Dynamic accuracy of inertial measurement units during simple pendulum motion

A motion measurement system based on inertial measurement units (IMUs) has been suggested as an alternative to contemporary video motion capture. This paper reports an investigation into the accuracy of IMUs in estimating 3D orientation during simple pendulum motion. The IMU vendor's (XSens Technologies) accuracy claim of 3° root mean squared (RMS) error is tested. IMUs are integrated electronic devices that contain accelerometers, magnetometers and gyroscopes. The motion of a pendulum swing was measured using both IMUs and video motion capture as a reference. The IMU raw data were processed by the Kalman filter algorithm supplied by the vendor and a custom fusion algorithm developed by the authors. The IMU measurement of pendulum motion using the vendor's Kalman filter algorithm did not compare well with the video motion capture with a RMS error of between 8.5° and 11.7° depending on the length and type of pendulum swing. The maximum orientation error was greater than 30°, occurring approximately eight seconds into the motion. The custom fusion algorithm estimation of orientation compared well with the video motion capture with a RMS error of between 0.8° and 1.3°. Future research should concentrate on developing a general purpose fusion algorithm and vendors of IMUs should provide details about the errors to be expected in different measurement situations, not just those in a ‘best case’ scenario.     

The static accuracy and calibration of inertial measurement units for 3D orientation

Inertial measurement units (IMUs) are integrated electronic devices that contain accelerometers, magnetometers and gyroscopes. Wearable motion capture systems based on IMUs have been advertised as alternatives to optical motion capture. In this paper, the accuracy of five different IMUs of the same type in measuring 3D orientation in static situations, as well as the calibration of the accelerometers and magnetometers within the IMUs, has been investigated. The maximum absolute static orientation error was 5.2°, higher than the 1° claimed by the vendor. If the IMUs are re-calibrated at the time of measurement with the re-calibration procedure described in this paper, it is possible to obtain an error of less than 1°, in agreement with the vendor's specifications (XSens Technologies B.V. 2005. Motion tracker technical documentation Mtx-B. Version 1.03. Available from: www.xsens.com).

The new calibration appears to be valid for at least 22 days providing the sensor is not exposed to high impacts. However, if several sensors are ‘daisy chained’ together changes to the magnetometer bias can cause heading errors of up to 15°. The results demonstrate the non-linear relationship between the vendor's orthogonality claim of < 0.1° and the accuracy of 3D orientation obtained from factory calibrated IMUs in static situations. The authors hypothesise that the high magnetic dip (64°) in our laboratory may have exacerbated the errors reported. For biomechanical research, small relative movements of a body segment from a calibrated position are likely to be more accurate than large scale global motion that may have an error of up to 9.8°.     

The static accuracy and calibration of inertial measurement units for 3D orientation

Inertial measurement units (IMUs) are integrated electronic devices that contain accelerometers, magnetometers and gyroscopes. Wearable motion capture systems based on IMUs have been advertised as alternatives to optical motion capture. In this paper, the accuracy of five different IMUs of the same type in measuring 3D orientation in static situations, as well as the calibration of the accelerometers and magnetometers within the IMUs, has been investigated. The maximum absolute static orientation error was 5.2 degrees , higher than the 1 degrees claimed by the vendor. If the IMUs are re-calibrated at the time of measurement with the re-calibration procedure described in this paper, it is possible to obtain an error of less than 1 degrees , in agreement with the vendor's specifications (XSens Technologies B.V. 2005. Motion tracker technical documentation Mtx-B. Version 1.03. Available from: www.xsens.com). The new calibration appears to be valid for at least 22 days providing the sensor is not exposed to high impacts. However, if several sensors are 'daisy chained' together changes to the magnetometer bias can cause heading errors of up to 15 degrees . The results demonstrate the non-linear relationship between the vendor's orthogonality claim of < 0.1 degrees and the accuracy of 3D orientation obtained from factory calibrated IMUs in static situations. The authors hypothesise that the high magnetic dip (64 degrees ) in our laboratory may have exacerbated the errors reported. For biomechanical research, small relative movements of a body segment from a calibrated position are likely to be more accurate than large scale global motion that may have an error of up to 9.8 degrees .     

