Kinematic analysis of the human wrist during pointing tasks

Wrist redundancy management during pointing tasks remains stable over time and in presence of a visuomotor perturbation

Pointing at a screen using wrist and forearm movements is a kinematically redundant task, and the Central Nervous System seems to manage this redundancy by using a simplifying strategy, named Donders' Law for the wrist. In this work we investigated (1) whether this simplifying approach is stable over time and (2) whether a visuomotor perturbation provided in the task space influences the strategy used to solve the redundancy problem. We conducted two experiments asking participants to perform the same pointing task in four different days (first experiment), and providing a visual perturbation, i.e. a visuomotor rotation to the controlled cursor (second experiment), while recording their wrist and forearm rotations. Results showed that the participant-specific wrist redundancy management (described by the Donders' surfaces) (1) neither changes over time (2) nor varies when a visuomotor perturbation is provided in the task space.

Orientation control strategies and adaptation to a visuomotor perturbation in rotational hand movements

Computational approaches to biological motor control are used to discover the building blocks of human motor behaviour. Models explaining features of human hand movements have been studied thoroughly, yet only a few studies attempted to explain the control of the orientation of the hand; instead, they mainly focus on the control of hand translation, predominantly in a single plane. In this study, we present a new methodology to study the way humans control the orientation of their hands in three dimensions and demonstrate it in two sequential experiments. We developed a quaternion-based score that quantifies the geodicity of rotational hand movements and evaluated it experimentally. In the first experiment, participants performed a simple orientation-matching task with a robotic manipulator. We found that rotations are generally performed by following a geodesic in the quaternion hypersphere, which suggests that, similarly to translation, the orientation of the hand is centrally controlled, possibly by optimizing geometrical properties of the hand’s rotation. This result established a baseline for the study of human response to perturbed visual feedback of the orientation of the hand. In the second experiment, we developed a novel visuomotor rotation task in which the rotation is applied on the hand’s rotation, and studied the adaptation of participants to this rotation, and the transfer of the adaptation to a different initial orientation. We observed partial adaptation to the rotation. The patterns of the transfer of the adaptation to a different initial orientation were consistent with the representation of the orientation in extrinsic coordinates. The methodology that we developed allows for studying the control of a rigid body without reducing the dimensionality of the task. The results of the two experiments open questions for future studies regarding the mechanisms underlying the central control of hand orientation. These results can be of benefit for many applications that involve fine manipulation of rigid bodies, such as teleoperation and neurorehabilitation.

Exploiting Spherical Projections To Generate Human-Like Wrist Pointing Movements

The mechanism behind the generation of human movements is of great interest in many fields (e.g. robotics and neuroscience) to improve therapies and technologies. Optimal Feedback Control (OFC) and Passive Motion Paradigm (PMP) are currently two leading theories capable of effectively producing human-like motions, but they require solving nonlinear inverse problems to find a solution. The main benefit of using PMP is the possibility of generating path-independent movements consistent with the stereotypical behaviour observed in humans, while the equivalent OFC formulation is path-dependent. Our results demonstrate how the path-independent behaviour observed for the wrist pointing task can be explained by spherical projections of the planar tasks. The combination of the projections with the fractal impedance controller eliminates the nonlinear inverse problem, which reduces the computational cost compared to previous methodologies. The motion exploits a recently proposed PMP architecture that replaces the nonlinear inverse optimisation with a nonlinear anisotropic stiffness impedance profile generated by the Fractal Impedance Controller, reducing the computational cost and not requiring a task-dependent optimisation.

Lateral differences of the forearm range of motion

Malunion is a common complication of distal radius fracture and often causes a reduction in the range of motion. The measurement of the range of motion is a part of the process for evaluating the final motion after a malunion of a distal radius fracture is diagnosed. However, the amount of range of motion reduced due to the malunion often is calculated upon the assumption that the motion is equal in both forearms. Although this assumption has been questioned, not much work has been conducted which defines the difference in range of motion between the two forearms. In this work, a methodology has been proposed to measure the forearm range of motion using inertial measurement units. The motion was measured in both forearms of a control group. Afterwards, the motion was compared between both forearm sides; then, differences and relationships were drawn. Our results indicated that the forearm rotational motion is larger in the dominant forearm. Moreover, pronation and supination motions differ among the limbs, supination being always larger than pronation. In the dominant forearm, supination is much larger than pronation, while in the non-dominant their magnitudes are rather close. These results provide important data for a more accurate way to determine how the malunion of a fracture or another pathology affects the forearm motion.

