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

Characterization of Human Shoulder Joint Stiffness Across 3D Arm Postures and Its Sex Differences

Understanding the characteristics of shoulder joint stiffness can offer insights into how the shoulder joint contributes to arm stability and assists in various arm postures and movements. This study aims to characterize posture-dependent shoulder stiffness in a three-dimensional (3D) space and investigate its potential sex differences. A multi-degree-of-freedom, parallel-actuated shoulder exoskeleton robot was used' to perturb the participant's shoulder joint and measure the resulting torque responses while participants relaxed their shoulder muscles. The group average results of 40 healthy individuals (20 males and 20 females) revealed that arm postures significantly affect shoulder stiffness, particularly in postures involving shoulder flexion/extension and horizontal flexion/extension. Shoulder stiffness consistently increased as the shoulder flexion angle decreased and the shoulder horizontal flexion/extension approached the limit of its range of motion. The comparative group results between males and females indicated that shoulder stiffness in males was greater than that in females across all 15 arm postures measured in this study. Even after normalizing the data by subject body mass, the female group showed significantly lower stiffness than the male group in 12 out of the 15 arm postures. The results highlight that 3D arm postures and sex significantly affect shoulder stiffness even under relaxed muscles. This study provides valuable foundations for future studies aimed at characterizing shoulder stiffness in the context of active muscles and dynamic movement tasks, evaluating changes in shoulder stiffness following neuromuscular injuries, and formulating rehabilitative training protocols for individuals suffering from shoulder problems.

A robot for overground physical human-robot interaction experiments

Many anticipated physical human-robot interaction (pHRI) applications in the near future are overground tasks such as walking assistance. For investigating the biomechanics of human movement during pHRI, this work presents Ophrie, a novel interactive robot dedicated for physical interaction tasks with a human in overground settings. Unique design requirements for pHRI were considered in implementing the one-arm mobile robot, such as the low output impedance and the ability to apply small interaction forces. The robot can measure the human arm stiffness, an important physical quantity that can reveal human biomechanics during overground pHRI, while the human walks alongside the robot. This robot is anticipated to enable novel pHRI experiments and advance our understanding of intuitive and effective overground pHRI.

Humans modulate arm stiffness to facilitate motor communication during overground physical human-robot interaction

Humans can physically interact with other humans adeptly. Some overground interaction tasks, such as guiding a partner across a room, occur without visual and verbal communication, which suggests that the information exchanges occur through sensing movements and forces. To understand the process of motor communication during overground physical interaction, we hypothesized that humans modulate the mechanical properties of their arms for increased awareness and sensitivity to ongoing interaction. For this, we used an overground interactive robot to guide a human partner across one of three randomly chosen paths while occasionally providing force perturbations to measure the arm stiffness. We observed that the arm stiffness was lower at instants when the robot's upcoming trajectory was unknown compared to instants when it was predicable - the first evidence of arm stiffness modulation for better motor communication during overground physical interaction.

Estimation of Involuntary Components of Human Arm Impedance in Multi-Joint Movements via Feedback Jerk Isolation

Stable and efficient coordination in physical human-robot interaction requires consideration of human feedback behavior. In unpredictable tasks, where voluntary cognitive feedback is too slow to guarantee desired task execution, the human must rely on involuntary intrinsic and reflexive feedback. The combined effects of these two feedback mechanisms and the inertial characteristics can be summarized in the involuntary impedance components. In this work, we present a method for the estimation of the involuntary impedance components of the human arm in multi-joint movements. We apply force perturbations to evoke feedback jerks that can be isolated using a high pass filter and limit the duration of the estimation interval to guarantee exclusion of voluntary cognitive feedback. Dynamic regressor representation of the rigid body dynamics of the arm and first order Taylor series expansion of the feedback behavior yield a model that is linear in the involuntary impedance components. The constant values of the inertial parameters are estimated in a static posture maintenance task and subsequently inserted to estimate the remaining components in a dynamic movement task. The method is validated with simulated data of a neuromechanical model of the human arm and its performance is compared to established methods from the literature. The results of the validation demonstrate superior estimation performance for moderate movement velocities, and less influence of the variability of the movements. The applicability to real data and the plausibility of the limited estimation interval are successfully demonstrated in an experiment with human participants.

On Primitives in Motor Control

The concept of primitives has been used in motor control both as a theoretical construct and as a means of describing the results of experimental studies involving multiple moving elements. This concept is close to Bernstein’s notion of engrams and level of synergies. Performance primitives have been explored in spaces of peripheral variables but interpreted in terms of neural control primitives. Performance primitives reflect a variety of mechanisms ranging from body mechanics to spinal mechanisms and to supraspinal circuitry. This review suggests that primitives originate at the task level as preferred time functions of spatial referent coordinates or at mappings from higher level referent coordinates to lower level, frequently abundant, referent coordinate sets. Different patterns of performance primitives can emerge depending, in particular, on the external force field.

