Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

Model-Based Upper-Limb Gravity Compensation Strategies for Active Dynamic Arm Supports

NeuroMuscular Disorders (NMDs) may induce difficulties to perform daily life activities in autonomy. For people with NMDs affecting the upper-limb mobility, Dynamic Arm Supports (DASs) turn out to be relevant assistive devices. In particular, active DASs benefit from an external power source to support severely impaired people. However, commercially available active devices are controlled with push buttons, which add cognitive load and discomfort. To alleviate this issue, we propose a new force-based assistive control framework. In this preliminary work, we focus on the computation of a feedforward force to compensate upper-limb gravity. Four strategies based on a biomechanical model of the upper limb, tuned using anthropometric measurements, are proposed and evaluated. The first one is based on the potential energy of the upper-limb, the second one makes a compromise between the shoulder and elbow torques, the third one minimizes the sum of the squared user joint torques and the last one uses a probabilistic approach to minimize the expected torque norm in the presence of model uncertainties. These strategies have been evaluated quantitatively through an experiment including nine participants with an active DAS prototype. The activity of six muscles was measured and used to compute the Mean Effort Index (MEI) which represents the global effort required to maintain the pose. A statistical analysis shows that the four strategies significantly lower the MEI (p-value < 0.001).

Analysis of Healthcare Push and Pull Task via JACK: Predicted Joint Accuracy during Full-Body Simulation

The posture accuracy of full-body dynamic simulation has been successfully evaluated in JACK Siemens software via analyzing two common push and pull tasks. The difference in joint angles between the actual and predicted human movement directly results in the strength of force exposed on the lumbar spine. In this study, the individual factors, such as body height, body weight, trunk and hip flexion, shoulder movement, and muscle strength between genders, have shown a strong association with the adopted postures and exposed spinal forces during task performance. To provide robust ergonomics analysis, these individual variables should be adequately considered in software design for the long-term goal of injury prevention in diverse occupational workplaces.

The Concurrent Control of Motion and Contact Force in the Presence of Predictable Disturbances

The simultaneous control of force and motion is important in everyday activities when humans interact with objects. While many studies have analyzed the control of movement within a perturbing force field, few have investigated its dual aspects of controlling a contact force in nonisometric conditions. The mechanism by which the central nervous system controls forces during movements is still unclear, and it can be elucidated by estimating the mechanical properties of the arm during tasks with concurrent motion and contact force goals. We investigate how arm mechanics change when a force control task is accomplished during low-frequency positional perturbations of the arm. Contrary to many force regulation algorithms implemented in robotics, where contact impedance is decreased to reduce force fluctuations in response to position disturbances, we observed a steady increase of arm endpoint stiffness as the task progressed. Based on this evidence, we propose a theoretical framework suggesting that an internal model of the perturbing trajectory is formed. We observed that force regulation in the presence of predictable positional disturbances is implemented using a position control strategy together with the modulation of the endpoint stiffness magnitude, where the direction of the endpoint stiffness ellipse's major axis is oriented toward the desired force.

Effects of age and sex on shoulder biomechanics and relative effort during functional tasks

Age-related decline in muscle strength can compromise shoulder function, which could increase the effort needed to perform activities of daily living (ADLs). The purpose of this cross-sectional study was to determine for the first time the relative shoulder effort during ADLs in healthy young and older adults. Ten healthy young adults and ten healthy older adults were tested for maximal isokinetic torque and on a set of ADL tasks. Using inverse dynamics, the shoulder torques during ADLs were referenced to the maximal isokinetic torque and relative effort was determined. Older compared to younger adults had >40% lower isokinetic shoulder abduction strength. The ratio of peak joint torque during six ADLs over the maximal isokinetic torque, i.e., relative effort, was higher in old (∼52%) compared with young adults (∼22%, p < 0.05). Relative effort in older adults was over 40% in overhead activities and particularly high in abduction and reaching tasks, over 60%. Healthy older compared with younger adults perform most ADL tasks involving the shoulder joint with nearly twice the level of relative effort. The concomitant reductions in maximal shoulder isokinetic torque and increases in relative effort may be related to the high prevalence of musculoskeletal pain and shoulder dysfunction in old age reported in epidemiological studies.

