMUs must be properly calibrated to ensure good data quality (section A.3). 1) Inertial measurement units: A single inertial measurement unit (IMU) consists of three different 3-axis sensors: an Invensense 3-axis gyroscope, STmicroelectronics 3-axis accelerometer and Honeywell 3-axis magnetometer. The gyroscope has selectable full-scale ranges of ±250, ±500, ±1000 and ±2000 degrees/second as well as softwareselectable low-pass filters. Each axis is represented with 16 bits. Similarly to the gyroscope, the accelerometer also offers a selectable range of ±2g, ±4g and ±8g and has 16-bit output per axis. It offers software selection of high-pass filters and sampling rates. The highest possible sampling rate is 1000 Hz. The magnetometer has a selectable range of ±0.88 to ±8.1 gauss. It uses a 12-bit analog-to-digital converter and has a significantly lower sampling rate in comparison with other two sensors. The maximum sampling rate is 160 Hz while the minimum is 0.75 Hz. All sensors are connected to an I 2C bus with a maximum data transfer rate of 222 Kbit/s. Each sensor provides 6 bytes of information, which makes a total of 18 bytes. The theoretically attainable transfer rate is 1.2 kHz.
Figure 2. The central unit. It has a separate antenna for each IMU and a size of 200x137x55 mm.
2) Data transmission and central unit: The IMUs are connected to a central unit via a wireless transmission system. On the IMU side, a ZigBit wireless transceiver is used. On the receiving side, a powerful Atmel receiver is used since there are no constraints on power consumption and size. This receiver has an amplified port for an external antenna and allows a working range of over 15 m. The receiver is connected via SPI to a central unit (Figure 2) which receives data from up to 8 IMUs simultaneously at a frequency of 300 Hz and transfer it to a personal computer via UDP. The central unit can be further upgraded to receive data from up to 16 IMUs, and multiple central units can be connected together, allowing large numbers of IMUs to be used simultaneously.
The IMU also has an integrated Atmel ZigBit wireless transceiver module for transmission of sensor outputs to a central unit. The module uses a Atmel processor with an 8MHz clock frequency, capability of I2C, SPI, UART communication and battery voltage control. The wireless part is managed by an Atmel RF Transceiver and dual-chip antenna. There are also two LED indicators to indicate operation and connection of the system. Furthermore, each IMU has a 3 V supply line, with all components operating at the same voltage. Total consumption during operation was measured as approximately 27 mA. Thus, a Wellpower battery with a rated capacity of 250 mAh was chosen for battery supply. With this capacity, the module can continuously run up to 8 hours. To add even more capacity, another battery can be added in parallel. The IMU itself (without battery) has a size of 30x20x5 mm and is shown in Fig. 1.
3) Calibration: In an ideal IMU, all sensors are orthogonal, have no bias and have the exact sensitivity specified by the manufacturer. Since this is not true in practice, a calibration procedure is necessary to determine the unorthogonality, bias and sensitivity of each sensor axis. We calibrated the accelerometers and magnetometers using the process described in [7]. Gyroscope biases are accounted for by the Kalman filter (section B.1). Four IMUs were mounted on a single plane of a rigid wooden cube with a 15-cm edge. The first two IMUs had the same orientation while the other two were rotated by 180 degrees around the vertical axis relative to the first two. Eight infrared Optotrak markers were also placed on two adjacent planes of the cube. Since only three markers are needed to calculate the orientation of the cube, this redundant configuration increased robustness. Mounting four IMUs allowed four to be calibrated simultaneously. The cube was rotated around the vertical axis in 16 steps of 22.5 degrees each. It was then placed on a perpendicular plane and again rotated around the vertical axis in 16 steps. Finally, it was placed on a plane perpendicular to both previous planes and the rotation was repeated again. The cube remained stationary in each orientation for at least five seconds. The signals from the accelerometer and magnetometer were averaged over each of the 48 5-second periods and input into an optimization algorithm that determined the best parameters for the sensor. Details of the algorithm are available in [7].
Figure 1. A single inertial measurement unit without a battery. Its size is 30x20x5 mm.
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B. Human body kinematics Having obtained raw measurements from the IMUs using the setup described in section A, it is necessary to fuse them into a form of information more relevant for body movement analysis: the angles of the different joints of the human body. For this purpose, Kalman filtering (section B.1) is used to track changes in the orientation of a single IMU while the factored quaternion algorithm (section B.2) provides the initial orientation of each IMU, allowing the absolute orientation to be determined. Once the orientation of each IMU is available, the orientation of the segment that the IMU is attached to can also be determined (section B.3). Finally, the angle of each joint is calculated from two adjacent segments (section B.4).
[
[
( )
] is the value of at time k, [ ] is the predicted value of at time k+1 made from at time , is the gyroscope noise, is the gyroscope bias noise, T is the sample time and is a 3x3 identity matrix. is a 4x4 skew-symmetric matrix composed of the raw gyroscope rate measurement vector [ ] at time k+1. ] ]
(2)
The matrix [ ], where e represents a general variable, is a standard cross product matrix defined as [
]
[
]
The matrix relates the gyroscope noise vector the gyroscope bias and is given by
( (
) )
]
(5)
(
)
[
]
(6)
2) Factored quaternion algorithm: A Kalman filter provides accurate orientation changes. However, it needs to be initialized with the initial orientation, which can be obtained using the factored quaternion algorithm (FQA) [9]. FQA is accurate only in stationary conditions with no outside accelerations and a constant magnetic field. The zero orientation of FQA is a coordinate system where the z-axis is pointed upward, away from the gravity acceleration, and the xaxis points to magnetic north. During initial stationary conditions, the person stands still and an absolute orientation quaternion ( ) is obtained for each IMU. During the measurement, the IMU’s orientation in the world coordinate ) is obtained by multiplying the FQA system ( quaternion ( ) , which represents the initial orientation, with the Kalman quaternion ( ) , which represents the change from the initial orientation. FQA quaternions are illustrated with black lines in Fig. 3, and further details about the algorithm are available in [9].
where
[
[
UKF is initialized with initial values of covariance matrices and initial values of the state vector. Initial values of are estimated during a one-second initialization phase during which the IMU is kept stationary. Since we know that the gyroscope output should be zero in this phase, the bias can be estimated. It is, crucial that the IMU is kept stationary during initialization. the initial orientation of the IMU, is determined with the FQA method described in section B.2.
