Real-time motion tracking of kinematic chains is a key prerequisite in the control of, e.g., robotic actuators and autonomous vehicles and also has numerous biomechanical applications. In recent years, it has been shown that, by placing inertial sensors on segments that are connected by rotational joints, the motion of that kinematic chain can be tracked accurately. These methods specifically avoid using magnetometer measurements, which are known to be unreliable since the magnetic field at the different sensor locations is typically different. They rely on the assumption that the motion of the kinematic chain is sufficiently rich to assure observability of the relative pose. However, a formal investigation of this crucial requirement has not yet been presented, and no specific conditions for observability have so far been given. In this work, we present an observability analysis and show that the relative pose of the body segments is indeed observable under a very mild condition on the motion. We support our results by simulation studies, in which we employ a state estimator that neither uses magnetometer measurements nor additional sensors and does not impose assumptions on the accelerometer to measure only the direction of gravity, nor on the range of motion or degrees of freedom of the joints. We investigate the effect of the amount of excitation and of stationary periods in the data on the accuracy of the estimates. We then use experimental data from two mechanical joints as well as from a human gait experiment to validate the observability criterion in practice and to show that small excitation levels are sufficient for obtaining accurate estimates even in the presence of time periods during which the motion is not observable.

Inertial measurement units are commonly used in a growing number of application fields to track or capture motions of kinematic chains, such as human limbs, exoskeletons or robotic actuators. A major challenge is the presence of magnetic disturbances that results in unreliable magnetometer readings. Recent research revealed that this problem can be overcome by exploitation of kinematic constraints. While typically each segment of the kinematic chain is equipped with an IMU, a novel approach called sparse inertial motion tracking aims at inferring the complete motion states from measurements of a reduced set of sensors. In the present contribution, we combine the magnetometer-free and the sparse approach for real-time motion tracking of double-hinge joint systems with non-parallel joint axes. Analyzing the observability of the system, we find a condition which assures that the relative orientations between all segments are uniquely determined by a kinematic constraint, which contains only the gyroscope readings. Furthermore, we propose a moving-horizon estimator and validate it in a simulation study of four movements, which differ by their degrees of excitation. The results of this study confirm the theoretical conjectures and demonstrate that magnetometer-free sparse inertial real-time motion tracking is feasible under precise and simple excitation conditions.

A major shortcoming in kinematic estimation using skin-attached inertial sensors is the alignment of sensor-embedded and segment-embedded coordinate systems. Only a correct alignment results in clinically relevant kinematics. Model-based inertial-sensor-to-bone alignment methods relate inertial sensor measurements with a model of the joint. Therefore, they do not rely on properly executed calibration movements or a correct sensor placement. However, it is unknown how accurate such model-based methods align the sensor axes and the underlying segment-embedded axes, as defined by clinical definitions. Also, validation of the alignment models is challenging, since an optical motion capture ground truth can be prone to disturbances from soft tissue movement, orientation estimation and manual palpation errors. We present an anatomical tibiofemoral ground truth on an unloaded cadaveric measurement set-up that intrinsically overcomes these disturbances. Additionally, we validate existing model-based alignment strategies. Modeling the degrees of freedom leads to the identification of rotation axes. However, there is no reason why these axes would align with the segment-embedded axes. Relative inertial-sensor orientation information and rich arbitrary movements showed to aid in identifying the underlying joint axes. The first dominant sagittal rotation axis aligned sufficiently well with the underlying segment-embedded reference. The estimated axes that relate to secondary kinematics tend to deviate from the underlying segment-embedded axes as much as their expected range of motion around the axes. In order to interpret the secondary kinematics, the alignment model should more closely match the biomechanics of the joint.

Skin-attached inertial sensors are increasingly used for kinematic analysis. However, their ability to measure outside-lab can only be exploited after correctly aligning the sensor axes with the underlying anatomical axes. Emerging model-based inertial-sensor-to-bone alignment methods relate inertial measurements with a model of the joint to overcome calibration movements and sensor placement assumptions. It is unclear how good such alignment methods can identify the anatomical axes. Any misalignment results in kinematic cross-talk errors, which makes model validation and the interpretation of the resulting kinematics measurements challenging. This study provides an anatomically correct ground-truth reference dataset from dynamic motions on a cadaver. In contrast with existing references, this enables a true model evaluation that overcomes influences from soft-tissue artifacts, orientation and manual palpation errors. This dataset comprises extensive dynamic movements that are recorded with multimodal measurements including trajectories of optical and virtual (via computed tomography) anatomical markers, reference kinematics, inertial measurements, transformation matrices and visualization tools. The dataset can be used either as a ground-truth reference or to advance research in inertial-sensor-to-bone-alignment.

