Kinematic analysis of over-determinate biomechanical systems

In this paper, we introduce a new general method for kinematic analysis of rigid multi body systems subject to holonomic constraints. The method extends the standard analysis of kinematically determinate rigid multi body systems to the over-determinate case. This is accomplished by introducing a constrained optimisation problem with the objective function given as a function of the set of system equations that are allowed to be violated while the remaining equations define the feasible set.

We show that exact velocity and acceleration analysis can also be performed by solving linear sets of equations, originating from differentiation of the Karush–Kuhn–Tucker optimality conditions.

The method is applied to the analysis of an 18 degrees-of-freedom gait model where the kinematical drivers are prescribed with data from a motion capture experiment.

The results show that significant differences are obtained between applying standard kinematic analysis or minimising the least-square errors on the two fully equivalent 3D gait models with only the way the experimental data is processed being different.     

Kinematic analysis of over-determinate biomechanical systems

In this paper, we introduce a new general method for kinematic analysis of rigid multi body systems subject to holonomic constraints. The method extends the standard analysis of kinematically determinate rigid multi body systems to the over-determinate case. This is accomplished by introducing a constrained optimisation problem with the objective function given as a function of the set of system equations that are allowed to be violated while the remaining equations define the feasible set. We show that exact velocity and acceleration analysis can also be performed by solving linear sets of equations, originating from differentiation of the Karush-Kuhn-Tucker optimality conditions. The method is applied to the analysis of an 18 degrees-of-freedom gait model where the kinematical drivers are prescribed with data from a motion capture experiment. The results show that significant differences are obtained between applying standard kinematic analysis or minimising the least-square errors on the two fully equivalent 3D gait models with only the way the experimental data is processed being different.     

Quantitative analysis of upper limbs during gait: a marker set protocol

Purpose: to develop a marker set for simultaneously assessing upper and lower limb biomechanics during gait.Methods: 24 healthy young subjects (mean age: 23.80 years) were assessed quantitatively using an optoelectronic system, two force platform and a video system. Passive markers were positioned according to the proposed marker set which enables acquiring the upper and lower limb movement simultaneously during Gait Analysis. In addition to the traditional parameters obtained from Gait Analysis, the shoulder and elbow angles were computed from markers coordinates of upper limbs; then, some significant parameters were identified and calculated. From shoulder and elbow position, angles, angular velocities, angular acceleration, moments, and powers were calculated for shoulder and elbow joints. Results: Kinematic and kinetic data were obtained in the three planes (sagittal, frontal, and transversal) for the shoulder and in the sagittal plane for the elbow. Normative ranges were obtained for these parameters from data of healthy participants. Conclusions: The proposed experimental set-up enables simultaneous assessment of upper and lower limb movement during gait. Thus, no further trials are required in addition to those acquired during standard gait analysis in order to assess upper limb motion, which also makes the experimental set-up feasible for clinical applications.     

Motion Control in Saccade and Smooth Pursuit for Bionic Eye Based on Three-dimensional Coordinates

Saccade and smooth pursuit are two important functions of human eye.In order to enable bionic eye to imitate the two functions,a control method that implements saccade and smooth pursuit based on the three-dimensional coordinates of target is proposed.An optimal observation position is defined for bionic eye based on three-dimensional coordinates.A kind of motion planning method with high accuracy is developed.The motion parameters of stepper motor consisting of angle acceleration and turning time are computed according to the position deviation,the target's angular velocity and the stepper motor's current angular velocity in motion planning.The motors are controlled with the motion parameters moving to given position with desired angular velocity in schedule time.The experimental results show that the bionic eye can move to optimal observation positions in 0.6 s from initial location and the accuracy of 3D coordinates is improved.In addition,the bionic eye can track a target within the error of less than 20 pixels based on three-dimensional coordinates.It is verified that saccade and smooth pursuit of bionic eye based on three-dimensional coordinates are feasible.     