(1)
[
]
and are accelerometer and magnetometer measurements at time k+1 expressed in the IMU’s body frame. and are the gravitational vector and Earth’s magnetic field expressed in the world coordinate frame.
The UKF’s time-update is described as:
[
(4)
where ( ) is a 3x3 orientation matrix calculated from the orientation quaternion as
UKF estimates the orientation of the IMU and the gyroscope measurement bias. The state vector used by UKF is [ ] , where [ ] is a unit quaternion with as the scalar part and [ ] as the vector part. The conjugate of represents the orientation of the IMU in the world coordinate frame. [ ] is the gyroscope measurement bias.
)
] ]
The measurement model describes the relationship between accelerometer and magnetometer measurements and the state vector . It is given by the equation
1) Kalman filtering: The unscented Kalman filter (UKF), a modified version of the linear Kalman filter, is used to track changes in orientation of a single IMU from the raw accelerometer, gyroscope and magnetometer outputs. UKF is commonly used for estimation of nonlinear systems and has been shown to outperform the Extended Kalman filter (a classical extension of the Kalman filter for estimation of nonlinear systems) in numerous examples. More detailed discussion of UKF can be found in [8].
(
[
3) Segment orientations: Having obtained the orientation of each IMU in the previous two sections, the next step is to obtain the initial orientation of all body segments in the global coordinate frame ( ) . In this way, we can describe the orientation of the segments regardless of the placement of the IMU on that segment. For general illustrations of all quaternions used in this section, please refer to Fig. 3.
(3) and
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By multiplying the IMU orientation in global coordinates (qIW) with qSI, we can then track segment orientation in global coordinates. 4) Joint angles: Once the orientation of each segment is known, it is necessary to compute joint angles. For that purpose, we need the difference in orientation between two coordinate systems attached to different segments of the person’s body. The quaternions representing the orientations of each segment were computed in the previous section. For a joint between two arbitrary segments 1 and 2, the joint quaternion is defined as (9) From this quaternion, it is trivial to obtain angles along different joint axes. In human motion analysis, the two important joint angles are the angles in the sagittal and coronal planes. Some joints (e.g. the knee) have a single dominant degree of freedom and are thus described with only one angle. C. Validation The calculated joint angles need to be validated before the system can be used in practice. We performed validation by comparing the joint angles calculated from the IMUs with the joint angles calculated using data from an optical contactless measurement system, the Optotrak Certus (Northern Digital Inc.), which is commonly used in gait research (e.g. [10]). All signals were sampled at 100 Hz.
Figure 3. Quaternions corresponding to initial IMU and segment orientations.
Since the subject stands still with feet side by side during the initialization phase, the initial coordinate system for all segments can be placed with the z-axis pointing upward. As the orientation is described in the world coordinate system, the [ ] initial z-axis of the segment can be described as
IMUs, Kalman filter and body kinematics calculation were validated in three phases. First, measurements were performed with the IMUs attached to a rigid cube. No joint angles were calculated in this phase – only the orientations of each IMU. This allowed us to validate the Kalman filter and FQA in the absence of segment orientation and joint angle calculation. Then, measurements were performed with a simple wooden mockup of a human leg. This allowed us to validate the entire system in a simplified, well-controlled situation. Finally, measurements were performed with the IMUs attached to a human during actual leg movement.
With the z-axis known, one more vector is required to define the coordinate system. This vector needs to have either a lateral or forward/backward component. One possible choice is to take advantage of the lower back IMU, which should have one axis pointed backward with no lateral component. This axis can be extracted from the FQA quaternion of the lower back mounted IMU and is thus noted as zFQA_0. However, this vector is not perpendicular to z0S. Nonetheless, by creating a cross product of z0S and zFQA_0, we obtain a third vector that is perpendicular to both and points to the left: [
]
1) Rigid cube: The same configuration of IMUs and Optotrak markers on a rigid cube previously used for calibration (section 2.1.3) was reused for validation. Six trials were conducted with the cube at different rotation velocities. The orientation of the cube changed by 8.5 degrees/second in the first two trials, 17.9 degrees/second in the second two trials and 51.1 degrees/second in the final three trials. The axis of rotation was varied throughout each trial.
(7)
By normalizing y0S, we obtain a second axis of the initial segment coordinate system. With two known axes, the third one (x0S) is defined as being perpendicular to the other two. The corresponding quaternion obtained from these three axes (q0S – green lines in Fig. 3) describes the starting orientation of all segments in the global coordinate system. Separate IMU and segment coordinate systems allow for a simplified procedure of attaching the IMUs to the person’s body: only the lower back IMU has to be attached symmetrically while all others may be placed arbitrarily on the segments. We can now compute the transformation from the coordinate systems of an IMU to the corresponding segment:
Differences between the IMUs and Optotrak were evaluated by calculating the absolute difference in the cube's orientation as estimated by the IMUs and the Optotrak. Results were averaged across all three axes and all six trials to obtain the final results. 2) Wooden leg mockup: The wooden mockup of a human leg consisted of a wooden foot, shank, thigh, and trunk connected together. All joint axes had the same direction. The starting pose of the leg was vertical, with the foot pointing forward. Four IMUs were mounted on the mockup: on top of
(8)
215
TABLE I.
the foot, on the front of the shank and thigh, and on the small of the back. Markers were placed on the lateral side with three markers defining two base vectors for the coordinate system placed on each segment.
sensitivity correction [gain] Sx
Three trials were conducted. During the first trial, the leg was moved 20 times in the sagittal plane at the hip and knee in such a way that the shank remained vertical. Each movement was approximately 60 degrees of rotation. The second trial consisted of raising the leg to a horizontal position, then performing 50 lateral movements. Each movement was approximately 7 degrees of rotation. The third trial consisted of 20 hip movements in the sagittal plane, with the ankle and knee locked. Each movement was approximately 20 degrees of rotation. At the beginning of each trial, the leg was stationary for five seconds while the FQA algorithm calculated the starting orientation.
