Measurement of multi-segment foot joint angles during gait using a wearable system

Usually the measurement of multi-segment foot and ankle complex kinematics is done with stationary motion capture devices which are limited to use in a gait laboratory. This study aimed to propose and validate a wearable system to measure the foot and ankle complex joint angles during gait in daily conditions, and then to investigate its suitability for clinical evaluations. The foot and ankle complex consisted of four segments (shank, hindfoot, forefoot, and toes), with an inertial measurement unit (3D gyroscopes and 3D accelerometers) attached to each segment. The angles between the four segments were calculated in the sagittal, coronal, and transverse planes using a new algorithm combining strap-down integration and detection of low-acceleration instants. To validate the joint angles measured by the wearable system, three subjects walked on a treadmill for five minutes at three different speeds. A camera-based stationary system that used a cluster of markers on each segment was used as a reference. To test the suitability of the system for clinical evaluation, the joint angle ranges were compared between a group of 10 healthy subjects and a group of 12 patients with ankle osteoarthritis, during two 50-m walking trials where the wearable system was attached to each subject. On average, over all joints and walking speeds, the RMS differences and correlation coefficients between the angular curves obtained using the wearable system and the stationary system were 1 deg and 0.93, respectively. Moreover, this system was able to detect significant alteration of foot and ankle function between the group of patients with ankle osteoarthritis and the group of healthy subjects. In conclusion, this wearable system was accurate and suitable for clinical evaluation when used to measure the multi-segment foot and ankle complex kinematics during long-distance walks in daily life conditions.     

Accuracy and repeatability of joint angles measured using a single camera markerless motion capture system

Markerless motion capture systems have developed in an effort to evaluate human movement in a natural setting. However, the accuracy and reliability of these systems remain understudied. Therefore, the goals of this study were to quantify the accuracy and repeatability of joint angles using a single camera markerless motion capture system and to compare the markerless system performance with that of a marker-based system. A jig was placed in multiple static postures with marker trajectories collected using a ten camera motion analysis system. Depth and color image data were simultaneously collected from a single Microsoft Kinect camera, which was subsequently used to calculate virtual marker trajectories. A digital inclinometer provided a measure of ground-truth for sagittal and frontal plane joint angles. Joint angles were calculated with marker data from both motion capture systems using successive body-fixed rotations. The sagittal and frontal plane joint angles calculated from the marker-based and markerless system agreed with inclinometer measurements by <0.5°. The systems agreed with each other by <0.5° for sagittal and frontal plane joint angles and <2° for transverse plane rotation. Both systems showed a coefficient of reliability <0.5° for all angles. These results illustrate the feasibility of a single camera markerless motion capture system to accurately measure lower extremity kinematics and provide a first step in using this technology to discern clinically relevant differences in the joint kinematics of patient populations.     

A novel functional calibration method for real-time elbow joint angles estimation with magnetic-inertial sensors

Magnetic-inertial measurement units (MIMUs) are often used to measure the joint angles between two body segments. To obtain anatomically meaningful joint angles, each MIMU must be computationally aligned (i.e., calibrated) with the anatomical rotation axes. In this paper, a novel four-step functional calibration method is presented for the elbow joint, which relies on a two-degrees-of-freedom elbow model. In each step, subjects are asked to perform a simple task involving either one-dimensional motions around some anatomical axes or a static posture. The proposed method was implemented on a fully portable wearable system, which, after calibration, was capable of estimating the elbow joint angles in real time. Fifteen subjects participated in a multi-session experiment that was designed to assess accuracy, repeatability and robustness of the proposed method. When compared against an optical motion capture system (OMCS), the proposed wearable system showed an accuracy of about 4° along each degree of freedom. The proposed calibration method was tested against different MIMU mountings, multiple repetitions and non-strict observance of the calibration protocol and proved to be robust against these factors. Compared to previous works, the proposed method does not require the wearer to maintain specific arm postures while performing the calibration motions, and therefore it is more robust and better suited for real-world applications.     