A sensitivity analysis method for the body segment inertial parameters based on ground reaction and joint moment regressor matrices

This paper presents a method allowing a simple and efficient sensitivity analysis of dynamics parameters of complex whole-body human model. The proposed method is based on the ground reaction and joint moment regressor matrices, developed initially in robotics system identification theory, and involved in the equations of motion of the human body. The regressor matrices are linear relatively to the segment inertial parameters allowing us to use simple sensitivity analysis methods. The sensitivity analysis method was applied over gait dynamics and kinematics data of nine subjects and with a 15 segments 3D model of the locomotor apparatus. According to the proposed sensitivity indices, 76 segments inertial parameters out the 150 of the mechanical model were considered as not influent for gait. The main findings were that the segment masses were influent and that, at the exception of the trunk, moment of inertia were not influent for the computation of the ground reaction forces and moments and the joint moments. The same method also shows numerically that at least 90% of the lower-limb joint moments during the stance phase can be estimated only from a force-plate and kinematics data without knowing any of the segment inertial parameters.     

Statistical method for prediction of gait kinematics with Gaussian process regression

We propose a novel methodology for predicting human gait pattern kinematics based on a statistical and stochastic approach using a method called Gaussian process regression (GPR). We selected 14 body parameters that significantly affect the gait pattern and 14 joint motions that represent gait kinematics. The body parameter and gait kinematics data were recorded from 113 subjects by anthropometric measurements and a motion capture system. We generated a regression model with GPR for gait pattern prediction and built a stochastic function mapping from body parameters to gait kinematics based on the database and GPR, and validated the model with a cross validation method. The function can not only produce trajectories for the joint motions associated with gait kinematics, but can also estimate the associated uncertainties. Our approach results in a novel, low-cost and subject-specific method for predicting gait kinematics with only the subject's body parameters as the necessary input, and also enables a comprehensive understanding of the correlation and uncertainty between body parameters and gait kinematics.     

Design of a marker-based human motion tracking system

In this paper a complete design of a high speed optical motion analyzer system has been described. The main core of the image processing unit has been implemented by the differential algorithm procedure. Some intelligent and conservative procedures that facilitate the search algorithm have also been proposed and implemented for the processing of human motions. Moreover, an optimized modified direct linear transformation (MDLT) method has been used to reconstruct 3D markers positions which are used for deriving kinematic characteristics of the motion. Consequently, a set of complete tests using some simple mechanical devices were conducted to verify the system outputs. Considering the system verification for human motion analysis, we used the system for gait analysis and the results including joint angles showed good compatibility with other investigations. Furthermore, a sport application example of the system has been quantitatively presented and discussed for Iranian National Karate-kas. The low computational cost, the high precision in detecting and reconstructing marker position with 2.39 mm error, and the capability of capturing from any number of cameras to increase the domain of operation of the subject, has made the proposed method a reliable approach for real-time human motion analysis. No special environment limitation, portability, low cost hardware and built in units for simulations and kinematic analysis are the other significant specifications of this system.     

Clinical Assessment of Spatiotemporal Gait Parameters in Patients and Older Adults

Spatial and temporal characteristics of human walking are frequently evaluated to identify possible gait impairments, mainly in orthopedic and neurological patients^1-4, but also in healthy older adults^5,6. The quantitative gait analysis described in this protocol is performed with a recently-introduced photoelectric system (see Materials table) which has the potential to be used in the clinic because it is portable, easy to set up (no subject preparation is required before a test), and does not require maintenance and sensor calibration. The photoelectric system consists of series of high-density floor-based photoelectric cells with light-emitting and light-receiving diodes that are placed parallel to each other to create a corridor, and are oriented perpendicular to the line of progression⁷. The system simply detects interruptions in light signal, for instance due to the presence of feet within the recording area. Temporal gait parameters and 1D spatial coordinates of consecutive steps are subsequently calculated to provide common gait parameters such as step length, single limb support and walking velocity⁸, whose validity against a criterion instrument has recently been demonstrated^7,9. The measurement procedures are very straightforward; a single patient can be tested in less than 5 min and a comprehensive report can be generated in less than 1 min.     