Simulation of variable impedance as an intervention for upper extremity motor exploration

Current methods in robot-assisted therapy are limited in providing predictions of the effectiveness of interventions. Our approach focuses on how robotic interaction can impact the distribution of movements expressed in the arm. Using data from a previous study with stroke survivors (n=10), we performed simulations to examine how changes in hand endpoint impedance would alter exploratory motion. We present methods for designing a custom training intervention, by relating the desired change in acceleration covariance in planar motion with a corresponding change in inertia matrix. We first characterized motor exploration in terms of overall covariance in acceleration, and secondly as covariance that varies with position in the workspace. Using a forward dynamics simulation of the hand endpoint impedance, we found that the variable change in endpoint inertia resulted in better recovery of acceleration covariance compared to the fixed change in inertia method. These results could significantly impact rehabilitation firstly in terms of design principles for altering coordination patterns through direct assistance. Furthermore, our work might serve to improve therapy by facilitating access to repeated practice of independent joint motion.

Reduced-complexity representation of the human arm active endpoint stiffness for supervisory control of remote manipulation

In this paper, a reduced-complexity model of the human arm endpoint stiffness is introduced and experimentally evaluated for the teleimpedance control of a compliant robotic arm. The modeling of the human arm endpoint stiffness behavior is inspired by human motor control principles on the predominant use of the arm configuration in directional adjustments of the endpoint stiffness profile, and the synergistic effect of muscular activations, which contributes to a coordinated modification of the task stiffness in all Cartesian directions. Calibration and identification of the model parameters are carried out experimentally, using perturbation-based arm endpoint stiffness measurements in different arm configurations and cocontraction levels of the chosen muscles. Consequently, the real-time model is used for the remote control of a compliant robotic arm while executing a drilling task, a representative example of tool use in environments with constraints and dynamic uncertainties. The results of this study illustrate that the proposed model enables the master to execute the remote task by modulation of the directions of the major axes of the endpoint stiffness ellipsoid and its volume using natural arm configurations and the cocontraction of the involved muscles, respectively.

Dynamic Parameter Identification of Subject-Specific Body Segment Parameters Using Robotics Formalism: Case Study Head Complex

Accurate knowledge of body segment inertia parameters (BSIP) improves the assessment of dynamic analysis based on biomechanical models, which is of paramount importance in fields such as sport activities or impact crash test. Early approaches for BSIP identification rely on the experiments conducted on cadavers or through imaging techniques conducted on living subjects. Recent approaches for BSIP identification rely on inverse dynamic modeling. However, most of the approaches are focused on the entire body, and verification of BSIP for dynamic analysis for distal segment or chain of segments, which has proven to be of significant importance in impact test studies, is rarely established. Previous studies have suggested that BSIP should be obtained by using subject-specific identification techniques. To this end, our paper develops a novel approach for estimating subject-specific BSIP based on static and dynamics identification models (SIM, DIM). We test the validity of SIM and DIM by comparing the results using parameters obtained from a regression model proposed by De Leva (1996, “Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters,” J. Biomech., 29(9), pp. 1223–1230). Both SIM and DIM are developed considering robotics formalism. First, the static model allows the mass and center of gravity (COG) to be estimated. Second, the results from the static model are included in the dynamics equation allowing us to estimate the moment of inertia (MOI). As a case study, we applied the approach to evaluate the dynamics modeling of the head complex. Findings provide some insight into the validity not only of the proposed method but also of the application proposed by De Leva (1996, “Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters,” J. Biomech., 29(9), pp. 1223–1230) for dynamic modeling of body segments.

Inexpensive Vision-Based System for the Direct Measurement of Ankle Stiffness During Quiet Standing

We created a sensor-fusion suite for the acquisition of biometric information that can be used for the estimation of human control strategy in a variety of everyday tasks. This work focuses on the experimental validation of the integrated motion capture subsystem based on raster images. Understanding human control strategies utilized in everyday activity requires measurement of several variables that can be grouped as kinematic, dynamic, and biological-feedback variables. Hence, there is a strong need for the acquisition, analysis, and synchronization of the information measured by a variety of transducers. Our system was able to capture the complex dynamics of a flexible robot by means of two inexpensive web cameras without compromising accuracy. After validating the vision system by means of the robotic device, a direct measure of the center of gravity (COG) position during the recovery from a fall was performed on two groups of human subjects separated by age. The instrumental setup was used to estimate how ankle operational stiffness changes as function of age. The results indicate a statistical increase of stiffness for the older group.

