Dynamic optimization of the sit-to-stand movement

The purpose of this study was to clarify criteria that can predict trajectories during the sit-to-stand movement. In particular, the minimum jerk and minimum torque-change models were examined. Three patterns of sit-to-stand movement from a chair, i.e., upright, natural, and leaning forward, were measured in five young participants using a 3-D motion analysis device (200 Hz). The trajectory of the center of mass and its smoothness were examined, and the optimal trajectories predicted by both models were evaluated. Trajectories of the center of mass predicted by the minimum torque-change model, rather than the minimum jerk model, resembled the measured movements in all rising movement patterns. The upright pattern required greater extension torque of the knee and ankle joints at the instant of seat-off. The leaning-forward pattern required greater extension hip torque and higher movement cost than the natural and upright patterns. These results indicate that the natural sit-to-stand movement might be a result of dynamic optimization.     

Representing and identifying alternative movement techniques for goal-directed manual tasks

Differences in motion patterns subserving the same movement goal can be identified qualitatively. These alternatives, which may characterize 'movement techniques' (e.g., the stoop and the squat lifting technique), may be associated with significantly different biomechanical constraints and physiological responses. Despite the widely shared understanding of the significance of alternative movement techniques, quantitative representation and identification of movement techniques have received little attention, especially for three-dimensional whole-body motions. In an attempt to systematically differentiate movement techniques, this study introduces a quantitative index termed joint contribution vector (JCV) representing a motion in terms of contributions of individual joint degrees-of-freedom to the achievement of the task goal. Given a set of uncharacterized (unlabeled) motions represented by joint angle trajectories (motion capture data), the JCV and statistical clustering methods enable automated motion classification to uncover a taxonomy of alternative movement techniques. The results of our motion data analyses show that the JCV was able to characterize and discern stoop and squat lifting motions, and also to identify movement techniques for a three-dimensional, whole-body, one-handed load-transfer task. The JCV index would facilitate consideration of alternative movement techniques in a variety of applications, including work method comparison and selection, and human motion modeling and simulation.     

Interpolation of segment Euler angles can provide a robust estimation of segment angular trajectories during asymmetric lifting tasks

Video-based field methods that estimate L5/S1 net joint moments from kinematics based on interpolation in the sagittal plane of joint angles alone can introduce a significant error on the interpolated joint angular trajectory when applied to asymmetric dynamic lifts. Our goal was to evaluate interpolation of segment Euler angles for a wide range of dynamic asymmetric lifting tasks using cubic spline methods by comparing the interpolated values with the continuous measured ones. For most body segments, the estimated trajectories of segment Euler angles have less than 5° RMSE (in each dimension) with 5-point cubic spline interpolation when there is no measurement error of interpolation points. Sensitivity analysis indicates that when the measurement error exists, the root mean square error (RMSE) of estimated trajectories increases. Comparison among different lifting conditions showed that lifting a load from a high initial position yielded a smaller RMSE than lifting from a low initial position. In conclusion, interpolation of segment Euler angles can provide a robust estimation of segment angular trajectories during asymmetric lifting when measurement error of interpolation points can be controlled at a low level.     

An approximate stochastic optimal control framework to simulate nonlinear neuro-musculoskeletal models in the presence of noise

Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while neglecting physiological noise, and stochastic simulations account for noise while simplifying the dynamics. We took advantage of recent approaches where stochastic optimal control problems are approximated using deterministic optimal control problems, which can be solved efficiently using direct collocation. We were thus able to extend predictions of stochastic optimal control as a theory of motor coordination to include muscle coordination and movement patterns emerging from non-linear musculoskeletal dynamics. In stochastic optimal control simulations of human standing balance, we demonstrated that the inclusion of muscle dynamics can predict muscle co-contraction as minimal effort strategy that complements sensorimotor feedback control in the presence of sensory noise. In simulations of reaching, we demonstrated that nonlinear multi-segment musculoskeletal dynamics enables complex perturbed and unperturbed reach trajectories under a variety of task conditions to be predicted. In both behaviors, we demonstrated how interactions between task constraint, sensory noise, and the intrinsic properties of muscle influence optimal muscle coordination patterns, including muscle co-contraction, and the resulting movement trajectories. Our approach enables a true minimum effort solution to be identified as task constraints, such as movement accuracy, can be explicitly imposed, rather than being approximated using penalty terms in the cost function. Our approximate stochastic optimal control framework predicts complex features, not captured by previous simulation approaches, providing a generalizable and valuable tool to study how musculoskeletal dynamics and physiological noise may alter neural control of movement in both healthy and pathological movements.     