Sensor-to-body calibration procedure for clinical motion analysis of lower limb using magnetic and inertial measurement units

Magnetic and Inertial measurement units (MIMUs) have become exceedingly popular for ambulatory human motion analysis during the past two decades. However, measuring anatomically meaningful segment and joint kinematics requires virtual alignment of the MIMU frame with the anatomical frame of its corresponding segment. Therefore, this paper presents a simple calibration procedure, based on MIMU readouts, to align the inertial frame of the MIMU with the anatomical frames, as recommended by ISB. The proposed calibration includes five seconds of quiet standing in a neutral posture followed by ten consecutive hip flexions/extensions. This procedure will independently calibrate MIMUs attached to the pelvis, thigh, shank, and foot. The accuracy and repeatability of the calibration procedure and the 3D joint angle estimation were validated against the gold standard motion capture system by an experimental study with ten able-bodied participants. The procedure showed high test-retest repeatability in aligning the MIMU frame with its corresponding anatomical frame, i.e., the helical angle between the MIMU and anatomical frames did not significantly differ between the test and retest sessions (except for thigh MIMU). Compared to previously introduced procedures, this procedure attained the highest inter-participant repeatability (inter-participant coefficient of variations of the helical angle: 20.5–42.2%). Further, the proposed calibration would reduce the offset errors of the 3D joint angle estimation (up to 12.8 degrees on average) compared to joint angle estimation without calibration (up to 26.3 degrees on average). The proposed calibration enables MIMU to measure clinically meaningful gait kinematics.     

Assessment of the measurement accuracy of inertial sensors during different tasks of daily living

The low cost and ease of use of inertial measurement units (IMUs) make them an attractive option for motion analysis tasks that cannot be easily measured in a laboratory. To date, only a limited amount of research has been conducted comparing commercial IMU systems to optoelectronic systems, the gold standard, for everyday tasks like stair climbing and inclined walking. In this paper, the 3D joint angles of the lower limbs are determined using both an IMU system and an optoelectronic system for twelve participants during stair ascent and descent, and inclined, declined and level walking. Three different datasets based on different hardware and anatomical models were collected for the same movement in an effort to determine the cause and quantify the errors involved with the analysis. Firstly, to calculate software errors, two different anatomical models were compared for one hardware system. Secondly, to calculate hardware errors, results were compared between two different measurement systems using the same anatomical model. Finally, the overall error between both systems with their native anatomical models was calculated. Statistical analysis was performed using statistical parametric mapping. When both systems were evaluated based on the same anatomical model, the number of trials with significant differences decreased markedly. Thus, the differences in joint angle measurement can mainly be attributed to the variability in the anatomical models used for calculations and not to the IMU hardware.     

Classification of deadlift biomechanics with wearable inertial measurement units

The deadlift is a compound full-body exercise that is fundamental in resistance training, rehabilitation programs and powerlifting competitions. Accurate quantification of deadlift biomechanics is important to reduce the risk of injury and ensure training and rehabilitation goals are achieved. This study sought to develop and evaluate deadlift exercise technique classification systems utilising Inertial Measurement Units (IMUs), recording at 51.2 Hz, worn on the lumbar spine, both thighs and both shanks. It also sought to compare classification quality when these IMUs are worn in combination and in isolation. Two datasets of IMU deadlift data were collected. Eighty participants first completed deadlifts with acceptable technique and 5 distinct, deliberately induced deviations from acceptable form. Fifty-five members of this group also completed a fatiguing protocol (3-Repition Maximum test) to enable the collection of natural deadlift deviations. For both datasets, universal and personalised random-forests classifiers were developed and evaluated. Personalised classifiers outperformed universal classifiers in accuracy, sensitivity and specificity in the binary classification of acceptable or aberrant technique and in the multi-label classification of specific deadlift deviations. Whilst recent research has favoured universal classifiers due to the reduced overhead in setting them up for new system users, this work demonstrates that such techniques may not be appropriate for classifying deadlift technique due to the poor accuracy achieved. However, personalised classifiers perform very well in assessing deadlift technique, even when using data derived from a single lumbar-worn IMU to detect specific naturally occurring technique mistakes.     

Human crawling performance and technique revealed by inertial measurement units

Human crawling performance and technique are of broad interest to roboticists, biomechanists, and military personnel. This study explores the variables that define crawling performance in the context of an outdoor obstacle course used by military organizations worldwide to evaluate the effects of load and personal equipment on warfighter performance. Crawling kinematics, measured from four body-worn inertial measurement units (IMUs) attached to the upper arms and thighs, are recorded for thirty-three participants. The IMU data is distilled to four metrics of crawling performance; namely, crawl speed, crawl stride time, ipsilateral limb coordination, and contralateral limb coordination. We hypothesize that higher performance (as identified by higher crawl speeds) is associated with more coordinated limbs and lower stride times. A cluster analysis groups participants into high and low performers exhibiting statistically significant differences across the four performance metrics. In particular, high performers exhibit superior limb coordination associated with a “diagonal gait” in which contralateral limbs move largely in-phase to produce faster crawl speeds and shorter crawl stride times. In contrast, low performers crawl at slower speeds with longer crawl stride times and less limb coordination. Beyond these conclusions, a major contribution of this study is a method for deploying wearable IMUs to study crawling in contextually relevant (i.e. non-laboratory) environments.     

