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 degrees 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 degrees and 11.7 degrees depending on the length and type of pendulum swing. The maximum orientation error was greater than 30 degrees , 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 degrees and 1.3 degrees . 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 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.     

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.     

A novel method for assessing the 3-D orientation accuracy of inertial/magnetic sensors

A novel method for assessing the accuracy of inertial/magnetic sensors is presented. The method, referred to as the “residual matrix” method, is advantageous because it decouples the sensor's error with respect to Earth's gravity vector (attitude residual error: pitch and roll) from the sensor's error with respect to magnetic north (heading residual error), while remaining insensitive to singularity problems when the second Euler rotation is close to ±90°. As a demonstration, the accuracy of an inertial/magnetic sensor mounted to a participant's forearm was evaluated during a reaching task in a laboratory. Sensor orientation was measured internally (by the inertial/magnetic sensor) and externally using an optoelectronic measurement system with a marker cluster rigidly attached to the sensor's enclosure. Roll, pitch and heading residuals were calculated using the proposed novel method, as well as using a common orientation assessment method where the residuals are defined as the difference between the Euler angles measured by the inertial sensor and those measured by the optoelectronic system. Using the proposed residual matrix method, the roll and pitch residuals remained less than 1° and, as expected, no statistically significant difference between these two measures of attitude accuracy was found; the heading residuals were significantly larger than the attitude residuals but remained below 2°. Using the direct Euler angle comparison method, the residuals were in general larger due to singularity issues, and the expected significant difference between inertial/magnetic sensor attitude and heading accuracy was not present.     

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.     

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.     

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.     

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.     

Measurement of stride parameters using a wearable GPS and inertial measurement unit

Both GPS and inertial measurement units (IMUs) have been extensively used in biomechanical studies. Expensive high accuracy GPS units can provide information about intrastride speed and position, but their application is limited by their size and cost. Single and double integration of acceleration from IMU provides information about short-term fluctuations in speed and position, but suffers from integration error over a longer period of time. The integration of GPS and IMU has been widely used in large and expensive units designed for survey and vehicle navigation. Here we propose a data fusion scheme, which is a Kalman filter based complementary filter and enhances the frequency response of the GPS and IMU used alone. We also report the design of a small (28 g) low cost GPS/IMU unit. Its accuracy after post-processing with the proposed data fusion scheme for determining average speed and intrastride variation was compared to a traditional high cost survey GPS. The low cost unit achieved an accuracy of 0.15 ms⁻¹ (s.d.) for horizontal speed in cycling and human running across a speed range of 3–10 ms⁻¹. The stride frequency and vertical displacement calculated based on measurements from the low cost GPS/IMU units had an s.d. of 0.08 Hz and 0.02 m respectively, compared to measurements from high performance OEM4 GPS units.     

Validation of magneto-inertial measuring units for measuring hip joint angles

Camera-based motion capture systems are the current gold standard for motion analysis. However, the use of wireless inertial sensor-based systems is increasing in popularity, largely due to convenient portability. The purpose of this study was to validate the use of wireless inertial sensors for measuring hip joint motion with a functional calibration requiring only one motion (walking) and neutral standing. Data were concurrently collected using a 10-camera motion capture system and a wireless inertial sensor-based system. Hip joint angles were measured for 10 participants during walking, jumping jack, and bilateral squat tasks and for a subset (n = 5) a jump turn task. Camera-based system hip joint angles were calculated from retro-reflective marker positions and sensor-based system angles were calculated in MATLAB using the sensor output quaternions. Most hip joint angles measured with the sensor-based system were within 6° of angles measured with the camera motion capture system. Accurate measurement of motion outside of a laboratory setting has broad implications for diagnosing movement abnormalities, monitoring sports performance, and assessing rehabilitation progress.     