Improving Healthcare Access: A Preliminary Design of a Low-Cost Arm Rehabilitation Device

A low-cost continuous passive motion (CPM) machine, the Gannon Exoskeleton for Arm Rehabilitation (GEAR), was designed. The focus of the machine is on the rehabilitation of primary functional movements of the arm. The device developed integrates two mechanisms consisting of a four-bar linkage and a sliding rod prismatic joint mechanism that can be mounted to a normal chair. When seated, the patient is connected to the device via a padded cuff strapped on the elbow. A set of springs have been used to maintain the system stability and help the lifting of the arm. A preliminary analysis via analytical methods is used to determine the initial value of the springs to be used in the mechanism given the desired gravity compensatory force. Subsequently, a multibody simulation was performed with the software simwise 4D by Design Simulation Technologies (DST). The simulation was used to optimize the stiffness of the springs in the mechanism to provide assistance to raising of the patient's arm. Furthermore, the software can provide a finite element analysis of the stress induced by the springs on the mechanism and the external load of the arm. Finally, a physical prototype of the mechanism was fabricated using polyvinyl chloride (PVC) pipes and commercial metal springs, and the reaching space was measured using motion capture. We believed that the GEAR has the potential to provide effective passive movement to individuals with no access to postoperative or poststroke rehabilitation therapy.

Endpoint stiffness magnitude increases linearly with a stronger power grasp

Humans can increase the endpoint stiffness of their arm to reduce self-generated movement variability and to reject unpredictable perturbations from the environment, like during handheld drilling, thereby increasing movement precision. Existing methods to estimate changes in the endpoint stiffness use robotic interfaces to apply position or force perturbations to measure the arm's dynamic response. We propose an alternative method of measuring changes in the power grasp force to estimate adaptations in the magnitude of the arm's endpoint stiffness. To validate our method, we examined how the strength of the power grasp, when holding onto a robotic manipulandum, affected the arm's endpoint stiffness in three different locations of the workspace. The endpoint stiffness magnitude increased linearly with the grasp force, and this linear relationship did not depend on the arm's posture or position in the workspace. The endpoint stiffness may have increased as a combination of greater grasp stiffness and greater arm stiffness, since larger co-contraction was observed in the elbow and shoulder with a stronger grasp. Changes in the grasp force could serve as a metric in assessing how humans adapt their endpoint stiffness magnitude.

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.

Stiffness as a control factor for object manipulation

During manipulation, force is exerted with the expectation that an object will move in an intended manner. This prediction is a learned coordination between force and movement. Mechanically, impedance is a way to describe this coordination, and object interaction could be anticipated by setting impedance before the hand moves the object. This strategy would be especially important at the end of a reach, because feedback is ineffective for rapid force changes. Since mechanical impedance is not subject to the time delays of feedback, it can, if set properly, produce the desired motion on impact. We examined this possibility by instructing subjects to move a handle to a specific target position along a track. The handle was locked in place until the subject exerted enough force to cross a threshold; the handle was then released abruptly to move along the track. We hypothesized that this ballistic release task would encourage subjects to modify impedance in anticipation of the upcoming movement and found that one component of impedance, stiffness, varied in a way that matched the behavioral demands of the task. Analysis suggests that this stiffness was set before the handle moved and governed the subsequent motion. We also found separate components of muscle activity that corresponded to stiffness and to changes in force. Our results show that subjects used a robust and efficient strategy to coordinate force and displacement by modulating muscle activity in a way that was behaviorally relevant in the task.NEW & NOTEWORTHY The arm can behave like a spring, and this mechanical behavior can be advantageous in situations requiring rapid changes in force and/or displacement. Selection of a proper "virtual" spring before the occurrence of a rapid transient could facilitate a desired responsive movement. We show that these spring-like arm mechanics, set in anticipation of an instantaneous force change, function as an efficient strategy to control movement when feedback is ineffective.

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.

On the Value of Estimating Human Arm Stiffness during Virtual Teleoperation with Robotic Manipulators

Teleoperated robotic systems are widely spreading in multiple different fields, from hazardous environments exploration to surgery. In teleoperation, users directly manipulate a master device to achieve task execution at the slave robot side; this interaction is fundamental to guarantee both system stability and task execution performance. In this work, we propose a non-disruptive method to study the arm endpoint stiffness. We evaluate how users exploit the kinetic redundancy of the arm to achieve stability and precision during the execution of different tasks with different master devices. Four users were asked to perform two planar trajectories following virtual tasks using both a serial and a parallel link master device. Users' arm kinematics and muscular activation were acquired and combined with a user-specific musculoskeletal model to estimate the joint stiffness. Using the arm kinematic Jacobian, the arm end-point stiffness was derived. The proposed non-disruptive method is capable of estimating the arm endpoint stiffness during the execution of virtual teleoperated tasks. The obtained results are in accordance with the existing literature in human motor control and show, throughout the tested trajectory, a modulation of the arm endpoint stiffness that is affected by task characteristics and hand speed and acceleration.