Driving a musculoskeletal model with inertial and magnetic measurement units

We developed and evaluated a new kinematic driver for musculoskeletal models using ambulatory inertial and magnetic measurement units (IMMUs). The new driver uses the orientation estimates based on sensor fusion of each individual IMMU and benefits from two important properties of musculoskeletal models. First, these models contain more complex, anatomical, kinematic models than those currently used for sensor fusion of multiple IMMUs and are continuously improved. Second, they allow movement between segment and measured sensor. For three different tasks, the new IMMU driver, (optical) marker drivers and a combination of both were used to reconstruct the motion. Maximal root mean square (RMS) joint angle differences with respect to the silver standard (combined IMMU/marker drivers) were found for the hip joint; 4°, 2° and 5° during squat, gait and slideboard tasks for IMMU-driven reconstructions, compared with 6°, 5° and 5° for marker-driven reconstructions, respectively. The measured angular velocities corresponded best to the IMMU-driven reconstructions, with a maximal RMS difference of 66°/s, compared with 108°/s and 91°/s for marker-driven reconstructions and silver standard. However, large oscillations in global accelerations occurred during IMMU-driven reconstructions resulting in a maximal RMS difference with respect to measured acceleration of 23 m/s², compared with 9 m/s² for reconstructions that included marker drivers. The new driver facilitates direct implementation of IMMU-based orientation estimates in currently available biomechanical models. As such, it can help in the rapid expansion of biomechanical analysis based on outdoor measurements.     

Identification of key events in baseball hitting using inertial measurement units

Quantification of baseball hitting mechanics under game conditions help players to become successful batters and prevent injuries. Inertial measurement units (IMUs) can measure motion without any spatial restriction and are thus becoming a popular tool to investigate sports biomechanics. Biomechanical analysis of hitting requires the accurate detection of key events including “foot-off” while leaning back (F_Off), “foot-on” during forward swing (F_On), and ball impact. Ten male university baseball players hit a ball suspended on a T pole five times in kick-hitting and glide-hitting styles. Three IMUs were attached on mid-pelvis and on each hand to record acceleration and orientation data. The key events identified by the three IMUs were compared with those retrieved by an optical motion capture system with force platforms. The timings of the local peak acceleration of the pelvis in the direction of the pitcher that were recorded by the IMU closely matched those of F_Off and F_On events detected by the ground reaction force. Root mean square error (RMSE) between each measurement for the F_Off and F_On events were 0.024 and 0.031 s, respectively. The timing of the negative peak of acceleration in the proximal direction of the hands corresponded to the impact time determined by an optical motion capture system. RMSEs for the knob and barrel-side hand were 0.009 and 0.011 s, respectively. Our results demonstrate how IMUs can be useful for analyzing baseball hitting mechanics.     

Evaluating the validity and reliability of inertial measurement units for determining knee and trunk kinematics during athletic landing and cutting movements

Inertial Measurement Units (IMUs) are promising alternatives to laboratory-based motion capture methods in biomechanical assessment of athletic movements. The aim of this study was to investigate the validity of an IMU system for determining knee and trunk kinematics during landing and cutting tasks for clinical and research applications in sporting populations. Twenty-seven participants performed five cutting and landing tasks while being recorded using a gold-standard optoelectronic motion capture system and an IMU system. Intra-class coefficients, Pearson’s r, root-mean-square error (RMSE), bias, and Bland-Altman limits of agreements between the motion capture and IMU systems were quantified for knee and trunk sagittal- and frontal-plane range-of-motion (ROM) and peak angles. Our results indicate that IMU validity was task-, joint-, and plane-dependent. Based on good-to-excellent (ICC) correlation, reasonable accuracy (RMSE < 5°), bias within 2°, and limits of agreements within 10°, we recommend the use of this IMU system for knee sagittal-plane ROM estimations during cutting, trunk sagittal-plane peak angle estimation during the double-leg landing task, trunk sagittal-plane ROM estimation for almost all tasks, and trunk frontal-plane peak angle estimation for the right single-leg landing task. Due to poor comparisons with the optoelectronic system, we do not recommend this IMU system for knee frontal-plane kinematic estimations.     