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.     

An Experimental Analysis of Overcoming Obstacle in Human Walking

In this paper, an experimental analysis of overcoming obstacle in human walking is carried out by means of a motion capture system. In the experiment, the lower body of an adult human is divided into seven segments, and three markers are pasted to each segment with the aim to obtain moving trajectory and to calculate joint variation during walking. Moreover, kinematic data in terms of displacement, velocity and acceleration are acquired as well. In addition, ground reaction forces are measured using force sensors. Based on the experimental results, features of overcoming obstacle in human walking are ana- lyzed. Experimental results show that the reason which leads to smooth walking can be identified as that the human has slight movement in the vertical direction during walking; the reason that human locomotion uses gravity effectively can be identified as that feet rotate around the toe joints during toe-off phase aiming at using gravitational potential energy to provide propulsion for swing phase. Furthermore, both normal walking gait and obstacle overcoming gait are characterized in a form that can provide necessary knowledge and useful databases for the implementation of motion planning and gait planning towards overcoming obstacle for humanoid robots.     

Effect of walking speed and severity of hip osteoarthritis on gait variability

Gait analysis in orthopaedic and neurological examinations is important; however, few studies assess gait variability at different walking speeds in patients with varying degrees of hip osteoarthritis. We aimed to clarify (1) how different controlled speeds and (2) various severities of hip osteoarthritis influence gait variability. Gait variability was described by the standard deviation (SD) of the spatial–temporal and mean standard deviation (MeanSD) of angular parameters. The spatial positions of the anatomical points for calculating gait parameters were determined in 20 healthy elderly controls and 20 patients with moderate and 20 patients with severe hip osteoarthritis with a zebris CMS-HS ultrasound-based motion analysis system at three walking speeds. The SD of the spatial–temporal and MeanSD of angular parameters of gait, which together describe gait variability, significantly depended on speed and osteoarthritis severity. The lowest variability in the gait was found near the self-selected walking speeds. Hip joint degeneration significantly worsened variability on the affected side, with non-affected joints and the pelvis compensating by increasing flexibility and adapting to step-by-step motions. Particular attention must be paid to improving gait stability and the reliability of limb movements in the presence of and increasing severity of osteoarthritis.     

In-vivo measurement of dynamic joint motion using high speed biplane radiography and CT: application to canine ACL deficiency

Dynamic assessment of three-dimensional (3D) skeletal kinematics is essential for understanding normal joint function as well as the effects of injury or disease. This paper presents a novel technique for measuring in-vivo skeletal kinematics that combines data collected from high-speed biplane radiography and static computed tomography (CT). The goals of the present study were to demonstrate that highly precise measurements can be obtained during dynamic movement studies employing high frame-rate biplane video-radiography, to develop a method for expressing joint kinematics in an anatomically relevant coordinate system and to demonstrate the application of this technique by calculating canine tibio-femoral kinematics during dynamic motion. The method consists of four components: the generation and acquisition of high frame rate biplane radiographs, identification and 3D tracking of implanted bone markers, CT-based coordinate system determination, and kinematic analysis routines for determining joint motion in anatomically based coordinates. Results from dynamic tracking of markers inserted in a phantom object showed the system bias was insignificant (-0.02 mm). The average precision in tracking implanted markers in-vivo was 0.064 mm for the distance between markers and 0.31 degree for the angles between markers. Across-trial standard deviations for tibio-femoral translations were similar for all three motion directions, averaging 0.14 mm (range 0.08 to 0.20 mm). Variability in tibio-femoral rotations was more dependent on rotation axis, with across-trial standard deviations averaging 1.71 degrees for flexion/extension, 0.90 degree for internal/external rotation, and 0.40 degree for varus/valgus rotation. Advantages of this technique over traditional motion analysis methods include the elimination of skin motion artifacts, improved tracking precision and the ability to present results in a consistent anatomical reference frame.     