Modeling and simulating the neuromuscular mechanisms regulating ankle and knee joint stiffness during human locomotion

This work presents an electrophysiologically and dynamically consistent musculoskeletal model to predict stiffness in the human ankle and knee joints as derived from the joints constituent biological tissues (i.e., the spanning musculotendon units). The modeling method we propose uses electromyography (EMG) recordings from 13 muscle groups to drive forward dynamic simulations of the human leg in five healthy subjects during overground walking and running. The EMG-driven musculoskeletal model estimates musculotendon and resulting joint stiffness that is consistent with experimental EMG data as well as with the experimental joint moments. This provides a framework that allows for the first time observing 1) the elastic interplay between the knee and ankle joints, 2) the individual muscle contribution to joint stiffness, and 3) the underlying co-contraction strategies. It provides a theoretical description of how stiffness modulates as a function of muscle activation, fiber contraction, and interacting tendon dynamics. Furthermore, it describes how this differs from currently available stiffness definitions, including quasi-stiffness and short-range stiffness. This work offers a theoretical and computational basis for describing and investigating the neuromuscular mechanisms underlying human locomotion.

Critical damping conditions for third order muscle models: implications for force control

Experimental results presented in the literature suggest that humans use a position control strategy to indirectly control force rather than direct force control. Modeling the muscle-tendon system as a third-order linear model, we provide an explanation of why an indirect force control strategy is preferred. We analyzed a third-order muscle system and verified that it is required for a faithful representation of muscle-tendon mechanics, especially when investigating critical damping conditions. We provided numerical examples using biomechanical properties of muscles and tendons reported in the literature. We demonstrated that at maximum isotonic contraction, for muscle and tendon stiffness within physiologically compatible ranges, a third-order muscle-tendon system can be under-damped. Over-damping occurs for values of the damping coefficient included within a finite interval defined by two separate critical limits (such interval is a semi-infinite region in second-order models). An increase in damping beyond the larger critical value would lead the system to mechanical instability. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved; thus resulting in an oscillatory free response of the system, independently of the value of the damping. Under such condition, combined with high muscle activation, oscillation of the system can be compensated only by active control.

Experimental measure of arm stiffness during single reaching movements with a time-frequency analysis

We tested an innovative method to estimate joint stiffness and damping during multijoint unfettered arm movements. The technique employs impulsive perturbations and a time-frequency analysis to estimate the arm's mechanical properties along a reaching trajectory. Each single impulsive perturbation provides a continuous estimation on a single-reach basis, making our method ideal to investigate motor adaptation in the presence of force fields and to study the control of movement in impaired individuals with limited kinematic repeatability. In contrast with previous dynamic stiffness studies, we found that stiffness varies during movement, achieving levels higher than during static postural control. High stiffness was associated with elevated reflexive activity. We observed a decrease in stiffness and a marked reduction in long-latency reflexes around the reaching movement velocity peak. This pattern could partly explain the difference between the high stiffness reported in postural studies and the low stiffness measured in dynamic estimation studies, where perturbations are typically applied near the peak velocity point.

Arm stiffness during assisted movement after stroke: the influence of visual feedback and training

Spasticity and muscular hypertonus are frequently found in stroke survivors and may have a significant effect on functional impairment. These abnormal neuro-muscular properties, which are quantifiable by the net impedance of the hand, have a direct consequence on arm mechanics and are likely to produce anomalous motor paths. Literature studies quantifying limb impedance in stroke survivors have focused on multijoint static tasks and single joint movements. Despite this research, little is known about the role of sensory motor integration in post-stroke impedance modulation. The present study elucidates this role by integrating an evaluation of arm impedance into a robotically mediated therapy protocol. Our analysis had three specific objectives: 1) obtaining a reliable measure for the mechanical proprieties of the upper limb during robotic therapy; 2) investigating the effects of robot-assisted training and visual feedback on arm stiffness and viscosity; 3) determining if the stiffness measure and its relationship with either training or visual feedback depend on arm position, speed, and level of assistance. This work demonstrates that the performance improvements produced by minimally assistive robot training are associated with decreased viscosity and stiffness in stroke survivors' paretic arm and that these mechanical impedance components are partially modulated by visual feedback.