Control Model for Dampening Hand Vibrations Using Information of Internal and External Coordinates

In the present study, we investigate a control mechanism that dampens hand vibrations. Here, we propose a control method with two components to suppress hand vibrations. The first is a passive suppression method that lowers the joint stiffness to passively dampen the hand vibrations. The second is an active suppression method that adjusts an equilibrium point based on skyhook control to actively dampen the hand vibrations. In a simulation experiment, we applied these two methods to dampen hand vibrations during the shoulder’s horizontal oscillation. We also conducted a measurement experiment wherein a subject’s shoulder was sinusoidally oscillated by a platform that generated horizontal oscillations. The results of the measurement experiments showed that the jerk of each part of the arm in a task using a cup filled with water was smaller than the shoulder jerk and that in a task with a cup filled with stones was larger than the shoulder jerk. Moreover, the amplitude of the hand trajectory in both horizontal and vertical directions was smaller in a task using a cup filled with water than in a task using a cup filled with stones. The results of the measurement experiments were accurately reproduced by the active suppression method based on skyhook control. These results suggest that humans dampen hand vibrations by controlling the equilibrium point through the information of the external workspace and the internal body state rather than by lowering joint stiffness only by using internal information.     

Synergic analysis of upper limb target-reaching movements

The topological invariance and synergies of human movements are discussed through the analysis and comparison of upper-limb target-reaching tasks. Five subjects were asked to perform different target-reaching tasks with different indices of difficulty, and the movements were captured using a Vicon 3D motion analysis system.Topological invariance was observed in the trajectories of different task performances. After normalization, the trajectories of the arm tips had very close patterns for different target-reaching tasks. Synergy in the target-reaching movements of the upper limbs was also found among the different joint angles. The joint angles can be fitted using the same format of functions proposed in this study. The parameters in the function can be taken as a characteristic feature of target-reaching movement patterns. A target-reaching movement can be determined by these parameters and the start and end positions.     

High curvature and jerk analyses of arm ataxia

We investigated high curvature analysis (HCA) and integrated absolute jerk (IAJ) for differentiating healthy and cerebellopathy (CB) patients performing pointing tasks. Seventeen CB patients and seventeen healthy controls were required to move a pointer at their preferred pace between two 50.8 cm laterally spaced targets while standing with their arm extended in front of their body. HCA was used to quantify the frequency of sharp turns in the horizontal-plane (anterior-posterior and medio-lateral) velocity trajectory of the hand-held pointer. IAJ was assessed by integration of absolute jerk (second time derivative of velocity) time histories in the anterior-posterior and medio-lateral directions. HCA scores and IAJ scores were then compared between CB patients and healthy controls; for both analyses, higher scores indicate less smooth movements. We hypothesized that CB patients would have less smooth movement trajectories than healthy controls due to upper extremity ataxia associated with cerebellar disease and degeneration. We found that CB patients had higher HCA scores than healthy controls (P = 0.014). Although CB patients had higher IAJ scores in both anterior-posterior (P = 0.060) and medio-lateral (P = 0.231) directions compared to the healthy controls, the differences were not significant. The difference in sensitivity between the HCA and the IAJ analysis might be explained by primitive neural activation commands, ubiquitous though only evident with some cerebellar dysfunctions, which produce sub-movements which are themselves minimal jerk curves. We conclude that HCA may be a useful tool for quantifying upper extremity ataxia in CB patients performing a repeated pointing task. Received: 17 December 1999 / Accepted in revised form: 7 July 2000     

Independent control of joint stiffness in the framework of the equilibrium-point hypothesis

In the framework of the equilibrium-point hypothesis, virtual trajectories and joint stiffness patterns have been reconstructed during two motor tasks practiced against a constant bias torque. One task required a voluntary increase in joint stiffness while preserving the original joint position. The other task involved fast elbow flexions over 36°. Joint stiffness gradually subsided after the termination of fast movements. In both tasks, the external torque could slowly and unexpectedly change. The subjects were required not to change their motor commands if the torque changed, i.e. “to do the same no matter what the motor did”. In both tasks, changes in joint stiffness were accompanied by unchanged virtual trajectories that were also independent of the absolute value of the bias torque. By contrast, the intercept of the joint compliant characteristic with the angle axis,r(t)-function, has demonstrated a clear dependence upon both the level of coactivation and external load. We assume that a template virtual trajectory is generated at a certain level of the motor hierarchy and is later scaled taking into account some commonly changing dynamic factors of the movement execution, for example, external load. The scaling leads to the generation of commands to the segmental structures that can be expressed, according to the equilibrium-point hypothesis, as changes in the thresholds of the tonic stretch reflex for corresponding muscles.     

