A robotic manipulator for the characterization of two-dimensional dynamic stiffness using stochastic displacement perturbations

Validation of Methods for Estimation of Knee Joint Mechanical Impedance During Locomotion Using a Torque-Controllable Knee Exoskeleton

The mechanical impedance of the joints of the leg governs the body's response to external disturbances, and its regulation is essential for the completion of tasks of daily life. However, it is still unclear how this quantity is regulated at the knee during dynamic tasks. In this work, we introduce a method to estimate the mechanical impedance of spring-mass systems using a torque-controllable exoskeleton with the intention of extending these methods to characterize the mechanical impedance of the human knee during locomotion. We characterize system bandwidth and intrinsic impedance and present a perturbation-based methodology to identify the mechanical impedance of known spring-mass systems. Our approach was able to obtain accurate estimates of stiffness and inertia, with errors under 3% and ∼13-16%, respectively. This work provides a qualitative and quantitative foundation that will enable accurate estimates of knee joint impedance during locomotion in future works.

On the effect of muscular cocontraction on the 3-D human arm impedance

Humans have the inherent ability to perform highly dexterous tasks with their arms, involving maintenance of posture, movement, and interaction with the environment. The latter requires the human to control the dynamic characteristics of the upper limb musculoskeletal system. These characteristics are quantitatively represented by inertia, damping, and stiffness, which are measures of mechanical impedance. Many previous studies have shown that arm posture is a dominant factor in determining the end point impedance on a horizontal plane. This paper presents the characterization of the end point impedance of the human arm in 3-D space. Moreover, it models the regulation of the arm impedance with muscle cocontraction. The characterization is made by route of experimental trials where human subjects maintained arm posture while their arms were perturbed by a robot arm. Furthermore, the subjects were asked to control the level of their arm muscles' cocontraction, using visual feedback, in order to investigate the effect of muscle cocontraction on the arm impedance. The results of this study show an anisotropic increase of arm stiffness due to muscle cocontraction. These results could improve our understanding of the human arm biomechanics, as well as provide implications for human motor control-specifically the control of arm impedance through muscle cocontraction.

Measuring the dynamic impedance of the human arm without a force sensor

Rehabilitation robots may be used to accurately measure the mechanical impedance of the human arm in order to quantitatively assess the motor function of a patient undergoing neurorehabilitation therapy. However, the high cost of these robotic systems and their required sensors has posed a barrier to widespread clinical use. We present a technique to measure the mechanical impedance of the human arm without the need for a physical force sensor to measure human-robot interaction forces. Instead, these forces are accurately estimated by a virtual sensor that incorporates the robot's kinematics and dynamics, along with acceleration measurements from an inexpensive accelerometer. The identification techniques are validated on a mass-spring system of known impedance and are subsequently applied to data collected from the human arm.

A novel mechatronic system for measuring end-point stiffness: mechanical design and preliminary tests

Measuring arm stiffness is of great interest for many disciplines from biomechanics to medicine especially because modulation of impedance represents one of the main mechanism underlying control of movement and interaction with external environment. Previous works have proposed different methods to identify multijoint hand stiffness by using planar or even tridimensional haptic devices, but the associated computational burden makes them not easy to implement. We present a novel mechanism conceived for measuring multijoint planar stiffness by a single measurement and in a reduced execution time. A novel mechanical rotary device applies cyclic radial perturbation to human arm of a known displacement and the force is acquired by means of a 6-axes commercial load cell. The outcomes suggest that the system is not only reliable but allows obtaining a bi-dimensional estimation of arm stiffness in reduced amount of time and the results are comparable with those reported in previous researches.

A portable air jet actuator device for mechanical system identification

System identification of limb mechanics can help diagnose ailments and can aid in the optimization of robotic limb control parameters and designs. An interesting fluid phenomenon--the Coandă effect--is utilized in a portable actuator to provide a stochastic binary force disturbance to a limb system. The design of the actuator is approached with the goal of creating a portable device which could be deployed on human or robotic limbs for in situ mechanical system identification. The viability of the device is demonstrated by identifying the parameters of an underdamped elastic beam system with fixed inertia and stiffness and variable damping. The nonparametric compliance impulse response yielded from the system identification is modeled as a second-order system and the resultant parameters are found to be in excellent agreement with those found using more traditional system identification techniques. The current design could be further miniaturized and developed as a portable, wireless, unrestrained mechanical system identification instrument for less intrusive and more widespread use.