Static accuracy analysis of Vicon T40s motion capture cameras arranged externally for motion capture in constrained aquatic environments

While the capabilities of land-based motion capture systems in biomechanical applications have been previously reported, the possibility of using motion tracking systems externally to reconstruct markers submerged inside an aquatic environment has been under explored. This study assesses the ability of a motion capture system (Vicon T40s) arranged externally to track a retro-reflective marker inside a glass tank filled with water and without water. The reflective tape used for marker creation in this study was of Safety of Life at Sea (SOLAS) grade as the conventional marker loses its reflective properties when submerged. The overall trueness calculated based on the mean marker distance errors, varied between 0.257 mm and 0.290 mm in different mediums (air, glass and water). The overall precision calculated based on mean standard deviation of mean marker distances at different locations varied between 0.046 mm and 0.360 mm in different mediums. Our results suggest, that there is no significant influence of the presence of water on the overall static accuracy of the marker center distances when markers were made of SOLAS grade reflective tape. Using optical motion tracking systems for evaluating locomotion in aquatic environment can help to better understand the effects of aquatic therapy in clinical rehabilitation, especially in scenarios that involve equipment, such as an underwater treadmill which generally have constrained capture volumes for motion capture.     

Inertial motion capture in conjunction with an artificial neural network can differentiate the gait patterns of hemiparetic stroke patients compared with able-bodied counterparts

Clinical gait analysis has proven to reduce uncertainties in selecting the appropriate quantity and type of treatment for patients with neuromuscular disorders. However, gait analysis as a clinical tool is under-utilised due to the limitations and cost of acquiring and managing data. To overcome these obstacles, inertial motion capture (IMC) recently emerged to counter the limitations attributed to other methods. This paper investigates the use of IMC for training and testing a back-propagation artificial neural network (ANN) for the purpose of distinguishing between hemiparetic stroke and able-bodied ambulation. Routine gait analysis was performed on 30 able-bodied control subjects and 28 hemiparetic stroke patients using an IMC system. An ANN was optimised to classify the two groups, achieving a repeatable network accuracy of 99.4%. It is concluded that an IMC system and appropriate computer methods may be useful for the planning and monitoring of gait rehabilitation therapy of stroke victims.     

Optimal inertial sensor location for ambulatory measurement of trunk inclination

Trunk inclination (TI) is used often to quantify back loading in ergonomic workplace evaluation. The aim of the present study was to determine whether TI can be obtained using a single inertial sensor (IS) on the back, and to determine the optimal IS location on the back for the estimation of TI. Gold standard TI, the angle between the vertical and the line connecting the L5/S1 joint and the trunk centre of mass, was measured using an optoelectronic system. Ten subjects performed experimental trials, each consisting of a symmetric and an asymmetric lifting task, and of a left–right lateral flexion movement. Trials were repeated and, in between trials, the IS was shifted in small steps from a location on the thorax towards a location on the sacrum. Optimal IS location was defined as the IS location with minimum root-mean-square (RMS) error between the gold standard TI and the IS TI. Averaged over subjects, the optimal IS location for symmetric and asymmetric lifting was at about 25% of the distance from the midpoint between the posterior superior iliac spines (MPSIS) to the C7 spinous process. The RMS error at this location, averaged over subjects, was 4.6±2.9°. For the left–right lateral flexion task, the optimal IS location was at about 30% of the MPSIS to C7 distance. Because in most activities of daily living, pure lateral flexion does not occur often, it is recommended place the IS at 25% of the distance from the MPSIS to C7.     