Grasping Objects with Environmentally Induced Position Uncertainty

Due to noisy motor commands and imprecise and ambiguous sensory information, there is often substantial uncertainty about the relative location between our body and objects in the environment. Little is known about how well people manage and compensate for this uncertainty in purposive movement tasks like grasping. Grasping objects requires reach trajectories to generate object-fingers contacts that permit stable lifting. For objects with position uncertainty, some trajectories are more efficient than others in terms of the probability of producing stable grasps. We hypothesize that people attempt to generate efficient grasp trajectories that produce stable grasps at first contact without requiring post-contact adjustments. We tested this hypothesis by comparing human uncertainty compensation in grasping objects against optimal predictions. Participants grasped and lifted a cylindrical object with position uncertainty, introduced by moving the cylinder with a robotic arm over a sequence of 5 positions sampled from a strongly oriented 2D Gaussian distribution. Preceding each reach, vision of the object was removed for the remainder of the trial and the cylinder was moved one additional time. In accord with optimal predictions, we found that people compensate by aligning the approach direction with covariance angle to maintain grasp efficiency. This compensation results in higher probability to achieve stable grasps at first contact than non-compensation strategies in grasping objects with directional position uncertainty, and the results provide the first demonstration that humans compensate for uncertainty in a complex purposive task.     

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.     

Reconstruction of equilibrium trajectories during whole-body movements

The framework of the equilibrium-point hypothesis was used to reconstruct equilibrium trajectories (ETs) of the ankle, hip and body center of mass during quick voluntary hip flexions (`Japanese courtesy bow') by standing subjects. Different spring loads applied to the subject's back were used to introduce smooth perturbations that are necessary to reconstruct ETs based on a series of trials at the same task. Time patterns of muscle torques were calculated using inverse dynamics techniques. A second-order linear model was employed to calculate the instantaneous position of the spring-like joint or center of mass characteristic at different times during the movement. ETs of the joints and of the center of mass had significantly different shapes from the actual trajectories. Integral measures of electromyographic bursts of activity in postural muscles demonstrated a relation to muscle length corresponding to the equilibrium-point hypothesis. Received: 3 March 1997 / Accepted in revised form: 2 November 1998     

Shoulder Kinematics and Spatial Pattern of Trapezius Electromyographic Activity in Real and Virtual Environments

The design of an industrial workstation tends to include ergonomic assessment steps based on a digital mock-up and a virtual reality setup. Lack of interaction and system fidelity is often reported as a main issue in such virtual reality applications. This limitation is a crucial issue as thorough ergonomic analysis is required for an investigation of the biomechanics. In the current study, we investigated the biomechanical responses of the shoulder joint in a simulated assembly task for comparison with the biomechanical responses in virtual environments. Sixteen male healthy novice subjects performed the task on three different platforms: real (RE), virtual (VE), and virtual environment with force feedback (VEF) with low and high precision demands. The subjects repeated the task 12 times (i.e., 12 cycles). High density electromyography from the upper trapezius and rotation angles of the shoulder joint were recorded and split into the cycles. The angular trajectories and velocity profiles of the shoulder joint angles over a cycle were computed in 3D. The inter-subject similarity in terms of normalized mutual information on kinematics and electromyography was investigated. Compared with RE the task in VE and VEF was characterized by lower kinematic maxima. The inter-subject similarity in RE compared with intra-subject similarity across the platforms was lower in terms of movement trajectories and greater in terms of trapezius muscle activation. The precision demand resulted in lower inter- and intra-subject similarity across platforms. The proposed approach identifies biomechanical differences in the shoulder joint in both VE and VEF compared with the RE platform, but these differences are less marked in VE mostly due to technical limitations of co-localizing the force feedback system in the VEF platform.     