Control of redundant pointing movements involving the wrist and forearm

The musculoskeletal system can move in more ways than are strictly necessary, allowing many tasks to be accomplished with a variety of limb configurations. Why some configurations are preferred has been a focus of motor control research, but most studies have focused on shoulder-elbow or whole arm movements. This study focuses on movements involving forearm pronation-supination (PS), wrist flexion-extension (FE), and wrist radial-ulnar deviation (RUD) and elucidates how these three degrees of freedom (DOF) combine to perform the common task of pointing, which only requires two DOF. Although pointing is more sensitive to FE and RUD than to PS and could be easily accomplished with FE and RUD alone, subjects tend to involve a small amount of PS. However, why we choose this behavior has been unknown and is the focus of this paper. With the use of a second-order model with lumped parameters, we tested a number of plausible control strategies involving minimization of work, potential energy, torque, and path length. None of these control schemes robustly predicted the observed behavior. However, an alternative control scheme, hypothesized to control the DOF that were most important to the task (FE and RUD) and ignore the less important DOF (PS), matched the observed behavior well. In particular, the behavior observed in PS appears to be a mechanical side effect caused by unopposed interaction torques. We conclude that moderately sized pointing movements involving the wrist and forearm are controlled by ignoring forearm rotation even though this strategy does not robustly minimize work, potential energy, torque, or path length. NEW & NOTEWORTHY Many activities require us to point our hands in a given direction using wrist and forearm rotations. Although there are infinitely many ways to do this, we tend to follow a stereotyped pattern. Why we choose this pattern has been unknown and is the focus of this paper. After testing a variety of hypotheses, we conclude that the pattern results from a simplifying strategy in which we focus on wrist rotations and ignore forearm rotation.

An Extended Passive Motion Paradigm for Human-Like Posture and Movement Planning in Redundant Manipulators

A major challenge in robotics and computational neuroscience is relative to the posture/movement problem in presence of kinematic redundancy. We recently addressed this issue using a principled approach which, in conjunction with nonlinear inverse optimization, allowed capturing postural strategies such as Donders' law. In this work, after presenting this general model specifying it as an extension of the Passive Motion Paradigm, we show how, once fitted to capture experimental postural strategies, the model is actually able to also predict movements. More specifically, the passive motion paradigm embeds two main intrinsic components: joint damping and joint stiffness. In previous work we showed that joint stiffness is responsible for static postures and, in this sense, its parameters are regressed to fit to experimental postural strategies. Here, we show how joint damping, in particular its anisotropy, directly affects task-space movements. Rather than using damping parameters to fit a posteriori task-space motions, we make the a priori hypothesis that damping is proportional to stiffness. This remarkably allows a postural-fitted model to also capture dynamic performance such as curvature and hysteresis of task-space trajectories during wrist pointing tasks, confirming and extending previous findings in literature.

Task-space separation principle: a force-field approach to motion planning for redundant manipulators

In this work, we address human-like motor planning in redundant manipulators. Specifically, we want to capture postural synergies such as Donders' law, experimentally observed in humans during kinematically redundant tasks, and infer a minimal set of parameters to implement similar postural synergies in a kinematic model. For the model itself, although the focus of this paper is to solve redundancy by implementing postural strategies derived from experimental data, we also want to ensure that such postural control strategies do not interfere with other possible forms of motion control (in the task-space), i.e. solving the posture/movement problem. The redundancy problem is framed as a constrained optimization problem, traditionally solved via the method of Lagrange multipliers. The posture/movement problem can be tackled via the separation principle which, derived from experimental evidence, posits that the brain processes static torques (i.e. posture-dependent, such as gravitational torques) separately from dynamic torques (i.e. velocity-dependent). The separation principle has traditionally been applied at a joint torque level. Our main contribution is to apply the separation principle to Lagrange multipliers, which act as task-space force fields, leading to a task-space separation principle. In this way, we can separate postural control (implementing Donders' law) from various types of tasks-space movement planners. As an example, the proposed framework is applied to the (redundant) task of pointing with the human wrist. Nonlinear inverse optimization (NIO) is used to fit the model parameters and to capture motor strategies displayed by six human subjects during pointing tasks. The novelty of our NIO approach is that (i) the fitted motor strategy, rather than raw data, is used to filter and down-sample human behaviours; (ii) our framework is used to efficiently simulate model behaviour iteratively, until it converges towards the experimental human strategies.