Validity of a novel method to measure vertical oscillation during running using a depth camera

Recent advancements in low-cost depth cameras may provide a clinically accessible alternative to conventional three-dimensional (3D) multi-camera motion capture systems for gait analysis. However, there remains a lack of information on the validity of clinically relevant running gait parameters such as vertical oscillation (VO). The purpose of this study was to assess the validity of measures of VO during running gait using raw depth data, in comparison to a 3D multi-camera motion capture system. Sixteen healthy adults ran on a treadmill at a standard speed of 2.7 m/s. The VO of their running gait was simultaneously collected from raw depth data (Microsoft Kinect v2) and 3D marker data (Vicon multi-camera motion capture system). The agreement between the VO measures obtained from the two systems was assessed using a Bland-Altman plot with 95% limits of agreement (LOA), a Pearson’s correlation coefficient (r), and a Lin’s concordance correlation coefficient (r_c). The depth data from the Kinect v2 demonstrated excellent results across all measures of validity (r = 0.97; r_c = 0.97; 95% LOA = −8.0 mm – 8.7 mm), with an average absolute error and percent error of 3.7 (2.1) mm and 4.0 (2.0)%, respectively. The findings of this study have demonstrated the ability of a low cost depth camera and a novel tracking method to accurately measure VO in running gait.     

Spatial reconstruction of the human motion based on images of a single camera

The inverse dynamic analysis procedures used in the study of the human gait require that the kinematics of the supporting biomechanical model is known beforehand. The first step to obtain the kinematic data is the reconstruction of human spatial motion, i.e., the evaluation of the anatomic points positions that enables to uniquely define the position of all anatomical segments. In photogrammetry, the projection of each anatomical point is described by two linear equations relating its three spatial coordinates with the two coordinates of the projected point. The need for the image of two cameras arises from the fact that three equations are necessary to find the original spatial position of the anatomical point. It is shown here that the kinematic constraint equations associated with a biomechanical model can be used as the extra set of equations required for the reconstruction process, instead of the equations associated with the second camera. With this methodology, the system of equations arising from the point projections and biomechanical model kinematic constraints are solved simultaneously. Since the system of equations has multiple solutions for each image, a strategy based on the minimization of the cost function associated to the smoothness of the reconstructed motion is devised, leading to an automated computer procedure enabling a unique reconstruction.     

Comparison of two normative paediatric gait databases

The availability of age-matched normative data is an essential component of clinical gait analyses. Comparison of normative gait databases is difficult due to the high-dimensionality and temporal nature of the various gait waveforms. The purpose of this study was to provide a method of comparing the sagittal joint angle data between two normative databases. We compared a modern gait database to the historical San Diego database using statistical classifiers developed by Tingley et al. (2002). Gait data were recorded from 60 children aged 1–13 years. A six-camera Vicon 512 motion analysis system and two force plates were utilized to obtain temporal-spatial, kinematic, and kinetic parameters during walking. Differences between the two normative data sets were explored using the classifier index scores, and the mean and covariance structure of the joint angle data from each lab. Significant differences in sagittal angle data between the two databases were identified and attributed to technological advances and data processing techniques (data smoothing, sampling, and joint angle approximations). This work provides a simple method of database comparison using trainable statistical classifiers.     