Accuracy of an optical active-marker system to track the relative motion of rigid bodies

The measurement of relative motion between two moving bones is commonly accomplished for in vitro studies by attaching to each bone a series of either passive or active markers in a fixed orientation to create a rigid body (RB). This work determined the accuracy of motion between two RBs using an Optotrak optical motion capture system with active infrared LEDs. The stationary noise in the system was quantified by recording the apparent change in position with the RBs stationary and found to be 0.04 degrees and 0.03 mm. Incremental 10 degrees rotations and 10-mm translations were made using a more precise tool than the Optotrak. Increasing camera distance decreased the precision or increased the range of values observed for a set motion and increased the error in rotation or bias between the measured and actual rotation. The relative positions of the RBs with respect to the camera-viewing plane had a minimal effect on the kinematics and, therefore, for a given distance in the volume less than or close to the precalibrated camera distance, any motion was similarly reliable. For a typical operating set-up, a 10 degrees rotation showed a bias of 0.05 degrees and a 95% repeatability limit of 0.67 degrees. A 10-mm translation showed a bias of 0.03 mm and a 95% repeatability limit of 0.29 mm. To achieve a high level of accuracy it is important to keep the distance between the cameras and the markers near the distance the cameras are focused to during calibration.     

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.     

Comparison of strain-gage and fiber-optic goniometry for measuring knee kinematics during activities of daily living and exercise

There is increasing interest in wearable sensor technology as a tool for rehabilitation applications in community or home environments. Recent studies have focused on evaluating inertial based sensing (accelerometers, gyroscopes, etc.) that provide only indirect measures of joint motion. Measurement of joint kinematics using flexible goniometry is more direct, and still popular in laboratory environments, but has received little attention as a potential tool for wearable systems. The aim of this study was to compare two goniometric devices: a traditional strain-gauge flexible goniometer, and a fiberoptic flexible goniometer, for measuring dynamic knee flexion/extension angles during activity of daily living: chair rise, and gait; and exercise: deep knee bends, against joint angles computed from a "gold standard" Vicon motion tracking system. Six young adults were recruited to perform the above activities in the lab while wearing a goniometer on each knee, and reflective markers for motion tracking. Kinematic data were collected simultaneously from the goniometers (one on each leg) and the motion tracking system (both legs). The results indicate that both goniometers were within 2-5 degrees of the Vicon angles for gait and chair rise. For some deep knee bend trials, disagreement with Vicon angles exceeded ten degrees for both devices. We conclude that both goniometers can record ADL knee movement faithfully and accurately, but should be carefully considered when high (>120?deg) knee flexion angles are required.     

Development of a Wearable Framework for the Assessment of a Mechanical-Based Indicator of Falling Risk in the Field

ObjectivesThe characterization of the instability of gait is a current challenge of biomechanics. Indeed, risks of falling naturally result from the difficulty to control perturbations of the locomotion pattern. Hence, the assessment of a synthetic parameter able to quantify the instability in real time will be useful for the prevention of falls occurring in this context. Thus, the objective of the present study, in two steps, was to propose and evaluate a relevant parameter to quantify the risk of fallings.Material and MethodsExperimental analysis of the gait of 11 able-bodied subjects from a motion capture system in laboratory condition was performed. The distance of the Body Center of Mass (BCOM) to the Minimal Moment Axis (MMA) was computed as a proxy of whole-body angular momentum variations. In a second step, we quantified the kinematics during gait with wearable Inertial Measurement Units (IMU) fixed on two individuals (one able bodied person and one person with transfemoral amputation). We compared the IMU-based BCOM kinematics with a motion capture reference system to verify the accuracy of our measures in the field.ResultsNormative thresholds of the distance of the Body Center of Mass (BCOM) to the Minimal Moment Axis (MMA) during able-bodied level walking were assessed. The average error between the BCoM displacement computed from the IMU and from the reference vicon data of 4 mm, 3 mm and 53 mm on the mediolateral, anteroposterior and vertical axes respectively.ConclusionAll these results make it possible to consider the determination of the risks of falls in the field at mid-term. the research on an optimal configuration that maintain the performance while simplifying the device will be essential to make it acceptable by the individuals.     