Kinesthetic Feedback During 2DOF Wrist Movements via a Novel MR-Compatible Robot

We demonstrate the interaction control capabilities of the MR-SoftWrist, a novel MR-compatible robot capable of applying accurate kinesthetic feedback to wrist pointing movements executed during fMRI. The MR-SoftWrist, based on a novel design that combines parallel piezoelectric actuation with compliant force feedback, is capable of delivering 1.5 N [Formula: see text] of torque to the wrist of an interacting subject about the flexion/extension and radial/ulnar deviation axes. The robot workspace, defined by admissible wrist rotation angles, fully includes a circle with a 20 deg radius. Via dynamic characterization, we demonstrate capability for transparent operation with low (10% of maximum torque output) backdrivability torques at nominal speeds. Moreover, we demonstrate a 5.5 Hz stiffness control bandwidth for a 14 dB range of virtual stiffness values, corresponding to 25%-125% of the device's physical reflected stiffness in the nominal configuration. We finally validate the possibility of operation during fMRI via a case study involving one healthy subject. Our validation experiment demonstrates the capability of the device to apply kinesthetic feedback to elicit distinguishable kinetic and neural responses without significant degradation of image quality or task-induced head movements. With this study, we demonstrate the feasibility of MR-compatible devices like the MR-SoftWrist to be used in support of motor control experiments investigating wrist pointing under robot-applied force fields. Such future studies may elucidate fundamental neural mechanisms enabling robot-assisted motor skill learning, which is crucial for robot-aided neurorehabilitation.

In Vivo Estimation of Human Forearm and Wrist Dynamic Properties

It is important to estimate the 3 degree-of-freedom (DOF) impedance of human forearm and wrist (i.e., forearm prono-supination, and wrist flexion-extension and radial-ulnar deviation) in motor control and in the diagnosis of altered mechanical resistance following stroke. There is, however, a lack of methods to characterize 3 DOF impedance. Thus, we developed a reliable and accurate impedance estimation method, the distal internal model based impedance control (dIMBIC)-based method, to characterize the 3 DOF impedance, including cross-coupled terms between DOFs, for the first time. Its accuracy and reliability were experimentally validated using a robot with substantial nonlinear joint friction. The 3 DOF human forearm and wrist impedance of eight healthy subjects was reliably characterized, and its linear behavior was verified. Thus, the dIMBIC-based method can provide us with 3 DOF forearm and wrist impedance regardless of nonlinear robot joint friction. It is expected that, with the proposed method, the 3 DOF impedance estimation can promote motor control studies and complement the diagnosis of altered wrist and forearm resistance post-stroke by providing objective impedance estimates, including cross-coupled terms.

A Donders' Like Law for Arm Movements: The Signal not the Noise

Experiments were done to determine whether the starting position of the arm influences its final configuration (posture) when pointing to, or grasping, targets located within the common workspace of the arm. Subjects were asked to point to, or grasp, each of six targets from five, or seven, widely spaced starting positions. We found that the variability (standard deviation) of the arm’s configuration, measured as the angle of inclination of the plane delimited by the arm and forearm, averaged about 4° for comfortable speed pointing movements and was only slightly higher for fast pointing movements. Comfortable speed reaches to grasp the targets were associated with slightly lower variability (3.5°) in final arm configuration. The average variability of repeated movements to a given target from a single start position (3.5°) was comparable to that of movements from different start positions to the same target (4.2°). A small difference in final arm inclination angle, averaged across all subjects and targets, of 3° was found between two pairs of starting positions. This small and possibly idiosyncratic effect is within the “noise” of final arm orientation variability for repeated movements (i.e., 3.5°). Thus, the variability of final posture is not for the most part due to different start positions, it is inherent to movement per se. Our results reconcile conflicting previous studies and are consistent with past works suggesting that a Donders’ like law is indeed largely upheld for unconstrained visually guided arm movements. In summary, considering movements within a typical work space, when the hand is moved voluntarily to a given spatial location the posture of the arm is nearly the same regardless of its starting position. Importantly, variability is inherent to the rule.