Sy
Sz
orthogonalization angle [rad]
bias [m/s2] Bx
By
Bz
1.0113 1.0041 0.9953 0.0846 0.0497 0.1072 1.5222 1.5714 1.5929
B. Validation: Rigid cube The absolute error (difference between orientations obtained from the IMUs and from the Optotrak, calculated across all three axes) is shown in Table II for the three different rotation speeds. TABLE II.
ABSOLUTE ERRORS FOR THE THREE ROTATION SPEEDS OF THE RIGID CUBE, SUMMARIZED AS THE MEDIAN VALUE AND THE 25TH AND 75TH PERCENTILES. absolute error [o]
speed
Differences between the IMUs and Optotrak were evaluated by calculating the absolute difference in each joint angle in the sagittal and coronal plane as estimated by the IMUs and the Optotrak. Results were averaged across all trials to obtain the final results. 3) Human: The final validation was done with a single human subject. IMUs were placed on the small of the back, the outside of the left thigh, the inside of the left shank and on top of the big toe. Each of the four IMUs corresponded to a body segment: trunk, thigh, shank, and foot. Each of those segments was additionally equipped with four Optotrak markers. Though four are not required to calculate orientation, they were used for redundancy. Six different trials were performed: subject makes 3 steps from a stationary position (15 times), subject walks in place (30 steps), hip flexion/extension in 2 starting orientations (10 times each), hip abduction/adduction in 2 starting orientations (10 times each), knee flexion/extension in 2 starting orientations (10 times each) and ankle flexion/extension in 2 starting orientations (10 times each). At the beginning of each trial, the subject stood perfectly still for five seconds in a starting configuration while the FQA algorithm calculated the starting orientation.
median
25th %
75th %
slow
0.74
0.29
1.52
medium
0.80
0.19
1.86
fast
1.10
0.38
2.28
C. Validation: Wooden leg mockup The absolute error (difference between joint angles obtained from the IMUs and from the Optotrak) is shown in Table III for the hip, knee and ankle. Errors are given in sagittal and coronal planes for the hip and ankle (which can be modelled as having two degrees of freedom) and in the sagittal plane for the knee (which can be modelled as having one degree of freedom). Furthermore, an example of joint angles for both the Optotrak and IMU is shown in Fig. 4. TABLE III. ABSOLUTE ERRORS FOR THE WOODEN LEG MOCKUP, SUMMARIZED AS THE MEDIAN VALUE AND THE 25TH AND 75TH PERCENTILES. absolute error [o]
joint angle
Differences between the IMUs and Optotrak were evaluated by calculating the absolute difference in each joint angle in the sagittal and coronal plane as estimated by the IMUs and the Optotrak. Results were averaged across all trials to obtain the final results. III.
CALIBRATION PARAMETERS FOR AN EXAMPLE ACCELEROMETER.
median
25th %
75th %
hip, sagittal
0.38
0.03
0.97
hip, coronal
0.43
0.06
1.60
knee, sagittal
0.53
0.09
1.31
ankle, sagittal
0.38
0.14
0.73
ankle, coronal
1.11
0.16
3.72
RESULTS
A. Calibration Table I shows the calibrated parameters for an example accelerometer: sensitivities and biases along each axis as well as the three orthogonalization angles. In the ideal case, all three sensitivities would be equal to 1, all three biases would be equal to 0, and all three orthogonalization angles would be equal to /2. Results for other sensors were similar and are thus not presented. Figure 4. Joint angles obtained for the wooden leg with both the IMU and Optotrak.
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markers on the skin during measurement. These factors should be less prominent with the cube and wooden leg (both very rigid), which partially explains why differences between the IMU and Optotrak are smaller for the cube and leg (around 1 degree) than the human measurements (up to 5 degrees).
D. Validation: Human The absolute error (difference between joint angles obtained from the IMUs and from the Optotrak) is shown in Table 4 for the hip, knee and ankle. Errors are given in sagittal and coronal planes for the hip and ankle (which can be modelled as having two degrees of freedom) and in the sagittal plane for the knee (which can be modelled as having one degree of freedom). Furthermore, an example of joint angles for both the Optotrak and IMU is shown in Fig. 5.
In an exoskeleton, the system could be used for event detection and decision-making (e.g. recognizing desired movements or potential instability). A possible weakness of the system when used with an exoskeleton would be the effect of metal and electronics on the magnetometer. However, if the additional noise renders the magnetometer unreliable, the Kalman filter can easily be adjusted so that it treats the magnetometer as less reliable or ignores it altogether, though this may decrease accuracy.
TABLE IV.
ABSOLUTE ERRORS FOR THE HUMAN LEG, SUMMARIZED AS THE MEDIAN VALUE AND THE 25TH AND 75TH PERCENTILES. absolute error [o]
joint angle
median
25th %
75th %
hip, sagittal
2.29
1.13
4.01
hip, coronal
2.86
0.99
6.65
knee, sagittal
1.75
0.88
3.09
ankle, sagittal
4.04
1.68
7.64
ankle, coronal
5.00
1.99
8.43
V.