A dynamic 3D biomechanical evaluation of the load on the low back during different patient-handling tasks

The objective of this study was to investigate the low-back loading during common patient-handling tasks. Ten female health care workers without formal training in patient handling performed nine patient-handling tasks including turning, lifting and repositioning a male stroke patient. The low-back loading was quantified by net moment, compression, and shear forces at the L4/L5 joint, measured muscle activity (EMG) in erector spinae muscles and rate of perceived exertion (RPE; Borg scale). The experiments were videotaped with a 50Hz video system using five cameras, and the ground and bedside reaction forces of the health care worker were recorded by means of force platforms and force transducers on the bed. The biomechanical load was calculated using a dynamic 3D seven-segment model of the lower part of the body, and the forces at the L4/L5 joint were estimated by a 14 muscles cross-sectional model of the low back (optimisation procedure). Compression force and torque showed high task dependency whereas the EMG data and the RPE values were more dependent on the subject. The peak compression during two tasks involving lifting the patient (4132/4433N) was significantly higher than all other tasks. Four tasks involving repositioning the patient in the bed (3179/3091/2932/3094N) did not differ, but showed higher peak compression than two tasks turning the patient in the bed (1618/2197N). Thus, in this study the patient-handling tasks could be classified into three groups-characterised by lifting, repositioning or turning-with different levels of peak net torque and compression at the L4/L5 joint.     

Speed-dependent reference joint trajectory generation for robotic gait support

For the control of actuated orthoses, or gait rehabilitation robotics, kinematic reference trajectories are often required. These trajectories, consisting of joint angles, angular velocities and accelerations, are highly dependent on walking-speed. We present and evaluate a novel method to reconstruct body-height and speed-dependent joint trajectories. First, we collected gait kinematics in fifteen healthy (middle) aged subjects (47–68), at a wide range of walking-speeds (0.5–5 kph). For each joint trajectory multiple key-events were selected (among which its extremes). Second, we derived regression-models that predict the timing, angle, angular velocity and acceleration for each key-event, based on walking-speed and the subject?s body-height. Finally, quintic splines were fitted between the predicted key-events to reconstruct a full gait cycle. Regression-models were obtained for hip ab-/adduction, hip flexion/extension, knee flexion/extension and ankle plantar-/dorsiflexion. Results showed that the majority of the key-events were dependent on walking-speed, both in terms of timing and amplitude, whereas the body-height had less effect. The reconstructed trajectories matched the measured trajectories very well, in terms of angle, angular velocity and acceleration. For the angles the RMSE between the reconstructed and measured trajectories was 2.6°. The mean correlation coefficient between the reconstructed and measured angular trajectories was 0.91. The method and the data presented in this paper can be used to generate speed-dependent gait patterns. These patterns can be used for the control of several robotic gait applications. Alternatively they can assist the assessment of pathological gait, where they can serve as a reference for “normal” gait.     

Lifting over an obstacle: effects of one-handed lifting and hand support on trunk kinematics and low back loading

Mechanical loading of the low back during lifting is a common cause of low back pain. In this study two-handed lifting is compared to one-handed lifting (with and without supporting the upper body with the free hand) while lifting over an obstacle. A 3-D linked segment model was combined with an EMG-assisted trunk muscle model to quantify kinematics and joint loads at the L5S1 joint. Peak total net moments (i.e., the net moment effect of all muscles and soft tissue spanning the joint) were found to be 10+/-3% lower in unsupported one-handed lifting compared to two-handed lifting, and 30+/-8% lower in supported compared to unsupported one-handed lifting. L5S1 joint forces also showed reductions, but not of the same magnitude (18+/-8% and 15+/-10%, respectively, for compression forces, and 15+/-17% and 11+/-14% respectively, for shear forces). Those reductions of low back load were mainly caused by a reduction of trunk and load moment arms relative to the L5S1 joint during peak loading, and, in the case of hand support, by a support force of about 250 N. Stretching one leg backward did not further reduce low back load estimates. Furthermore, one-handed lifting caused an 6+/-8 degrees increase in lateral flexion, a 9+/-5 degrees increase in twist and a 6+/-6 degrees decrease in flexion. Support with the free hand caused a small further increase in lumbar twisting. It is concluded that one-handed lifting, especially with hand support, reduces L5S1 loading but increases asymmetry in movements and moments about the lumbar spine.     

Measuring movement irregularity in the upper motor neurone syndrome using normalised average rectified jerk.