Validity and reliability of a shoe-embedded sensor module for measuring foot progression angle during over-ground walking

Wearable systems are becoming increasingly popular for gait assessment outside of laboratory settings. A single shoe-embedded sensor module can measure the foot progression angle (FPA) during walking. The FPA has important clinical utility, particularly in populations with knee osteoarthritis, as it is a target for biomechanical treatments. However, the validity and the day-to-day reliability of FPA measurement using wearable systems during over-ground walking has yet to be established. Two gait analysis sessions on 20 healthy adults were conducted. During both sessions, participants performed natural over-ground walking in a motion capture laboratory and on a 100 m linear section of outdoor athletics track. FPA was measured in the laboratory via marker trajectory data, while the sensor module measured FPA during the outdoor track walking. Validity was examined by comparing the laboratory- and sensor-measured average FPA. Day-to-day reliability was examined by comparing the sensor-measured FPA between the first and second gait analysis sessions. Average absolute error between motion capture and sensor measured FPA were 1.7° and 2.1° at session 1 and 2, respectively. A Bland and Altman plot indicated no systematic bias, with 95% limit of agreement widths of 4.2° – 5.1°. Intraclass correlation coefficient (ICC_2k) analysis resulted in good to excellent validity (ICC = 0.89 – 0.91) and reliability (ICC = 0.95). Overall, the shoe-embedded sensor module is a valid and reliable method of measuring FPA during over-ground walking without the need for laboratory equipment.     

Similar sensorimotor transformations control balance during standing and walking

Standing and walking balance control in humans relies on the transformation of sensory information to motor commands that drive muscles. Here, we evaluated whether sensorimotor transformations underlying walking balance control can be described by task-level center of mass kinematics feedback similar to standing balance control. We found that delayed linear feedback of center of mass position and velocity, but not delayed linear feedback from ankle angles and angular velocities, can explain reactive ankle muscle activity and joint moments in response to perturbations of walking across protocols (discrete and continuous platform translations and discrete pelvis pushes). Feedback gains were modulated during the gait cycle and decreased with walking speed. Our results thus suggest that similar task-level variables, i.e. center of mass position and velocity, are controlled across standing and walking but that feedback gains are modulated during gait to accommodate changes in body configuration during the gait cycle and in stability with walking speed. These findings have important implications for modelling the neuromechanics of human balance control and for biomimetic control of wearable robotic devices. The feedback mechanisms we identified can be used to extend the current neuromechanical models that lack balance control mechanisms for the ankle joint. When using these models in the control of wearable robotic devices, we believe that this will facilitate shared control of balance between the user and the robotic device.     

Functional calibration procedure for 3D knee joint angle description using inertial sensors

Measurement of three-dimensional (3D) knee joint angle outside a laboratory is of benefit in clinical examination and therapeutic treatment comparison. Although several motion capture devices exist, there is a need for an ambulatory system that could be used in routine practice. Up-to-date, inertial measurement units (IMUs) have proven to be suitable for unconstrained measurement of knee joint differential orientation. Nevertheless, this differential orientation should be converted into three reliable and clinically interpretable angles. Thus, the aim of this study was to propose a new calibration procedure adapted for the joint coordinate system (JCS), which required only IMUs data. The repeatability of the calibration procedure, as well as the errors in the measurement of 3D knee angle during gait in comparison to a reference system were assessed on eight healthy subjects. The new procedure relying on active and passive movements reported a high repeatability of the mean values (offset<1°) and angular patterns (SD<0.3° and CMC>0.9). In comparison to the reference system, this functional procedure showed high precision (SD<2° and CC>0.75) and moderate accuracy (between 4.0° and 8.1°) for the three knee angle. The combination of the inertial-based system with the functional calibration procedure proposed here resulted in a promising tool for the measurement of 3D knee joint angle. Moreover, this method could be adapted to measure other complex joint, such as ankle or elbow.     