CONCLUSIONS
We have successfully developed a system of inertial measurement units consisting of three-axial accelerometers, gyroscopes and magnetometers. Using Kalman filtering and the factored quaternion algorithm, the system can measure joint angles with a median absolute error of less than 5 degrees for actual human movement compared to a reference Optotrak system. The system is small, wireless and open-architecture, allowing it to be either be used for human movement analysis on its own or integrated into an assistive exoskeleton to assist with the exoskeleton's decision-making processes. REFERENCES [1]
J. F. Veneman, R. Kruidhof, E. E. Hekman, R. Ekkelenkamp, E. H. van Asseldonk and H. van der Kooij, “Design and evaluation of the LOPES exoskeleton robot for interactive gait rehabilitation,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 15, pp. 379-386, 2007. [2] H. Kawamoto and Y. Sankai, “Power assist method based on phase sequence and muscle force coordination for HAL,” Adv. Robotics, vol. 19, pp. 717-734, 2005. [3] C. J. Walsh, K. Endo and H. Herr, “A quasi-passive leg exoskeleton for load-carrying augmentation,” Int. J. Hum. Robot., vol. 4, pp. 487-506, 2007. [4] T. Wannier, C. Bastiaanse, G. Colombo and V. Dietz, “Arm to leg coordination in humans during walking, creeping and swimming activities,” Exp. Brain Res., vol. 141, pp. 375-379, 2001. [5] M. Mihelj, “Inverse kinematics of human arm based on multisensor data integration”, J. Intell. Robot Syst., vol. 47, pp. 139-153, 2006. [6] R. Zhu and Z. Zhou, “Realtime articulated human motion tracking using tri-axis inertial/magnetic sensors package”, IEEE Trans. Neural Syst. Rehabil. Eng., vol. 12, pp. 295-302, 2004. [7] D. Jurman, M. Jankovec, R. Kamnik and M. Topič, “Calibration and data fusion solution for the miniature attitude and heading reference system,” Sens. Actuat. A-Phys., vol. 138, pp. 411-420, 2007. [8] R. van der Merwe and E. A. Wan, “Sigma-Point Kalman Filters for Integrated Navigation,” Proceedings of the 60th Annual Meeting of The Institute of Navigation, Dayton, OH, June 2004, pp. 641-654. [9] X. Yun, E. R. Bachmann and R. B. McGhee, “A simplified quaternionbased algorithm for orientation estimation from Earth gravity and magnetic field measurements,” IEEE Trans. Instrum. Meas., vol. 57, pp. 638-650, 2008. [10] Y. Huang, O. G. Meijer, J. Lin, S. M. Brujin, X. Lin, H.Hu et al., “The effects of stride length and stride frequency on trunk coordination in human walking,” Gait Posture, vol. 31, pp. 444-449, 2010. [11] J. M. Jasiewicz, J. H. Allum, J. W. Middleton, A. Barriskill, P. Condie, B. Purcell et al., “Gait event detection using linear accelerometers or angular velocity transducers in able-bodied and spinal-cord injured individuals,” Gait Posture, vol. 24, pp. 502-509, 2006.
Figure 5. Joint angles obtained for the human leg with both the IMU and Optotrak.
IV.
DISCUSSION
Validation results from the rigid cube and wooden leg show that our IMUs can measure orientations and angles with a median error of approximately 1 degree compared to the Optotrak system, which is widely used in gait analysis. Results from actual human measurements are slightly worse, but the median error is still under 3 degrees for the hip and knee and 4-5 degrees for the ankle. In most cases, differences between the IMUs and Optotrak are noticeably smaller in the sagittal plane than the coronal plane. This is good since sagittal joint rotation is predominant when walking straight ahead, and thus many events in gait can be detected by only taking movement in the sagittal plane into account (e.g. [11]). However, rotations in the coronal plane are important when turning and during unstable conditions such as potential falls, so they should not be ignored. It is currently uncertain why errors in the coronal plane are larger than in the sagittal plane or why the error for the ankle is larger than for the other two joints.
f
The difference between the IMU and Optotrak results should, of course, not be considered solely a failing on the part of the IMUs. Though the Optotrak itself is very accurate, errors are introduced by factors such as the shifting of infrared
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Development and validation of a wearable inertial measurement system for use with lower limb exoskeletons Tadej Beravs, Peter Reberšek, Domen Novak, Janez Podobnik, Marko Munih Laboratory of Robotics University of Ljubljana Ljubljana, Slovenia [email protected] sensors is required. Among them are sensors that measure human body kinematics. For instance, the MIT leg exoskeleton [3] measures hip and knee angles using rotary potentiometers. Similarly, the HAL [2] uses accelerometers and gyroscopes in addition to potentiometers to measure joint angles. Since upper and lower body movement are strongly coordinated during walking [4], it would be useful for exoskeletons to also measure upper body movement using separate sensors.
Abstract—This paper presents a system of inertial measurement units, each consisting of an accelerometer, gyroscope and magnetometer. They are characterized by a small size, wireless transmission, and open architecture, with the purpose of either integration into lower limb exoskeletons or general human movement analysis. Kalman filtering and the factored quaternion algorithm are used to track the orientation of each unit, and angles of the human joints are calculated from multiple units. After calibration, the system was tested with a wooden leg mockup and an actual human. The Optotrak optical measurement system was used as a reference. Differences between the inertial measurement system and the Optotrak were less than 2 degrees for the wooden leg and less than 5 degrees for the human leg, suggesting that the system represents a promising possibility for wearable movement tracking and analysis. Keywords-inertial measurement analysis; exoskeleton; sensor fusion
I.
unit;
human
In our own research, we aim for a wearable sensor system for the upper and lower body that can be either integrated in an exoskeleton or used for general human movement analysis. An optimal solution are so-called inertial measurement units (IMUs), which combine an accelerometer, a gyroscope and optionally a magnetometer [5, 6]. For exoskeletons, IMUs would be superior to potentiometers since they can be attached directly to the human body and thus detect small movements earlier than potentiometers. They have been previously used in commercially available systems such as the Xsens MVN (Xsens Technologies B. V.). However, since no commercial solutions with adequate real-time capabilities can be found for our own applications, we sought to develop our own IMU system that would have advantages over existing systems.
movement
INTRODUCTION
Exoskeletons for the lower limbs are generally designed either for human performance augmentation or to provide assistance to physically impaired persons. Exoskeletons purely meant for clinical therapy purposes are currently non-portable, treadmill-based devices (e.g. the Lokomat (Hocoma A. G.) and the LOPES [1]). However, there is a great interest in developing wearable robots (autonomous orthoses) that can provide assistance in everyday life. One example is the Hybrid Assistive Leg (HAL) exoskeleton [2], which is also targeted at assistive and rehabilitative applications. A second example is the eLEGS (Berkeley Bionics), primarily aimed at paraplegics.