Preliminary design of a novel system for estimating end-point stiffness

Quantification of arm stiffness is of great interest for a wide group of different research branches, because modulation of muscular stiffness represents the principal mechanism of motor control of movements. Past literature concentrated efforts in defining different methods to identify multijont hand stiffness, but the required computational burden make them hard to implelement. In the present work we aim to propose a novel design of a single degree of freedom mechanism conceived to estimate arm stiffness in a reduced amount of time; a rotary mechanism coupled to a commercial six axes force sensor allows to apply known cyclic radial perturbation to the human arm and acquiring the restoring forces. The outcomes have reported that the device is reliable and stiffness measurements on a test bench can be performed in a reduced amount of time (about 1 second). A modular system has been also developed to conduct experiment on humans while performing motor adaptation.

Stochastic estimation of human arm impedance under nonlinear friction in robot joints: a model study

The basic assumption of stochastic human arm impedance estimation methods is that the human arm and robot behave linearly for small perturbations. In the present work, we have identified the degree of influence of nonlinear friction in robot joints to the stochastic human arm impedance estimation. Internal model based impedance control (IMBIC) is then proposed as a means to make the estimation accurate by compensating for the nonlinear friction. From simulations with a nonlinear Lugre friction model, it is observed that the reliability and accuracy of the estimation are severely degraded with nonlinear friction: below 2 Hz, multiple and partial coherence functions are far less than unity; estimated magnitudes and phases are severely deviated from that of a real human arm throughout the frequency range of interest; and the accuracy is not enhanced with an increase of magnitude of the force perturbations. In contrast, the combined use of stochastic estimation and IMBIC provides with accurate estimation results even with large friction: the multiple coherence functions are larger than 0.9 throughout the frequency range of interest and the estimated magnitudes and phases are well matched with that of a real human arm. Furthermore, the performance of suggested method is independent of human arm and robot posture, and human arm impedance. Therefore, the IMBIC will be useful in measuring human arm impedance with conventional robot, as well as in designing a spatial impedance measuring robot, which requires gearing.

A modular planar robotic manipulandum with end-point torque control

Robotic manipulanda are extensively used in investigation of the motor control of human arm movements. They permit the application of translational forces to the arm based on its state and can be used to probe issues ranging from mechanisms of neural control to biomechanics. However, most current designs are optimized for studying either motor learning or stiffness. Even fewer include end-point torque control which is important for the simulation of objects and the study of tool use. Here we describe a modular, general purpose, two-dimensional planar manipulandum (vBOT) primarily optimized for dynamic learning paradigms. It employs a carbon fibre arm arranged as a parallelogram which is driven by motors via timing pulleys. The design minimizes the intrinsic dynamics of the manipulandum without active compensation. A novel variant of the design (WristBOT) can apply torques at the handle using an add-on cable drive mechanism. In a second variant (StiffBOT) a more rigid arm can be substituted and zero backlash belts can be used, making the StiffBOT more suitable for the study of stiffness. The three variants can be used with custom built display rigs, mounting, and air tables. We investigated the performance of the vBOT and its variants in terms of effective end-point mass, viscosity and stiffness. Finally we present an object manipulation task using the WristBOT. This demonstrates that subjects can perceive the orientation of the principal axis of an object based on haptic feedback arising from its rotational dynamics.

Stochastic estimation of arm mechanical impedance during robotic stroke rehabilitation

This paper presents a stochastic method to estimate the multijoint mechanical impedance of the human arm suitable for use in a clinical setting, e.g., with persons with stroke undergoing robotic rehabilitation for a paralyzed arm. In this context, special circumstances such as hypertonicity and tissue atrophy due to disuse of the hemiplegic limb must be considered. A low-impedance robot was used to bring the upper limb of a stroke patient to a test location, generate force perturbations, and measure the resulting motion. Methods were developed to compensate for input signal coupling at low frequencies apparently due to human-machine interaction dynamics. Data was analyzed by spectral procedures that make no assumption about model structure. The method was validated by measuring simple mechanical hardware and results from a patient's hemiplegic arm are presented.

Robotics and virtual reality: a perfect marriage for motor control research and rehabilitation

This article's goal is to outline the motivations, progress, and future objectives for the development of a state-of-the-art device that allows humans to visualize and feel synthetic objects superimposed on the physical world. The programming flexibility of these devices allows for a variety of scientific questions to be answered in psychology, neurophysiology, rehabilitation, haptics, and automatic control. The benefits are most probable in rehabilitation of brain-injured patients, for whom the costs are high, therapist time is limited, and repetitive practice of movements has been shown to be beneficial. Moreover, beyond simple therapy that guides, strengthens, or stretches, the technology affords a variety of exciting potential techniques that can combine our knowledge of the nervous system with the tireless, precise, and swift capabilities of a robot. Because this is a prototype, the system will also guide new experimental methods by probing the levels of quality that are necessary for future design cycles and related technology. Very important to the project is the early and intimate involvement of therapists and other clinicians in the design of software and its user interface. Inevitably, it should also lead the way to new modes of practice and to the commercialization of haptic/graphic systems.