Shoulder motor performance assessment in the sagittal plane in children with hemiplegia during single joint pointing tasks

Background

Pointing is a motor task extensively used during daily life activities and it requires complex visuo-motor transformation to select the appropriate movement strategy. The study of invariant characteristics of human movements has led to several theories on how the brain solves the redundancy problem, but the application of these theories on children affected by hemiplegia is limited. This study aims at giving a quantitative assessment of the shoulder motor behaviour in children with hemiplegia during pointing tasks.

Methods

Eight children with hemiplegia were involved in the study and were asked to perform movements on the sagittal plane with both arms, at low and high speed. Subject movements were recorded using an optoelectronic system; a 4-DOF model of children arm has been developed to calculate kinematic and dynamic variables. A set of evaluation indexes has been extracted in order to quantitatively assess whether and how children modify their motor control strategies when perform movements with the more affected or less affected arm.

Results

In low speed movements, no differences can be seen in terms of movement duration and peak velocity between the More Affected arm (MA) and the Less Affected arm (LA), as well as in the main characteristics of movement kinematics and dynamics. As regards fast movements, remarkable differences in terms of strategies of motor control can be observed: while movements with LA did not show any significant difference in Dimensionless Jerk Index (JI) and Dimensionless Torque-change Cost index (TC) between the elevation and lowering phases, suggesting that motor control optimization is similar for movements performed with or against gravity, movements with MA showed a statistically significant increase of both JI and TC during lowering phase.

Conclusions

Results suggest the presence of a different control strategy for fast movements in particular during lowering phase. Results suggest that motor control is not able to optimize Jerk and Torque-change cost functions in the same way when controls the two arms, suggesting that children with hemiplegia do not actively control MA lowering fast movements, in order to take advantage of the passive inertial body properties, rather than to attempt its optimal control.

H-Man: a planar, H-shape cabled differential robotic manipulandum for experiments on human motor control

In the last decades more robotic manipulanda have been employed to investigate the effect of haptic environments on motor learning and rehabilitation. However, implementing complex haptic renderings can be challenging from technological and control perspectives. We propose a novel robot (H-Man) characterized by a mechanical design based on cabled differential transmission providing advantages over current robotic technology. The H-Man transmission translates to extremely simplified kinematics and homogenous dynamic properties, offering the possibility to generate haptic channels by passively blocking the mechanics, and eliminating stability concerns. We report results of experiments characterizing the performance of the device (haptic bandwidth, Z-width, and perceived impedance). We also present the results of a study investigating the influence of haptic channel compliance on motor learning in healthy individuals, which highlights the effects of channel compliance in enhancing proprioceptive information. The generation of haptic channels to study motor redundancy is not easy for actual robots because of the needs of powerful actuation and complex real-time control implementation. The mechanical design of H-Man affords the possibility to promptly create haptic channels by mechanical stoppers (on one of the motors) without compromising the superior backdriveability and high isotropic manipulability. This paper presents a novel robotic device for motor control studies and robotic rehabilitation. The hardware was designed with specific emphasis on the mechanics that result in a system that is easy to control, homogeneous, and is intrinsically safe for use.

Dynamics of wrist and forearm rotations

Human movement generally involves multiple degrees of freedom (DOF) coordinated in a graceful and seemingly effortless manner even though the underlying dynamics are generally complex. Understanding these dynamics is important because it exposes the challenges that the neuromuscular system faces in controlling movement. Despite the importance of wrist and forearm rotations in everyday life, the dynamics of movements involving wrist and forearm rotations are currently unknown. Here we present equations of motion describing the torques required to produce movements combining flexion-extension (FE) and radial-ulnar deviation (RUD) of the wrist and pronation-supination (PS) of the forearm. The total torque is comprised of components required to overcome the effects of inertia, damping, stiffness, and gravity. Using experimentally measured kinematic data and subject-specific impedance parameters (inertia, damping, and stiffness), we evaluated movement torques to test the following hypotheses: the dynamics of wrist and forearm rotations are (1) dominated by stiffness, not inertial or damping effects, (2) significantly coupled through interaction torques due to stiffness and damping (but not inertia), and (3) too complex to be well approximated by a simple, linear model. We found that (1) the dynamics of movements combining the wrist and forearm are similar to wrist rotations in that stiffness dominates over inertial and damping effects (p<0.0001) by approximately an order of magnitude, (2) the DOF of the wrist and forearm are significantly coupled through stiffness, while interactions due to inertia and damping are small, and (3) despite the complexity of the exact equations of motion, the dynamics of wrist and forearm rotations are well approximated by a simple, linear (but still coupled) model (the mean error in predicting torque was less than 1% of the maximum torque). The exact and approximate models are presented for modeling wrist and forearm rotations in future studies.