First, by using novel 3-axis integrated electronic sensor components, we wish to minimize the size and weight of the sensor. The implemented sensor is only 30 mm in width and a few millimeters in height (for comparison, the Xsens MTX is 58x50 mm with a height of 23 mm). This also removes the need to position the different sensors (e.g. one accelerometer for each axis) perpendicularly to each other since an integrated electronic sensor component already has perpendicularly positioned sensors inside the circuit. Second, each sensor needs to be connected to a central unit wirelessly so as not to impede the wearer. Additionally, to allow easy integration into larger systems such as an exoskeleton, the new system needs to have a modular design, open-source architecture, high-frequency real-time capability and the possibility of full customization. The development and validation of this system is presented in the following sections.
From a sensory viewpoint, a lower limb exoskeleton can be treated as an intelligent robot that requires inputs from several sensors to properly interact with the human body and the environment. Such an intelligent robot faces several challenges. First, it needs to combine information from different sensors to form a complete representation of the environment – both internal and external. Second, it needs to make intelligent decisions to, for example, respond to events such as the wearer's desire to change his/her walking pattern or even potentially dangerous events such as unstable gait. In order to address these challenges, a complex network of This work was supported by the EU within the EVRYON Collaborative Project STREP (FP7-ICT-2007-3-231451) and additionally supported by the Slovenian Research Agency.
978-1-61284-868-6/11/$26.00 ©2011 IEEE
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II.
MATERIALS AND METHODS
A. Hardware design Our wearable system for body movement measurement is based on inertial measurement units (IMUs) placed on the human body (section A.1). However, data transmission from the IMUs over classic wire connections is unfeasible since these wires would impede the subject during walking. Thus, it is necessary to implement a wireless transmission system, (section A.2). Finally, the IMUs must be properly calibrated to ensure good data quality (section A.3). 1) Inertial measurement units: A single inertial measurement unit (IMU) consists of three different 3-axis sensors: an Invensense 3-axis gyroscope, STmicroelectronics 3-axis accelerometer and Honeywell 3-axis magnetometer. The gyroscope has selectable full-scale ranges of ±250, ±500, ±1000 and ±2000 degrees/second as well as softwareselectable low-pass filters. Each axis is represented with 16 bits. Similarly to the gyroscope, the accelerometer also offers a selectable range of ±2g, ±4g and ±8g and has 16-bit output per axis. It offers software selection of high-pass filters and sampling rates. The highest possible sampling rate is 1000 Hz. The magnetometer has a selectable range of ±0.88 to ±8.1 gauss. It uses a 12-bit analog-to-digital converter and has a significantly lower sampling rate in comparison with other two sensors. The maximum sampling rate is 160 Hz while the minimum is 0.75 Hz. All sensors are connected to an I 2C bus with a maximum data transfer rate of 222 Kbit/s. Each sensor provides 6 bytes of information, which makes a total of 18 bytes. The theoretically attainable transfer rate is 1.2 kHz.
Figure 2. The central unit. It has a separate antenna for each IMU and a size of 200x137x55 mm.
2) Data transmission and central unit: The IMUs are connected to a central unit via a wireless transmission system. On the IMU side, a ZigBit wireless transceiver is used. On the receiving side, a powerful Atmel receiver is used since there are no constraints on power consumption and size. This receiver has an amplified port for an external antenna and allows a working range of over 15 m. The receiver is connected via SPI to a central unit (Figure 2) which receives data from up to 8 IMUs simultaneously at a frequency of 300 Hz and transfer it to a personal computer via UDP. The central unit can be further upgraded to receive data from up to 16 IMUs, and multiple central units can be connected together, allowing large numbers of IMUs to be used simultaneously.
The IMU also has an integrated Atmel ZigBit wireless transceiver module for transmission of sensor outputs to a central unit. The module uses a Atmel processor with an 8MHz clock frequency, capability of I2C, SPI, UART communication and battery voltage control. The wireless part is managed by an Atmel RF Transceiver and dual-chip antenna. There are also two LED indicators to indicate operation and connection of the system. Furthermore, each IMU has a 3 V supply line, with all components operating at the same voltage. Total consumption during operation was measured as approximately 27 mA. Thus, a Wellpower battery with a rated capacity of 250 mAh was chosen for battery supply. With this capacity, the module can continuously run up to 8 hours. To add even more capacity, another battery can be added in parallel. The IMU itself (without battery) has a size of 30x20x5 mm and is shown in Fig. 1.
3) Calibration: In an ideal IMU, all sensors are orthogonal, have no bias and have the exact sensitivity specified by the manufacturer. Since this is not true in practice, a calibration procedure is necessary to determine the unorthogonality, bias and sensitivity of each sensor axis. We calibrated the accelerometers and magnetometers using the process described in [7]. Gyroscope biases are accounted for by the Kalman filter (section B.1). Four IMUs were mounted on a single plane of a rigid wooden cube with a 15-cm edge. The first two IMUs had the same orientation while the other two were rotated by 180 degrees around the vertical axis relative to the first two. Eight infrared Optotrak markers were also placed on two adjacent planes of the cube. Since only three markers are needed to calculate the orientation of the cube, this redundant configuration increased robustness. Mounting four IMUs allowed four to be calibrated simultaneously. The cube was rotated around the vertical axis in 16 steps of 22.5 degrees each. It was then placed on a perpendicular plane and again rotated around the vertical axis in 16 steps. Finally, it was placed on a plane perpendicular to both previous planes and the rotation was repeated again. The cube remained stationary in each orientation for at least five seconds. The signals from the accelerometer and magnetometer were averaged over each of the 48 5-second periods and input into an optimization algorithm that determined the best parameters for the sensor. Details of the algorithm are available in [7].