Movement irregularity is a feature of the upper motor neurone (UMN) syndrome which is difficult to measure. Average rectified jerk (ARJ) has been proposed as a measure of this movement irregularity, but ARJ depends upon the duration of movement. Since movements may be slower in UMN patients, duration dependence compromises ARJ as a measure of irregularity. A normalisation technique is proposed that generates a measure of movement irregularity which is independent of movement duration: normalised average rectified jerk (NARJ). This paper presents a validation of NARJ in the UMN syndrome. Nine control subjects, nine left hemiparetic stroke patients and nine right hemiparetic stroke patients were studied. Test movements comprised elbow extension/flexion in the horizontal plane; these were recorded with an electro-goniometer and accelerometer. The effectiveness of the normalisation technique has been demonstrated using trajectories of various durations; some of these were artificially generated from participants' trajectories, in order to preserve the movement profile. The variability of NARJ and ARJ have been compared in a sample of control subjects. NARJ has been criterion validated by correlation with expert subjective rating of irregularity in a heterogeneous set of trajectories. Construct validity has been tested by discrimination between movements of control subjects, left hemiparetic stroke patients and right hemiparetic stroke patients. When comparing trajectories of identical profile but two-fold difference in movement duration, NARJ differed only 2.6% whereas ARJ differed 706%. NARJ was less reproducible in healthy participants than ARJ: median non-parametric coefficients of variation for repeated movements were 55% and 41%, respectively. Spearman rank correlation coefficient for NARJ and expert rating was 0.92 (p<0.01). NARJ measurements on right hemiparetic patients differ significantly from those made on the control group (p<0.02); corresponding ARJ measurements do not attain statistical significance. NARJ is a valid measure of movement irregularity in the UMN syndrome.     

Biomechanical analysis of manual lifting tasks

This paper presents the findings of a study conducted to determine peak forces generated in the human spine while the individual is engaged in lifting maximum acceptable weight. Calculations of forces and moments, acting on each body segment, were based on film data collected on four individuals for twelve variations of the manual lifting task. The variations were defined by: box-size (three different boxes were used), presence or absence of handles, and symmetry and asymmetry of the lifting task (sagittal and nonsagittal lifting). In general, lower loads were accepted for lift when lifting asymmetrically or when lifting boxes without handles or when lifting bigger boxes. However, peak forces (compressive and shear forces in the spine and ground reaction forces) for these situations were not always lower than those generated when handling either compact boxes or boxes with handles or when lifting boxes symmetrically in the sagittal plane. On the basis of these results, it was concluded that lifting loads asymmetrically or in boxes without handles or in bulky boxes is relatively much more stressful than lifting the same load symmetrically or in boxes with handles or in compact boxes.     

Role of heel lifting in standing balance recovery: A simulation study

Although lifting the heels has frequently been observed during balance recovery, the function of this movement has generally been overlooked. The present study aimed to investigate the functional role of heel lifting during regaining balance from a perturbed state. Computer simulation was employed to objectively examine the effect of allowing/constraining heel lifting on balance performance. The human model consisted of 3 rigid body segments connected by frictionless joints. Movements were driven by joint torques depending on current joint angle, angular velocity, and activation level. Starting from forward-inclined and static straight-body postures, the optimization goal was to recover balance effectively (so that ground projection of the mass center returned to the inside of the base of support) and efficiently by adjusting ankle and hip joint activation levels. Allowing/constraining heel lifting resulted in virtually identical movements when balance was mildly perturbed at the smallest lean angle (8°). At larger lean angles (8.5° and 9°), heel lifting assisted balance recovery more evidently with larger joint movements. Partial and altered timings of ankle/hip torque activation due to constraining heel lifting reduced linear and angular momentum generation for avoiding forward falling, and resulted in hindered balancing performance.     

Analysis of a muscular control system in human movements

In this work, we have studied a muscular control system under experimental conditions for analyzing the dynamic behavior of individual muscles and theoretical considerations for elucidating its control strategy. Movement of human limbs is achieved by joint torques and each torque is specified as the sum of torques generated by muscle forces. The behavior of individual muscles is controlled by the neural input which is estimated by means of an electromyogram (EMG). In this study, the EMGs for a flexor and an extensor are measured in elbow joint movements and the dynamic behavior of individual muscles is analyzed. As a result, it is verified that both a flexor and an extensor are activated throughout the entire movement and that the activation of muscles is controlled above a specific limit independent of the hand-held load. Subsequently, a system model for simulating elbow joint movements is developed which includes the muscle dynamic relationship between the neural input and the isometric force. The minimum limit of muscle activation that has been confirmed in experiments is provided as a constraint of the neural input and the criterion is defined by a derivative of the isometric force of individual muscles. The optimal trajectories formulated under these conditions are quantitatively compared with the experimentally observed trajectories, and the control strategy of a muscular control system is studied. Finally, a muscular control system in multi-joint arm movements is discussed with regard to the comparative analysis between observed and optimal trajectories. Received: 7 April 1999 / Accepted in revised form: 27 July 1999