Accuracy map of an optical motion capture system with 42 or 21 cameras in a large measurement volume

Optical motion capture is commonly used in biomechanics to measure human kinematics. However, no studies have yet examined the accuracy of optical motion capture in a large capture volume (>100 m³), or how accuracy varies from the center to the extreme edges of the capture volume. This study measured the dynamic 3D errors of an optical motion capture system composed of 42 OptiTrack Prime 41 cameras (capture volume of 135 m³) by comparing the motion of a single marker to the motion reported by a ThorLabs linear motion stage. After spline interpolating the data, it was found that 97% of the capture area had error below 200 μm. When the same analysis was performed using only half (21) of the cameras, 91% of the capture area was below 200 μm of error. The only locations that exceeded this threshold were at the extreme edges of the capture area, and no location had a mean error exceeding 1 mm. When measuring human kinematics with skin-mounted markers, uncertainty of marker placement relative to underlying skeletal features and soft tissue artifact produce errors that are orders of magnitude larger than the errors attributed to the camera system itself. Therefore, the accuracy of this OptiTrack optical motion capture system was found to be more than sufficient for measuring full-body human kinematics with skin-mounted markers in a large capture volume (>100 m³).     

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.     

Verification of accuracy and validity of gait phase detection system using motion sensors for applying walking assistive FES

In this study, we have analysed heel strike (HS) and toe off (TO) of normal individuals and hemiplegic patients, taking advantage of output curves acquired from various sensors, and verified the validity of sensor detection methods and their effectiveness when they were used for hemiplegic gaits. Gait phase detections using three different motion sensors were valid, since they all had reliabilities more than 95%, when compared with foot velocity algorithm. Results showed that the tilt sensor and the gyrosensor could detect gait phase more accurately in normal individuals. Vertical acceleration could detect HS most accurately in hemiplegic patient group A. The gyrosensor could detect HS and TO most accurately in hemiplegic patient groups A and B. The detection of TO from all sensor signals was valid in both the patient groups A and B. However, the vertical acceleration detected HS validly in patient group A and the gyrosensor detected HS validly in patient group B.     

Functional limits of agreement applied as a novel method comparison tool for accuracy and precision of inertial measurement unit derived displacement of the distal limb in horses

Over ground motion analysis in horses is limited by a small number of strides and restraints of the indoor gait laboratory. Inertial measurement units (IMUs) are transforming the knowledge of human motion and objective clinical assessment through the opportunity to obtain clinically relevant data under various conditions. When using IMUs on the limbs of horses to determine local position estimates, conditions with high dynamic range of both accelerations and rotational velocities prove particularly challenging. Here we apply traditional method agreement and suggest a novel method of functional data analysis to compare motion capture with IMUs placed over the fetlock joint in seven horses. We demonstrate acceptable accuracy and precision at less than or equal to 5% of the range of motion for detection of distal limb mounted cranio-caudal and vertical position. We do not recommend the use of the latero-medial position estimate of the distal metacarpus/metatarsus during walk where the average error is 10% and the maximum error 111% of the range. We also show that functional data analysis and functional limits of agreement are sensitive methods for comparison of cyclical data and could be applied to differentiate changes in gait for individuals across time and conditions.     

Evaluation of the kinetic energy of the torso by magneto-inertial measurement unit during the sit-to-stand movement

Sit-to-stand tests are used in geriatrics as a qualitative issue in order to evaluate motor control and stability. In terms of measured indicators, it is traditionally the duration of the task that is reported, however it appears that the use of the kinetic energy as a new quantitative criterion allows getting a better understanding of musculoskeletal deficits of elderly subjects. The aim of this study was to determine the feasibility to obtain the measure of kinetic energy using magneto-inertial measurement units (MIMU) during sit-to-stand movements at various paces. 26 healthy subjects contributed to this investigation. Measured results were compared to a marker-based motion capture using the correlation coefficient and the normalized root mean square error (nRMSE). nRMSE were below 10% and correlation coefficients were over 0.97. In addition, errors on the mean kinetic energy were also investigated using Bland-Altman 95% limits of agreement (0.63 J–0.77 J), RMSE (0.29 J–0.38 J) and correlation coefficient (0.96–0.98). The results obtained highlighted that the method based on MIMU data could be an alternative to optoelectronic data acquisition to assess the kinetic energy of the torso during the sit-to-stand test, suggesting this method as being a promising alternative to determine kinetic energy during the sit-to-stand movement.