Figure 1. A single inertial measurement unit without a battery. Its size is 30x20x5 mm.
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B. Human body kinematics Having obtained raw measurements from the IMUs using the setup described in section A, it is necessary to fuse them into a form of information more relevant for body movement analysis: the angles of the different joints of the human body. For this purpose, Kalman filtering (section B.1) is used to track changes in the orientation of a single IMU while the factored quaternion algorithm (section B.2) provides the initial orientation of each IMU, allowing the absolute orientation to be determined. Once the orientation of each IMU is available, the orientation of the segment that the IMU is attached to can also be determined (section B.3). Finally, the angle of each joint is calculated from two adjacent segments (section B.4).
[
[
( )
] is the value of at time k, [ ] is the predicted value of at time k+1 made from at time , is the gyroscope noise, is the gyroscope bias noise, T is the sample time and is a 3x3 identity matrix. is a 4x4 skew-symmetric matrix composed of the raw gyroscope rate measurement vector [ ] at time k+1. ] ]
(2)
The matrix [ ], where e represents a general variable, is a standard cross product matrix defined as [
]
[
]
The matrix relates the gyroscope noise vector the gyroscope bias and is given by
( (
) )
]
(5)
(
)
[
]
(6)
2) Factored quaternion algorithm: A Kalman filter provides accurate orientation changes. However, it needs to be initialized with the initial orientation, which can be obtained using the factored quaternion algorithm (FQA) [9]. FQA is accurate only in stationary conditions with no outside accelerations and a constant magnetic field. The zero orientation of FQA is a coordinate system where the z-axis is pointed upward, away from the gravity acceleration, and the xaxis points to magnetic north. During initial stationary conditions, the person stands still and an absolute orientation quaternion ( ) is obtained for each IMU. During the measurement, the IMU’s orientation in the world coordinate ) is obtained by multiplying the FQA system ( quaternion ( ) , which represents the initial orientation, with the Kalman quaternion ( ) , which represents the change from the initial orientation. FQA quaternions are illustrated with black lines in Fig. 3, and further details about the algorithm are available in [9].
where
[
[
UKF is initialized with initial values of covariance matrices and initial values of the state vector. Initial values of are estimated during a one-second initialization phase during which the IMU is kept stationary. Since we know that the gyroscope output should be zero in this phase, the bias can be estimated. It is, crucial that the IMU is kept stationary during initialization. the initial orientation of the IMU, is determined with the FQA method described in section B.2.
(1)
[
]
and are accelerometer and magnetometer measurements at time k+1 expressed in the IMU’s body frame. and are the gravitational vector and Earth’s magnetic field expressed in the world coordinate frame.
The UKF’s time-update is described as:
[
(4)
where ( ) is a 3x3 orientation matrix calculated from the orientation quaternion as
UKF estimates the orientation of the IMU and the gyroscope measurement bias. The state vector used by UKF is [ ] , where [ ] is a unit quaternion with as the scalar part and [ ] as the vector part. The conjugate of represents the orientation of the IMU in the world coordinate frame. [ ] is the gyroscope measurement bias.
)
] ]
The measurement model describes the relationship between accelerometer and magnetometer measurements and the state vector . It is given by the equation
1) Kalman filtering: The unscented Kalman filter (UKF), a modified version of the linear Kalman filter, is used to track changes in orientation of a single IMU from the raw accelerometer, gyroscope and magnetometer outputs. UKF is commonly used for estimation of nonlinear systems and has been shown to outperform the Extended Kalman filter (a classical extension of the Kalman filter for estimation of nonlinear systems) in numerous examples. More detailed discussion of UKF can be found in [8].
(
[
3) Segment orientations: Having obtained the orientation of each IMU in the previous two sections, the next step is to obtain the initial orientation of all body segments in the global coordinate frame ( ) . In this way, we can describe the orientation of the segments regardless of the placement of the IMU on that segment. For general illustrations of all quaternions used in this section, please refer to Fig. 3.
(3) and
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By multiplying the IMU orientation in global coordinates (qIW) with qSI, we can then track segment orientation in global coordinates. 4) Joint angles: Once the orientation of each segment is known, it is necessary to compute joint angles. For that purpose, we need the difference in orientation between two coordinate systems attached to different segments of the person’s body. The quaternions representing the orientations of each segment were computed in the previous section. For a joint between two arbitrary segments 1 and 2, the joint quaternion is defined as (9) From this quaternion, it is trivial to obtain angles along different joint axes. In human motion analysis, the two important joint angles are the angles in the sagittal and coronal planes. Some joints (e.g. the knee) have a single dominant degree of freedom and are thus described with only one angle. C. Validation The calculated joint angles need to be validated before the system can be used in practice. We performed validation by comparing the joint angles calculated from the IMUs with the joint angles calculated using data from an optical contactless measurement system, the Optotrak Certus (Northern Digital Inc.), which is commonly used in gait research (e.g. [10]). All signals were sampled at 100 Hz.
Figure 3. Quaternions corresponding to initial IMU and segment orientations.
Since the subject stands still with feet side by side during the initialization phase, the initial coordinate system for all segments can be placed with the z-axis pointing upward. As the orientation is described in the world coordinate system, the [ ] initial z-axis of the segment can be described as
IMUs, Kalman filter and body kinematics calculation were validated in three phases. First, measurements were performed with the IMUs attached to a rigid cube. No joint angles were calculated in this phase – only the orientations of each IMU. This allowed us to validate the Kalman filter and FQA in the absence of segment orientation and joint angle calculation. Then, measurements were performed with a simple wooden mockup of a human leg. This allowed us to validate the entire system in a simplified, well-controlled situation. Finally, measurements were performed with the IMUs attached to a human during actual leg movement.