A force-controlled planar haptic device for movement control analysis of the human arm

This paper describes the design and application of a haptic device to study the mechanical properties of the human arm during interaction with compliant environments. Estimates of the human endpoint admittance can be obtained by recording position deviations as a result of force perturbations. Previous studies attempted to estimate the impedance by recording force as a result of position perturbations, but these experiments do not require a feasible task of human beings. A general problem of force-controlled haptic devices is the occurrence of contact instability, especially where a small virtual mass is required. This negative effect is reduced by the use of a lightweight but stiff manipulator and a robust servo-based admittance controller. The virtual admittance is accurate to at least 13 Hz, attaining a minimum virtual mass of 1.7 kg (isotropic, without damping and stiffness). The properties of known test loads were estimated with an accuracy higher than 98%, up to 20 Hz. The application of the manipulator is evaluated by an experiment with a subject performing a position maintenance task. With this device it is possible to study the adaptability of the neuromuscular system to a variety of environments, enabling a new and functional approach to human motion research.

Closed-loop multivariable system identification for the characterization of the dynamic arm compliance using continuous force disturbances: a model study

This study presents a new multivariable closed-loop identification technique for estimating the dynamic compliance of the multijoint human arm during posture maintenance. The method is designed for the application of continuous force disturbances that facilitate interaction of the limb with the environment. The dynamic compliance of the arm arises from different physiological mechanisms and is important for maintaining stable postures and to suppress disturbances. Estimates can be useful to analyze the ability of the nervous system to adapt the arm compliance to different types of disturbances and environments. The technique is linear and requires no a priori knowledge of the system. Linear system behavior is justified for posture tasks where the hand position deviates slightly from a reference position. Interaction results in a closed-loop configuration of arm and environment. The problem with previous methods is the restriction to open-loop systems. With the current technique, the dynamic arm compliance is separately estimated from the closed-loop. The accuracy of the identification technique is tested by simulations for different values of the dynamic compliance of the arm and environment and for different methodological parameters. It is concluded that the identification technique is accurate, even for short observation periods and severe noise.

Voluntary control of static endpoint stiffness during force regulation tasks

The goals of this study were to determine the degree to which subjects could voluntarily modulate static endpoint stiffness orientation and to quantify the effects of simultaneously generated voluntary endpoint forces on this ability. Static endpoint stiffness, which characterizes the relationship between externally imposed displacements of the hand and the elastic forces generated in response, was estimated in real time during the application of planar, stochastic perturbations of endpoint position. This estimation was accomplished using a real-time parametric identification algorithm on measured force and position data. Subjects were provided with real-time visual feedback of endpoint stiffness, and their ability to modulate the orientation of maximum static stiffness was measured for different endpoint force magnitudes and directions. We found that individuals can voluntarily change stiffness orientation but that the magnitude of these changes is small, the range of available stiffness orientations decreases as endpoint force exertion increases, and endpoint force direction significantly constrains direction and magnitude of the stiffness orientations that can be achieved. Given these findings it appears unlikely that static endpoint stiffness orientation is controlled independently of force by voluntary neural mechanisms during postural tasks.

Postural arm control following cervical spinal cord injury

This study used estimates of dynamic endpoint stiffness to quantify postural arm stability following cervical spinal cord injury (SCI) and to investigate how this stability was affected by functional neuromuscular stimulation (FNS). Measurements were made in the horizontal plane passing through the glenohumeral joint on three SCI-impaired arms, which ranged in functional level from a weak C5 to a strong C6. Endpoint stiffness, which characterizes the relationship between externally imposed hand displacements and the resultant forces, was estimated during the application of planar, stochastic perturbations to each arm. These estimates were used in conjunction with voluntary endpoint force measurements to quantify stability and strength during voluntary contractions and during voluntary contractions in the presence of triceps FNS. The primary findings were: 1) the differences in the force generating capabilities of these arms were due primarily to differences in shoulder strength; 2) measurements of strength alone could not be used to predict arm stability; and 3) triceps FNS improved postural arm stability for all tested conditions. These results suggest strategies for improved control of FNS systems designed to restore arm function following cervical SCI and underscore the importance of examining the effects of FNS on both strength and stability.