Assessment of intersegmental coordination of rats during walking at different speeds – Application of continuous relative phase

The present study investigated the feasibility and reliability of continuous relative phase (CRP) and deviation phase (DP) to assess intersegmental hind limb coordination pattern and coordination variability in rats during walking. Twenty-six adult rats walked at 8 m/min, 12 m/min and 16 m/min while two-dimensional kinematics were recorded. Segment angles and segment angular velocities of the paw, shank and thigh on the left hind-limb were extracted from 15 strides and CRP was calculated for the paw-shank and shank-thigh coupling. The effect of walking speed on the time point average curve of the CRP (ACRP) and DP and on the mean ACRP and mean DP was established by statistical parametric mapping (SPM) and a one-way ANOVA for repeated measures. Absolute and relative reliability were assessed by measurement error and intra-class correlation coefficient. The SPM analysis revealed time dependent differences in the effect of speed. Thus, the CRP of the paw-shank coupling decreased with increasing speed during most of the gait cycle while the CRP of the shank-thigh coupling was decreased during the swing phase. The session-to-session reliability was fair to good for the coordination measure and poor for the variability measure.     

Gait posture estimation using wearable acceleration and gyro sensors

A method for gait analysis using wearable acceleration sensors and gyro sensors is proposed in this work. The volunteers wore sensor units that included a tri-axis acceleration sensor and three single axis gyro sensors. The angular velocity data measured by the gyro sensors were used to estimate the translational acceleration in the gait analysis. The translational acceleration was then subtracted from the acceleration sensor measurements to obtain the gravitational acceleration, giving the orientation of the lower limb segments. Segment orientation along with body measurements were used to obtain the positions of hip, knee, and ankle joints to create stick figure models of the volunteers. This method can measure the three-dimensional positions of joint centers of the hip, knee, and ankle during movement. Experiments were carried out on the normal gait of three healthy volunteers. As a result, the flexion–extension (F–E) and the adduction–abduction (A–A) joint angles of the hips and the flexion–extension (F–E) joint angles of the knees were calculated and compared with a camera motion capture system. The correlation coefficients were above 0.88 for the hip F–E, higher than 0.72 for the hip A–A, better than 0.92 for the knee F–E. A moving stick figure model of each volunteer was created to visually confirm the walking posture. Further, the knee and ankle joint trajectories in the horizontal plane showed that the left and right legs were bilaterally symmetric.     

A method for measurement of joint kinematics in vivo by registration of 3-D geometric models with cine phase contrast magnetic resonance imaging data

A new method is presented for measuring joint kinematics by optimally matching modeled trajectories of geometric surface models of bones with cine phase contrast (cine-PC) magnetic resonance imaging data. The incorporation of the geometric bone models (GBMs) allows computation of kinematics based on coordinate systems placed relative to full 3-D anatomy, as well as quantification of changes in articular contact locations and relative velocities during dynamic motion. These capabilities are additional to those of cine-PC based techniques that have been used previously to measure joint kinematics during activity. Cine-PC magnitude and velocity data are collected on a fixed image plane prescribed through a repetitively moved skeletal joint. The intersection of each GBM with a simulated image plane is calculated as the model moves along a computed trajectory, and cine-PC velocity data are sampled from the regions of the velocity images within the area of this intersection. From the sampled velocity data, the instantaneous linear and angular velocities of a coordinate system fixed to the GBM are estimated, and integration of the linear and angular velocities is used to predict updated trajectories. A moving validation phantom that produces motions and velocity data similar to those observed in an experiment on human knee kinematics was designed. This phantom was used to assess cine-PC rigid body tracking performance by comparing the kinematics of the phantom measured by this method to similar measurements made using a magnetic tracking system. Average differences between the two methods were measured as 2.82 mm rms for anterior/posterior tibial position, and 2.63 deg rms for axial rotation. An intertrial repeatability study of human knee kinematics using the new method produced rms differences in anterior/posterior tibial position and axial rotation of 1.44 mm and 2.35 deg. The performance of the method is concluded to be sufficient for the effective study of kinematic changes caused to knees by soft tissue injuries.     

3D gait assessment in young and elderly subjects using foot-worn inertial sensors