Three-dimensional measurement of rearfoot motion during running

Excessive ranges of motion during running have been speculated to be connected to injuries to the lower extremities. Movement of the foot and lower leg has commonly been studied with two-dimensional techniques. However, differences in the alignment of the longitudinal axis of the foot with the camera axis will produce measurement errors for projected angles of the lower extremities. A three-dimensional approach would not have this limitation. The purpose of this study is to present a three-dimensional model for calculation of angles between lower leg and foot, lower leg and ground, and foot and ground, and to compare results from treadmill running derived from this model with results derived from a two-dimensional model for different alignment angles between foot axis and camera axis. A two camera Selspot system was used to obtain three-dimensional information on motion of the studied segments. It was found that several two-dimensional variables measured from a posterior view are very sensitive to the alignment angle between the foot and the camera axis. Some variables change as much as 1 degrees for every 2 degrees of change of the alignment angle. The large influence of rotations other than the measured one in two-dimensional measurements makes advisable the use of a three-dimensional model when studying motion between foot and lower leg during running.     

The influence of inertial sensor sampling frequency on the accuracy of measurement parameters in rearfoot running

Increasingly, inertial sensors are being used for running analyses. The aim of this study was to systematically investigate the influence of inertial sensor sampling frequencies (SF) on the accuracy of kinematic, spatio-temporal, and kinetic parameters. We hypothesized that running analyses at lower SF result in less signal information and therefore the inability to sufficiently interpret measurement data. Twenty-one subjects participated in this study. Rearfoot strikers ran on an indoor running track at a velocity of 3.5 ± 0.1 ms^?1. A uniaxial accelerometer was attached at the tibia and an inertial measurement unit was mounted at the heel of the right shoe. All sensors were synchronized at the start and data was measured with 1000 Hz (reference SF). Datasets were reduced to 500, 333, 250, 200, and 100 Hz in post-processing. The results of this study showed that a minimum SF of 500 Hz should be used to accurately measure kinetic parameters (e.g. peak heel acceleration). In contrast, stride length showed accurate results even at 333 Hz. 200 Hz were required to calculate parameters accurately for peak tibial acceleration, stride duration, and all kinematic measurements. The information from this study is necessary to correctly interpret measurement data of existing investigations and to plan future studies.     

The development and concurrent validity of a real-time algorithm for temporal gait analysis using inertial measurement units

The use of inertial measurement units (IMUs) for gait analysis has emerged as a tool for clinical applications. Shank gyroscope signals have been utilized to identify heel-strike and toe-off, which serve as the foundation for calculating temporal parameters of gait such as single and double limb support time. Recent publications have shown that toe-off occurs later than predicted by the dual minima method (DMM), which has been adopted as an IMU-based gait event detection algorithm. In this study, a real-time algorithm, Noise-Zero Crossing (NZC), was developed to accurately compute temporal gait parameters. Our objective was to determine the concurrent validity of temporal gait parameters derived from the NZC algorithm against parameters measured by an instrumented walkway. The accuracy and precision of temporal gait parameters derived using NZC were compared to those derived using the DMM. The results from Bland-Altman Analysis showed that the NZC algorithm had excellent agreement with the instrumented walkway for identifying the temporal gait parameters of Gait Cycle Time (GCT), Single Limb Support (SLS) time, and Double Limb Support (DLS) time. By utilizing the moment of zero shank angular velocity to identify toe-off, the NZC algorithm performed better than the DMM algorithm in measuring SLS and DLS times. Utilizing the NZC algorithm’s gait event detection preserves DLS time, which has significant clinical implications for pathologic gait assessment.     

Photographic measurement of pleural surface motion during lung oscillation

The regional pleural surface expansion of an excised dog lung was measured during high-frequency ventilation (HFV) using synchronized stroboscopic photography to stop lung motion at 20 evenly spaced intervals over a respiratory cycle during ventilation at 1 Hz with a volume of 100 ml, 15 Hz with 100 ml, or 30 Hz with 50 ml. The lungs were also photographed during quasi-static deflation. The pleural surface was marked with ink dots to form 84 approximately square figures. The side lengths and areas of each of the 84 "squares" were measured for each frame of each photo sequence. At 1 Hz and during the quasi-static deflation the lung ventilated nearly synchronously, although minor nonuniformities were noted on both small and large length scales. At 15 and 30 Hz, the lung expanded asynchronously and nonuniformly, with a 78% increase in surface expansion per 100 ml of tracheal tidal volume, as frequency was increased from 1 to 30 Hz. These nonuniformities in expansion suggest marked interregional airflow and elastic wave propagation in the parenchyma during HFV.     