Third-Order Muscle Models: The Role of Oscillatory Behavior In Force Control

This paper presents the analysis of a third-order linear differential equation representing a muscle-tendon system, including the identification of critical damping conditions. We analytically verified that this model is required for a faithful representation of muscle-skeletal muscles and provided numerical examples using the biomechanical properties of muscles and tendon reported in the literature. We proved the existence of a theoretical threshold for the ratio between tendon and muscle stiffness above which critical damping can never be achieved, thus resulting in an oscillatory free response of the system, independently of the value of the damping. Oscillation of the limb can be compensated only by active control, which requires creating an internal model of the limb mechanics. We demonstrated that, when admissible, over-damping of the muscle-tendon system occurs for damping values included within a finite interval between two separate critical limits. The same interval is a semi-infinite region in second-order models. Moreover, an increase in damping beyond the second critical point rapidly brings the system to mechanical instability.

Identification of Human Inertia Properties Using a Momentum-Based Approach

This paper presents a momentum-based approach for identifying the barycentric parameters of a human body. The human body is modeled as a multiple rigid-body dynamical system with a tree-type topology using the principle of impulse and momentum. Since the resulting impulse-momentum equations are linear in terms of the unknown barycentric parameters, these parameters can be easily solved using the least-square method or other well-understood solution techniques. The approach does not require measuring or estimating accelerations and internal forces because they do not appear in the impulse-momentum equations and, thus, the resulting identification procedure is less demanding on the measurement and also less sensitive to measurement errors in comparison with other existing methods derived based on Newton-Euler or Lagrangian equations. The momentum-based approach has been studied by dynamics simulations with the consideration of possible measurement errors. The study showed good results.

Comparing Two Computational Mechanisms for Explaining Functional Recovery in Robot-Therapy of Stroke Survivors

In this paper we discuss two possible strategies of movement control that can be used by stroke survivors during rehabilitation robotics training. To perform a reaching task in a minimally assistive force field, subjects either can move following the trajectory provided by the assistive force or they can use an internal representation of a minimum jerk trajectory from their starting position to the target. We used the stiffness and damping values directly estimated from the experimental data to simulate the trajectories that result by taking into account both hypotheses. The comparison of the simulated results with the data collected on four hemiparetic subjects supports the hypothesis that the central nervous system (CNS) is still able to correctly plan the movement, although a normal execution is impaired.

Measuring multi-joint stiffness during single movements: numerical validation of a novel time-frequency approach

This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

Influence of visual feedback in the regulation of arm stiffness following stroke

Stroke survivors strongly rely on visual feedback to control their movements, since segmental reflexes are characterized by an inherent hyper-excitability. To test the effect of visual feedback on the modulation of arm stability we estimated the stiffness of the paretic arm in nine stroke survivors during robot mediated therapy, where subjects trained with and without vision. While several studies found a negligible effect in unimpaired individuals, our results highlighted a marked reduction of stroke survivors' arm stiffness in absence of visual feedback.

Multijoint arm stiffness during movements following stroke: implications for robot therapy

Impaired arm movements in stroke appear as a set of stereotypical kinematic patterns, characterized by abnormal joint coupling, which have a direct consequence on arm mechanics and can be quantified by the net arm stiffness at the hand. The current available measures of arm stiffness during functional tasks have limited clinical use, since they require several repetitions of the same test movement in many directions. Such procedure is difficult to obtain in stroke survivors who have lower fatigue threshold and increased variability compared to unimpaired individuals. The present study proposes a novel, fast quantitative measure of arm stiffness during movements by means of a Time-Frequency technique and the use of a reassigned spectrogram, applied on a trial-by-trial basis with a single perturbation. We tested the technique feasibility during robot mediated therapy, where a robot helped stroke survivors to regain arm mobility by providing assistive forces during a hitting task to 13 targets covering the entire reachable workspace. The endpoint stiffness of the paretic arm was estimated at the end of each hitting movements by suddenly switching of the assistive forces and observing the ensuing recoil movements. In addition, we considered how assistive forces influence stiffness. This method will provide therapists with improved tools to target the treatment to the individual's specific impairment and to verify the effects of the proposed exercises.