This study describes the validation of a new wearable system for assessment of 3D spatial parameters of gait. The new method is based on the detection of temporal parameters, coupled to optimized fusion and de-drifted integration of inertial signals. Composed of two wirelesses inertial modules attached on feet, the system provides stride length, stride velocity, foot clearance, and turning angle parameters at each gait cycle, based on the computation of 3D foot kinematics. Accuracy and precision of the proposed system were compared to an optical motion capture system as reference. Its repeatability across measurements (test-retest reliability) was also evaluated. Measurements were performed in 10 young (mean age 26.1±2.8 years) and 10 elderly volunteers (mean age 71.6±4.6 years) who were asked to perform U-shaped and 8-shaped walking trials, and then a 6-min walking test (6 MWT). A total of 974 gait cycles were used to compare gait parameters with the reference system. Mean accuracy±precision was 1.5±6.8 cm for stride length, 1.4±5.6 cm/s for stride velocity, 1.9±2.0 cm for foot clearance, and 1.6±6.1° for turning angle. Difference in gait performance was observed between young and elderly volunteers during the 6 MWT particularly in foot clearance. The proposed method allows to analyze various aspects of gait, including turns, gait initiation and termination, or inter-cycle variability. The system is lightweight, easy to wear and use, and suitable for clinical application requiring objective evaluation of gait outside of the lab environment.     

Kinematic analysis of a multi-segment foot model for research and clinical applications: a repeatability analysis

An unbiased understanding of foot kinematics has been difficult to achieve due to the complexity of foot structure and motion. We have developed a protocol for evaluation of foot kinematics during barefoot walking based on a multi-segment foot model. Stereophotogrammetry was used to measure retroreflective markers on three segments of the foot plus the tibia. Repeatability was evaluated between-trial, between-day and between-tester using two subjects and two testers. Subtle patterns and ranges of motion between segments of the foot were consistently detected. We found that repeatability between different days or different testers is primarily subject to variability of marker placement more than inter-tester variability or skin movement. Differences between inter-segment angle curves primarily represent a shift in the absolute value of joint angles from one set of trials to another. In the hallux, variability was greater than desired due to vibration of the marker array used. The method permits objective foot measurement in gait analysis using skin-mounted markers. Quantitative and objective characterisation of the kinematics of the foot during activity is an important area of clinical and research evaluation. With this work we hope to have provided a firm basis for a common protocol for in vivo foot study.     

Cluster-based upper body marker models for three-dimensional kinematic analysis: Comparison with an anatomical model and reliability analysis

Quantifying angular joint kinematics of the upper body is a useful method for assessing upper limb function. Joint angles are commonly obtained via motion capture, tracking markers placed on anatomical landmarks. This method is associated with limitations including administrative burden, soft tissue artifacts, and intra- and inter-tester variability. An alternative method involves the tracking of rigid marker clusters affixed to body segments, calibrated relative to anatomical landmarks or known joint angles. The accuracy and reliability of applying this cluster method to the upper body has, however, not been comprehensively explored. Our objective was to compare three different upper body cluster models with an anatomical model, with respect to joint angles and reliability. Non-disabled participants performed two standardized functional upper limb tasks with anatomical and cluster markers applied concurrently. Joint angle curves obtained via the marker clusters with three different calibration methods were compared to those from an anatomical model, and between-session reliability was assessed for all models. The cluster models produced joint angle curves which were comparable to and highly correlated with those from the anatomical model, but exhibited notable offsets and differences in sensitivity for some degrees of freedom. Between-session reliability was comparable between all models, and good for most degrees of freedom. Overall, the cluster models produced reliable joint angles that, however, cannot be used interchangeably with anatomical model outputs to calculate kinematic metrics. Cluster models appear to be an adequate, and possibly advantageous alternative to anatomical models when the objective is to assess trends in movement behavior.     

A Novel Application of Musculoskeletal Ultrasound Imaging

Ultrasound is an attractive modality for imaging muscle and tendon motion during dynamic tasks and can provide a complementary methodological approach for biomechanical studies in a clinical or laboratory setting. Towards this goal, methods for quantification of muscle kinematics from ultrasound imagery are being developed based on image processing. The temporal resolution of these methods is typically not sufficient for highly dynamic tasks, such as drop-landing. We propose a new approach that utilizes a Doppler method for quantifying muscle kinematics. We have developed a novel vector tissue Doppler imaging (vTDI) technique that can be used to measure musculoskeletal contraction velocity, strain and strain rate with sub-millisecond temporal resolution during dynamic activities using ultrasound. The goal of this preliminary study was to investigate the repeatability and potential applicability of the vTDI technique in measuring musculoskeletal velocities during a drop-landing task, in healthy subjects. The vTDI measurements can be performed concurrently with other biomechanical techniques, such as 3D motion capture for joint kinematics and kinetics, electromyography for timing of muscle activation and force plates for ground reaction force. Integration of these complementary techniques could lead to a better understanding of dynamic muscle function and dysfunction underlying the pathogenesis and pathophysiology of musculoskeletal disorders.     