Changes of Shoulder, Elbow, and Wrist Stiffness Matrix Post Stroke

Stroke affects multiple joints in the arm with stereotypical patterns of arm deformity involving the shoulder, elbow, wrist, and hand and with disrupted coordination of multiple joints in active movements. However, there is a lack of systematic methods to evaluate multi-joints and multi-degree of freedoms (DOF) neuro-mechanical changes, especially for complex systems with three or more joints/DOFs involved. This paper used a novel systematic method to characterize dynamics and control of the shoulder, elbow, and wrist of the human arm individually and simultaneously, including the couplings across the multiple joints during controlled movements. A novel method was developed to decompose the complex system into manageable single-joint level for more reliable characterizations. The method was used in clinical studies to characterize the multi-joint changes associated with spastic impaired arm of 11 patients post stroke and 12 healthy controls. It was found that stroke survivors showed not only increased stiffness at the individual joints locally but also significantly higher couplings across the joints. The relative increases in couplings are often higher than that of the local joint stiffness. The multi-joint characterization provided a tool to characterize impairment of individual patients, which would allow more focused impairment-specific treatment. In general, the decomposition method can be used for even more complex systems, making characterization of intractable system dynamics of three or more joints/DOFs manageable.

Proximal-distal differences in movement smoothness reflect differences in biomechanics

Smoothness is a hallmark of healthy movement. Past research indicates that smoothness may be a side product of a control strategy that minimizes error. However, this is not the only reason for smooth movements. Our musculoskeletal system itself contributes to movement smoothness: the mechanical impedance (inertia, damping, and stiffness) of our limbs and joints resists sudden change, resulting in a natural smoothing effect. How the biomechanics and neural control interact to result in an observed level of smoothness is not clear. The purpose of this study is to 1) characterize the smoothness of wrist rotations, 2) compare it with the smoothness of planar shoulder-elbow (reaching) movements, and 3) determine the cause of observed differences in smoothness. Ten healthy subjects performed wrist and reaching movements involving different targets, directions, and speeds. We found wrist movements to be significantly less smooth than reaching movements and to vary in smoothness with movement direction. To identify the causes underlying these observations, we tested a number of hypotheses involving differences in bandwidth, signal-dependent noise, speed, impedance anisotropy, and movement duration. Our simulations revealed that proximal-distal differences in smoothness reflect proximal-distal differences in biomechanics: the greater impedance of the shoulder-elbow filters neural noise more than the wrist. In contrast, differences in signal-dependent noise and speed were not sufficiently large to recreate the observed differences in smoothness. We also found that the variation in wrist movement smoothness with direction appear to be caused by, or at least correlated with, differences in movement duration, not impedance anisotropy.NEW & NOTEWORTHY This article presents the first thorough characterization of the smoothness of wrist rotations (flexion-extension and radial-ulnar deviation) and comparison with the smoothness of reaching (shoulder-elbow) movements. We found wrist rotations to be significantly less smooth than reaching movements and determined that this difference reflects proximal-distal differences in biomechanics: the greater impedance (inertia, damping, stiffness) of the shoulder-elbow filters noise in the command signal more than the impedance of the wrist.

Vibrations of Fractal Structures: On the Nonlinearities of Damping by Branching

To study the effect of damping due to branching in trees and fractal structures, a harmonic analysis was performed on a finite element model using commercially available software. The model represented a three-dimensional (3D) fractal treelike structure, with properties based on oak wood and with several branch configurations. As branches were added to the model using a recursive algorithm, the effects of damping due to branching became apparent: the first natural frequency amplitude decreased, the first peak widened, and the natural frequency decreased, whereas higher frequency oscillations remained mostly unaltered. To explain this nonlinear effect observable in the spectra of branched structures, an analytical interpretation of the damping was proposed. The analytical model pointed out the dependency of Cartesian damping from the Coriolis forces and their derivative with respect to the angular velocity of each branch. The results provide some insight on the control of chaotic systems. Adding branches can be an effective way to dampen slender structures but is most effective for large deformation of the structure.

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.

Unintentional changes in the apparent stiffness of the multi-joint limb

We explored the phenomenon of unintentional changes in the apparent stiffness of the human arm produced by transient changes in the external force. The subjects performed a positional task against a constant baseline force and were instructed not to react to changes in the force. A HapticMaster robot produced a smooth force increase (a perturbation) leading to a hand movement, followed by a dwell time. No visible hand drift was observed during the dwell time. After the robot force dropped to its initial baseline value, the hand moved toward the initial position but stopped short of it. Small perturbations were applied at different time intervals along different directions during the dwell time. Arm apparent stiffness distribution in a horizontal plane was approximated with an ellipse. The apparent stiffness magnitude along the main axis of the ellipse showed a non-monotonic increase with dwell time, while the apparent stiffness along the minor axis did not change significantly. We interpreted the early part of the changes in the apparent stiffness as due to peripheral muscle properties. The later part is interpreted as caused by a combination of two processes: a drift in the referent hand coordinate due to the hypothesized back-coupling between the referent and actual hand coordinates and an implicit instruction to keep the hand steady when no changes in robot-generated force took place. The data provide support for the idea of back-coupling between the referent and actual body configurations, which may be an important contributor to stability of motor actions.