Inertial motion capture relies on accurate sensor-to-segment calibration. When two segments are connected by a hinge joint, for example in human knee or finger joints as well as in many robotic limbs, then the joint axis vector must be identified in the intrinsic sensor coordinate systems. Methods for estimating the joint axis using accelerations and angular rates of arbitrary motion have been proposed, but the user must perform sufficiently informative motion in a predefined initial time window to accomplish complete identifiability. Another drawback of state of the art methods is that the user has no way of knowing if the calibration was successful or not. To achieve plug-and-play calibration, it is therefore important that 1) sufficiently informative data can be extracted even if large portions of the data set consist of non-informative motions, and 2) the user knows when the calibration has reached a sufficient level of accuracy. In the current paper, we propose a novel method that achieves both of these goals. The method combines acceleration- and angular rate information and finds a globally optimal estimate of the joint axis. Methods for sample selection, that overcome the limitation of a dedicated initial calibration time window, are proposed. The sample selection allows estimation to be performed using only a small subset of samples from a larger data set as it deselects non-informative and redundant measurements. Finally, an uncertainty quantification method that assures validity of the estimated joint axis parameters, is proposed. Experimental validation of the method is provided using a mechanical joint performing a large range of motions. Angular errors in the order of 2 ∘ were achieved using 125-1000 selected samples. The proposed method is the first truly plug-and-play method that overcome the need for a specific calibration phase and, regardless of the user's motions, it provides an accurate estimate of the joint axis as soon as possible.

This editorial provides a concise introduction to the methods and applications of inertial sensors. We briefly describe the main characteristics of inertial sensors and highlight the broad range of applications as well as the methodological challenges. Finally, for the reader’s guidance, we give a succinct overview of the papers included in this special issue.

In inertial motion tracking of kinematic chains, inertial measurement units (IMUs) are attached to each segment in order to track their motion in three-dimensional space. Determining the relations between the functional axes of a joint and the local coordinate system of the attached sensor is a crucial requirement. For the case of hinge joints, methods have been proposed that exploit kinematic constraints to automatically identify the local hinge joint axis coordinates from the raw data of almost arbitrary motions. However, to current date, it remains unclear which joint motions are sufficiently rich for the joint axis to become identifiable. We consider a commonly used gyroscope-based kinematic constraint and present a novel accelerometer-based kinematic constraint. We study conditions of identifiability by analyzing the nonlinear constraint equations and present practical conditions for the minimum excitation that is required. Among other results, we prove that planar motions and subsequent motions of both ends of the joint are sufficient as long as the joint axis does not remain perfectly horizontal. Theoretical results are validated in experimental studies of a human upper limb wearing an exoskeleton. Despite the typical IMU-related measurement inaccuracies and although the human elbow joint is only an approximate hinge joint, the cost function defined by the kinematic constraints exhibits a distinct global minimum at the true joint axis coordinates if the motion fulfills the proposed requirements.

Low back pain (LBP) is a leading cause of activity limitation. Objective assessment of the spinal motion plays a key role in diagnosis and treatment of LBP. We propose a method that facilitates clinical assessment of lower back motions by means of a wireless inertial sensor network. The sensor units are attached to the right and left side of the lumbar region, the pelvis and the thighs, respectively. Since magnetometers are known to be unreliable in indoor environments, we use only 3D accelerometer and 3D gyroscope readings. Compensation of integration drift in the horizontal plane is achieved by estimating the gyroscope biases from automatically detected initial rest phases. For the estimation of sensor orientations, both a smoothing algorithm and a filtering algorithm are presented. From these orientations, we determine three-dimensional joint angles between the thighs and the pelvis and between the pelvis and the lumbar region. We compare the orientations and joint angles to measurements of an optical motion tracking system that tracks each skin-mounted sensor by means of reflective markers. Eight subjects perform a neutral initial pose, then flexion/extension, lateral flexion, and rotation of the trunk. The root mean square deviation between inertial and optical angles is about one degree for angles in the frontal and sagittal plane and about two degrees for angles in the transverse plane (both values averaged over all trials). We choose five features that characterize the initial pose and the three motions. Interindividual differences of all features are found to be clearly larger than the observed measurement deviations. These results indicate that the proposed inertial sensor-based method is a promising tool for lower back motion assessment.