With the z-axis known, one more vector is required to define the coordinate system. This vector needs to have either a lateral or forward/backward component. One possible choice is to take advantage of the lower back IMU, which should have one axis pointed backward with no lateral component. This axis can be extracted from the FQA quaternion of the lower back mounted IMU and is thus noted as zFQA_0. However, this vector is not perpendicular to z0S. Nonetheless, by creating a cross product of z0S and zFQA_0, we obtain a third vector that is perpendicular to both and points to the left: [
]
1) Rigid cube: The same configuration of IMUs and Optotrak markers on a rigid cube previously used for calibration (section 2.1.3) was reused for validation. Six trials were conducted with the cube at different rotation velocities. The orientation of the cube changed by 8.5 degrees/second in the first two trials, 17.9 degrees/second in the second two trials and 51.1 degrees/second in the final three trials. The axis of rotation was varied throughout each trial.
(7)
By normalizing y0S, we obtain a second axis of the initial segment coordinate system. With two known axes, the third one (x0S) is defined as being perpendicular to the other two. The corresponding quaternion obtained from these three axes (q0S – green lines in Fig. 3) describes the starting orientation of all segments in the global coordinate system. Separate IMU and segment coordinate systems allow for a simplified procedure of attaching the IMUs to the person’s body: only the lower back IMU has to be attached symmetrically while all others may be placed arbitrarily on the segments. We can now compute the transformation from the coordinate systems of an IMU to the corresponding segment:
Differences between the IMUs and Optotrak were evaluated by calculating the absolute difference in the cube's orientation as estimated by the IMUs and the Optotrak. Results were averaged across all three axes and all six trials to obtain the final results. 2) Wooden leg mockup: The wooden mockup of a human leg consisted of a wooden foot, shank, thigh, and trunk connected together. All joint axes had the same direction. The starting pose of the leg was vertical, with the foot pointing forward. Four IMUs were mounted on the mockup: on top of
(8)
215
TABLE I.
the foot, on the front of the shank and thigh, and on the small of the back. Markers were placed on the lateral side with three markers defining two base vectors for the coordinate system placed on each segment.
sensitivity correction [gain] Sx
Three trials were conducted. During the first trial, the leg was moved 20 times in the sagittal plane at the hip and knee in such a way that the shank remained vertical. Each movement was approximately 60 degrees of rotation. The second trial consisted of raising the leg to a horizontal position, then performing 50 lateral movements. Each movement was approximately 7 degrees of rotation. The third trial consisted of 20 hip movements in the sagittal plane, with the ankle and knee locked. Each movement was approximately 20 degrees of rotation. At the beginning of each trial, the leg was stationary for five seconds while the FQA algorithm calculated the starting orientation.
Sy
Sz
orthogonalization angle [rad]
bias [m/s2] Bx
By
Bz
1.0113 1.0041 0.9953 0.0846 0.0497 0.1072 1.5222 1.5714 1.5929
B. Validation: Rigid cube The absolute error (difference between orientations obtained from the IMUs and from the Optotrak, calculated across all three axes) is shown in Table II for the three different rotation speeds. TABLE II.
ABSOLUTE ERRORS FOR THE THREE ROTATION SPEEDS OF THE RIGID CUBE, SUMMARIZED AS THE MEDIAN VALUE AND THE 25TH AND 75TH PERCENTILES. absolute error [o]
speed
Differences between the IMUs and Optotrak were evaluated by calculating the absolute difference in each joint angle in the sagittal and coronal plane as estimated by the IMUs and the Optotrak. Results were averaged across all trials to obtain the final results. 3) Human: The final validation was done with a single human subject. IMUs were placed on the small of the back, the outside of the left thigh, the inside of the left shank and on top of the big toe. Each of the four IMUs corresponded to a body segment: trunk, thigh, shank, and foot. Each of those segments was additionally equipped with four Optotrak markers. Though four are not required to calculate orientation, they were used for redundancy. Six different trials were performed: subject makes 3 steps from a stationary position (15 times), subject walks in place (30 steps), hip flexion/extension in 2 starting orientations (10 times each), hip abduction/adduction in 2 starting orientations (10 times each), knee flexion/extension in 2 starting orientations (10 times each) and ankle flexion/extension in 2 starting orientations (10 times each). At the beginning of each trial, the subject stood perfectly still for five seconds in a starting configuration while the FQA algorithm calculated the starting orientation.
median
25th %
75th %
slow
0.74
0.29
1.52
medium
0.80
0.19
1.86
fast
1.10
0.38
2.28
C. Validation: Wooden leg mockup The absolute error (difference between joint angles obtained from the IMUs and from the Optotrak) is shown in Table III for the hip, knee and ankle. Errors are given in sagittal and coronal planes for the hip and ankle (which can be modelled as having two degrees of freedom) and in the sagittal plane for the knee (which can be modelled as having one degree of freedom). Furthermore, an example of joint angles for both the Optotrak and IMU is shown in Fig. 4. TABLE III. ABSOLUTE ERRORS FOR THE WOODEN LEG MOCKUP, SUMMARIZED AS THE MEDIAN VALUE AND THE 25TH AND 75TH PERCENTILES. absolute error [o]
joint angle
Differences between the IMUs and Optotrak were evaluated by calculating the absolute difference in each joint angle in the sagittal and coronal plane as estimated by the IMUs and the Optotrak. Results were averaged across all trials to obtain the final results. III.
CALIBRATION PARAMETERS FOR AN EXAMPLE ACCELEROMETER.
median
25th %
75th %
hip, sagittal
0.38
0.03
0.97
hip, coronal
0.43
0.06
1.60
knee, sagittal
0.53
0.09
1.31
ankle, sagittal
0.38
0.14
0.73
ankle, coronal
1.11
0.16
3.72
RESULTS
A. Calibration Table I shows the calibrated parameters for an example accelerometer: sensitivities and biases along each axis as well as the three orthogonalization angles. In the ideal case, all three sensitivities would be equal to 1, all three biases would be equal to 0, and all three orthogonalization angles would be equal to /2. Results for other sensors were similar and are thus not presented. Figure 4. Joint angles obtained for the wooden leg with both the IMU and Optotrak.