Estimation of temporal parameters during sprint running using a trunk-mounted inertial measurement unit

The purpose of this study was to identify consistent features in the signals supplied by a single inertial measurement unit (IMU), or thereof derived, for the identification of foot-strike and foot-off instants of time and for the estimation of stance and stride duration during the maintenance phase of sprint running. Maximal sprint runs were performed on tartan tracks by five amateur and six elite athletes, and durations derived from the IMU data were validated using force platforms and a high-speed video camera, respectively, for the two groups. The IMU was positioned on the lower back trunk (L1 level) of each athlete. The magnitudes of the acceleration and angular velocity vectors measured by the IMU, as well as their wavelet-mediated first and second derivatives were computed, and features related to foot-strike and foot-off events sought. No consistent features were found on the acceleration signal or on its first and second derivatives. Conversely, the foot-strike and foot-off events could be identified from features exhibited by the second derivative of the angular velocity magnitude. An average absolute difference of 0.005 s was found between IMU and reference estimates, for both stance and stride duration and for both amateur and elite athletes. The 95% limits of agreement of this difference were less than 0.025 s. The results proved that a single, trunk-mounted IMU is suitable to estimate stance and stride duration during sprint running, providing the opportunity to collect information in the field, without constraining or limiting athletes' and coaches' activities.     

Stride length determination during overground running using a single foot-mounted inertial measurement unit

From a research perspective, detailed knowledge about stride length (SL) is important for coaches, clinicians and researchers because together with stride rate it determines the speed of locomotion. Moreover, individual SL vectors represent the integrated output of different biomechanical determinants and as such provide valuable insight into the control of running gait. In recent years, several studies have tried to estimate SL using body-mounted inertial measurement units (IMUs) and have reported promising results. However, many studies have used systems based on multiple sensors or have only focused on estimating SL for walking. Here we test the concurrent validity of a single foot-mounted, 9-degree of freedom IMU to estimate SL for running. We employed a running-specific, Kalman filter based zero-velocity update (ZUPT) algorithm to calculate individual SL vectors with the IMU and compared the results to SLs that were simultaneously recorded by a 6-camera 3D motion capture system. The results showed that the analytical procedures were able to successfully identify all strides that were recorded by the camera system and that excellent levels of absolute agreement (ICC(3,1) = 0.955) existed between the two methods. The findings demonstrate that individual SL vectors can be accurately estimated with a single foot-mounted IMU when running in a controlled laboratory setting.     

Study of cradle and pendulum motion for applications to health care

Hammocks and cradles have long been appreciated, but in a very limited way. Aside from being emotionally soothing the devices affect the skin and all deep body components. While structurally simple they are functionally quite sophisticated and could very well affect the pattern of health care across the board--acute, rehabilitation and home care--because of potential physiologic, economic and logistic advantages.     

Unity of measurement and motion

Issues addressed in H.H. Pattee's origin of life laboratory in the 1960s and their connection to the physics–evolution–language problematic are indicated. The problem of quantum measurement played a central role. The problem is herein examined in the light of the fluctuon model; in particular, as the model applies to gravity. The main conclusion is that measurement and motion are a unitary process. All accelerations are accompanied by a cycle involving the annihilation and creation of superpositions. Gravitational collapse is also a cyclic process in the fluctuon model. By a suitable transformation, it can be seen that interactions underlying superpositional collapse are the same as those operative in gravitational collapse. Implications for the origin of cellular life and the development of symbolic systems are considered.     

An effortless procedure to align the local frame of an inertial measurement unit to the local frame of another motion capture system

Inertial measurement units (IMUs) offer great opportunities to analyze segmental and joints kinematics. When combined with another motion capture system (MCS), for example, to validate new IMU-based applications or to develop mixed systems, it is necessary to align the local frame of the IMU sensors to the local frame of the MCS. Currently, all alignment methods use landmarks on the IMU's casing. Therefore, they can only be used with well-documented IMUs and they are prone to error when the IMU's casing is small. This study proposes an effortless procedure to align the local frame of any IMU to the local frame of any other MCS able to measure the orientation of its local frame. The general concept of this method is to derive the gyroscopic angles for both devices during an alignment movement, and then to use an optimization algorithm to calculate the alignment matrix between both local frames. The alignment movement consists of rotations around three more or less orthogonal axes and it can easily be performed by hands. To test the alignment procedure, an IMU and a magnetic marker were attached to a plate, and 20 alignment movements were recorded. The maximum errors of alignment (accuracy±precision) were 1.02°±0.32° and simulations showed that the method was robust against noise that typically affect IMUs. In conclusion, this study describes an efficient alignment procedure that is quick and easy to perform, and that does not require any alignment device or any knowledge about the IMU casing.