Quantification of gait parameters with inertial sensors and inverse kinematics

Measuring human gait is important in medicine to obtain outcome parameter for therapy, for instance in Parkinson’s disease. Recently, small inertial sensors became available which allow for the registration of limb-position outside of the limited space of gait laboratories. The computation of gait parameters based on such recordings has been the subject of many scientific papers. We want to add to this knowledge by presenting a 4-segment leg model which is based on inverse kinematic and Kalman filtering of data from inertial sensors. To evaluate the model, data from four leg segments (shanks and thighs) were recorded synchronously with accelerometers and gyroscopes and a 3D motion capture system while subjects (n = 12) walked at three different velocities on a treadmill. Angular position of leg segments was computed from accelerometers and gyroscopes by Kalman filtering and compared to data from the motion capture system. The four-segment leg model takes the stance foot as a pivotal point and computes the position of the remaining segments as a kinematic chain (inverse kinematics). Second, we evaluated the contribution of pelvic movements to the model and evaluated a five segment model (shanks, thighs and pelvis) against ground-truth data from the motion capture system and the path of the treadmill.ResultsWe found the precision of the Kalman filtered angular position is in the range of 2–6° (RMS error). The 4-segment leg model computed stride length and length of gait path with a constant undershoot of 3% for slow and 7% for fast gait. The integration of a 5th segment (pelvis) into the model increased its precision. The advantages of this model and ideas for further improvements are discussed.     

Measuring 3D Hand and Finger Kinematics—A Comparison between Inertial Sensing and an Opto-Electronic Marker System

Objective analysis of hand and finger kinematics is important to increase understanding of hand function and to quantify motor symptoms for clinical diagnosis. The aim of this paper is to compare a new 3D measurement system containing multiple miniature inertial sensors (PowerGlove) with an opto-electronic marker system during specific finger tasks in three healthy subjects. Various finger movements tasks were performed: flexion, fast flexion, tapping, hand open/closing, ab/adduction and circular pointing. 3D joint angles of the index finger joints and position of the thumb and index were compared between systems. Median root mean square differences of the main joint angles of interest ranged between 3.3 and 8.4deg. Largest differences were found in fast and circular pointing tasks, mainly in range of motion. Smallest differences for all 3D joint angles were observed in the flexion tasks. For fast finger tapping, the thumb/index amplitude showed a median difference of 15.8mm. Differences could be explained by skin movement artifacts caused by relative marker movements of the marker system, particularly during fast tasks; large movement accelerations and angular velocities which exceeded the range of the inertial sensors; and by differences in segment calibrations between systems. The PowerGlove is a system that can be of value to measure 3D hand and finger kinematics and positions in an ambulatory setting. The reported differences need to be taken into account when applying the system in studies understanding the hand function and quantifying hand motor symptoms in clinical practice.     

Optimization-based prediction of asymmetric human gait

An optimization-based formulation and solution method are presented to predict asymmetric human gait for a large-scale skeletal model. Predictive dynamics approach is used in which both the joint angles and joint torques are treated as unknowns in the equations of motion. For the optimization formulation, the joint angle profiles are treated as the primary unknowns, and velocities and accelerations are calculated using them. In numerical implementation, the joint angle profiles are discretized using the B-spline interpolation. An algorithm is presented to inversely calculate the joint torques and the ground reaction forces. The sum of the joint-torques squared, called the dynamic effort, is minimized as the human performance measure. Constraints are imposed on the joint strengths (torques) and joint ranges of motion along with other physical constraints. The formulation is validated by simulating a symmetric gait and comparing the results with the experimental data. Then asymmetric gait motion is simulated, where the left and right step lengths are different. The kinematics and kinetics results from the simulation are presented and discussed. Predicted ground reaction forces are explained by using the inverted pendulum model. Predicted kinematics and kinetics have trends that are similar to those reported in the literature. Potential practical applications of the formulation and the solution approach are discussed.