Two-dimensional video-based analysis of human gait using pose estimation

Human gait analysis is often conducted in clinical and basic research, but many common approaches (e.g., three-dimensional motion capture, wearables) are expensive, immobile, data-limited, and require expertise. Recent advances in video-based pose estimation suggest potential for gait analysis using two-dimensional video collected from readily accessible devices (e.g., smartphones). To date, several studies have extracted features of human gait using markerless pose estimation. However, we currently lack evaluation of video-based approaches using a dataset of human gait for a wide range of gait parameters on a stride-by-stride basis and a workflow for performing gait analysis from video. Here, we compared spatiotemporal and sagittal kinematic gait parameters measured with OpenPose (open-source video-based human pose estimation) against simultaneously recorded three-dimensional motion capture from overground walking of healthy adults. When assessing all individual steps in the walking bouts, we observed mean absolute errors between motion capture and OpenPose of 0.02 s for temporal gait parameters (i.e., step time, stance time, swing time and double support time) and 0.049 m for step lengths. Accuracy improved when spatiotemporal gait parameters were calculated as individual participant mean values: mean absolute error was 0.01 s for temporal gait parameters and 0.018 m for step lengths. The greatest difference in gait speed between motion capture and OpenPose was less than 0.10 m s⁻¹. Mean absolute error of sagittal plane hip, knee and ankle angles between motion capture and OpenPose were 4.0°, 5.6° and 7.4°. Our analysis workflow is freely available, involves minimal user input, and does not require prior gait analysis expertise. Finally, we offer suggestions and considerations for future applications of pose estimation for human gait analysis.     

Design Study of a Cable-based Gait Training Machine

This paper deals with a design approach of a gait training machine based on a quantitative gait analysis.The proposed training machine is composed of a body weight support device and a cable-driven parallel robot.This paper is focused on the cable-driven robot,which controls the pose of the lower limb through an orthosis placed on the patient's leg.The cable robot reproduces a normal gait movement through the motion of the orthosis.A motion capture system is used to perform the quantitative analysis of a normal gait,which will be used as an input to the inverse dynamic model of the cable robot.By means of an optimization algorithm,the optimal design parameters,which minimize the tensions in the cables,are determined.Two constraints are considered,i.e.,a non-negative tension in the cables at all times,and a free cable/end-effector collision.Once the optimal solution is computed,a power analysis is carried out in order to size the robot actuators.The proposed approach can be easily extended for the design study of a similar type of cable robots.     

Artefact-reduced kinematics measurement using a geometric finger model with mixture-prior particle filtering

It is challenging to measure the finger's kinematics of underlying bones in vivo. This paper presents a new method of finger kinematics measurement, using a geometric finger model and several markers deliberately stuck on skin surface. Using a multiple-view camera system, the optimal motion parameters of finger model were estimated using the proposed mixture-prior particle filtering. This prior, consisting of model and marker information, avoids generating improper particles for achieving near real-time performance. This method was validated using a planar fluoroscopy system that worked simultaneously with photographic system. Ten male subjects with asymptomatic hands were investigated in experiments. The results showed that the kinematic parameters could be estimated more accurately by the proposed method than by using only markers. There was 20–40% reduction in skin artefacts achieved for finger flexion/extension. Thus, this profile system can be developed as a tool of reliable kinematics measurement with good applicability for hand rehabilitation.     

A novel approach to predicting human ingress motion using an artificial neural network

Due to the increased availability of digital human models, the need for knowing human movement is important in product design process. If the human motion is derived rapidly as design parameters change, a developer could determine the optimal parameters. For example, the optimal design of the door panel of an automobile can be obtained for a human operator to conduct the easiest ingress and egress motion. However, acquiring motion data from existing methods provides only unrealistic motion or requires a great amount of time. This not only leads to an increased time consumption for a product development, but also causes inefficiency of the overall design process. To solve such problems, this research proposes an algorithm to rapidly and accurately predict full-body human motion using an artificial neural network (ANN) and a motion database, as the design parameters are varied. To achieve this goal, this study refers to the processes behind human motor learning procedures. According to the previous research, human generate new motion based on past motion experience when they encounter new environments. Based on this principle, we constructed a motion capture database. To construct the database, motion capture experiments were performed in various environments using an optical motion capture system. To generate full-body human motion using this data, a generalized regression neural network (GRNN) was used. The proposed algorithm not only guarantees rapid and accurate results but also overcomes the ambiguity of the human motion objective function, which has been pointed out as a limitation of optimization-based research. Statistical criteria were utilized to confirm the similarity between the generated motion and actual human motion. Our research provides the basis for a rapid motion prediction algorithm that can include a variety of environmental variables. This research contributes to an increase in the usability of digital human models, and it can be applied to various research fields.