216
markers on the skin during measurement. These factors should be less prominent with the cube and wooden leg (both very rigid), which partially explains why differences between the IMU and Optotrak are smaller for the cube and leg (around 1 degree) than the human measurements (up to 5 degrees).
D. Validation: Human The absolute error (difference between joint angles obtained from the IMUs and from the Optotrak) is shown in Table 4 for the hip, knee and ankle. Errors are given in sagittal and coronal planes for the hip and ankle (which can be modelled as having two degrees of freedom) and in the sagittal plane for the knee (which can be modelled as having one degree of freedom). Furthermore, an example of joint angles for both the Optotrak and IMU is shown in Fig. 5.
In an exoskeleton, the system could be used for event detection and decision-making (e.g. recognizing desired movements or potential instability). A possible weakness of the system when used with an exoskeleton would be the effect of metal and electronics on the magnetometer. However, if the additional noise renders the magnetometer unreliable, the Kalman filter can easily be adjusted so that it treats the magnetometer as less reliable or ignores it altogether, though this may decrease accuracy.
TABLE IV.
ABSOLUTE ERRORS FOR THE HUMAN LEG, SUMMARIZED AS THE MEDIAN VALUE AND THE 25TH AND 75TH PERCENTILES. absolute error [o]
joint angle
median
25th %
75th %
hip, sagittal
2.29
1.13
4.01
hip, coronal
2.86
0.99
6.65
knee, sagittal
1.75
0.88
3.09
ankle, sagittal
4.04
1.68
7.64
ankle, coronal
5.00
1.99
8.43
V.
CONCLUSIONS
We have successfully developed a system of inertial measurement units consisting of three-axial accelerometers, gyroscopes and magnetometers. Using Kalman filtering and the factored quaternion algorithm, the system can measure joint angles with a median absolute error of less than 5 degrees for actual human movement compared to a reference Optotrak system. The system is small, wireless and open-architecture, allowing it to be either be used for human movement analysis on its own or integrated into an assistive exoskeleton to assist with the exoskeleton's decision-making processes. REFERENCES [1]
J. F. Veneman, R. Kruidhof, E. E. Hekman, R. Ekkelenkamp, E. H. van Asseldonk and H. van der Kooij, “Design and evaluation of the LOPES exoskeleton robot for interactive gait rehabilitation,” IEEE Trans. Neural Syst. Rehabil. Eng., vol. 15, pp. 379-386, 2007. [2] H. Kawamoto and Y. Sankai, “Power assist method based on phase sequence and muscle force coordination for HAL,” Adv. Robotics, vol. 19, pp. 717-734, 2005. [3] C. J. Walsh, K. Endo and H. Herr, “A quasi-passive leg exoskeleton for load-carrying augmentation,” Int. J. Hum. Robot., vol. 4, pp. 487-506, 2007. [4] T. Wannier, C. Bastiaanse, G. Colombo and V. Dietz, “Arm to leg coordination in humans during walking, creeping and swimming activities,” Exp. Brain Res., vol. 141, pp. 375-379, 2001. [5] M. Mihelj, “Inverse kinematics of human arm based on multisensor data integration”, J. Intell. Robot Syst., vol. 47, pp. 139-153, 2006. [6] R. Zhu and Z. Zhou, “Realtime articulated human motion tracking using tri-axis inertial/magnetic sensors package”, IEEE Trans. Neural Syst. Rehabil. Eng., vol. 12, pp. 295-302, 2004. [7] D. Jurman, M. Jankovec, R. Kamnik and M. Topič, “Calibration and data fusion solution for the miniature attitude and heading reference system,” Sens. Actuat. A-Phys., vol. 138, pp. 411-420, 2007. [8] R. van der Merwe and E. A. Wan, “Sigma-Point Kalman Filters for Integrated Navigation,” Proceedings of the 60th Annual Meeting of The Institute of Navigation, Dayton, OH, June 2004, pp. 641-654. [9] X. Yun, E. R. Bachmann and R. B. McGhee, “A simplified quaternionbased algorithm for orientation estimation from Earth gravity and magnetic field measurements,” IEEE Trans. Instrum. Meas., vol. 57, pp. 638-650, 2008. [10] Y. Huang, O. G. Meijer, J. Lin, S. M. Brujin, X. Lin, H.Hu et al., “The effects of stride length and stride frequency on trunk coordination in human walking,” Gait Posture, vol. 31, pp. 444-449, 2010. [11] J. M. Jasiewicz, J. H. Allum, J. W. Middleton, A. Barriskill, P. Condie, B. Purcell et al., “Gait event detection using linear accelerometers or angular velocity transducers in able-bodied and spinal-cord injured individuals,” Gait Posture, vol. 24, pp. 502-509, 2006.
Figure 5. Joint angles obtained for the human leg with both the IMU and Optotrak.
IV.
DISCUSSION
Validation results from the rigid cube and wooden leg show that our IMUs can measure orientations and angles with a median error of approximately 1 degree compared to the Optotrak system, which is widely used in gait analysis. Results from actual human measurements are slightly worse, but the median error is still under 3 degrees for the hip and knee and 4-5 degrees for the ankle. In most cases, differences between the IMUs and Optotrak are noticeably smaller in the sagittal plane than the coronal plane. This is good since sagittal joint rotation is predominant when walking straight ahead, and thus many events in gait can be detected by only taking movement in the sagittal plane into account (e.g. [11]). However, rotations in the coronal plane are important when turning and during unstable conditions such as potential falls, so they should not be ignored. It is currently uncertain why errors in the coronal plane are larger than in the sagittal plane or why the error for the ankle is larger than for the other two joints.
f
The difference between the IMU and Optotrak results should, of course, not be considered solely a failing on the part of the IMUs. Though the Optotrak itself is very accurate, errors are introduced by factors such as the shifting of infrared
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