Accuracy and repeatability of parameter estimation methods from ambulatory data for the wrist joint

In this paper, as a preliminary study, we show that accuracy and repeatability in ambulatory measurements of wrist joint are related to movement conditions which are going to be used in a calibration procedure. We chose two representative in-vivo, non-invasive calibration methods of the human upper limb, from those available in literature, to estimate joint parameters. Developing an analytical model of wrist joint we used sets of synthetic data each of which containing different number of samples, joint covariations and noise to estimate the repeatability and accuracy of the methods in estimation. Afterwards, we used our mechanical mock-up to examine single joint motions as well as the rotation of both joints (i.e. flexion-extension rotation and radial-ulnar deviation) on accuracy and repeatability by calculating the mean and standard deviation of the relative errors. Finally, we show that the accuracy of adapted method (its relative error was less than 7%) is better than the other method in estimating the joint parameters.

The passive stiffness of the wrist and forearm

Because wrist rotation dynamics are dominated by stiffness (Charles SK, Hogan N. J Biomech 44: 614-621, 2011), understanding how humans plan and execute coordinated wrist rotations requires knowledge of the stiffness characteristics of the wrist joint. In the past, the passive stiffness of the wrist joint has been measured in 1 degree of freedom (DOF). Although these 1-DOF measurements inform us of the dynamics the neuromuscular system must overcome to rotate the wrist in pure flexion-extension (FE) or pure radial-ulnar deviation (RUD), the wrist rarely rotates in pure FE or RUD. Instead, understanding natural wrist rotations requires knowledge of wrist stiffness in combinations of FE and RUD. The purpose of this report is to present measurements of passive wrist stiffness throughout the space spanned by FE and RUD. Using a rehabilitation robot designed for the wrist and forearm, we measured the passive stiffness of the wrist joint in 10 subjects in FE, RUD, and combinations. For comparison, we measured the passive stiffness of the forearm (in pronation-supination), as well. Our measurements in pure FE and RUD agreed well with previous 1-DOF measurements. We have linearized the 2-DOF stiffness measurements and present them in the form of stiffness ellipses and as stiffness matrices useful for modeling wrist rotation dynamics. We found that passive wrist stiffness was anisotropic, with greater stiffness in RUD than in FE. We also found that passive wrist stiffness did not align with the anatomical axes of the wrist; the major and minor axes of the stiffness ellipse were rotated with respect to the FE and RUD axes by ∼20°. The direction of least stiffness was between ulnar flexion and radial extension, a direction used in many natural movements (known as the "dart-thrower's motion"), suggesting that the nervous system may take advantage of the direction of least stiffness for common wrist rotations.

Cartesian stiffness for wrist joints: analysis on the Lie group of 3D rotations and geometric approximation for experimental evaluation

This paper is concerned with the analysis and the numerical evaluation from experimental measurements of the static, Cartesian stiffness of wrist joints, in particular the human wrist. The primary aim is to extend from Euclidean spaces to so(3), the group of rigid body rotations, previous methods for assessing the end-point stiffness of the human arm, typically performed via a robotic manipulandum. As a first step, the geometric definition of Cartesian stiffness from current literature is specialised to the group so(3). Emphasis is placed on the choice of the unique, natural, affine connection on so(3) which guarantees symmetry of the stiffness matrix in presence of conservative fields for any configuration, also out of equilibrium. As the main contribution of this study, a coordinate-independent approximation based on the geometric notion of geodesics is proposed which provides a working equation for evaluating stiffness directly from experimental measurements. Finally, a graphical representation of the stiffness is discussed which extends the ellipse method often used for end-point stiffness visualisation and which is suitable to compare stiffness matrices evaluated at different configurations.

Pointing with the wrist: a postural model for Donders' law

The central nervous system uses stereotypical combinations of the three wrist/forearm joint angles to point in a given (2D) direction in space. In this paper, we first confirm and analyze this Donders' law for the wrist as well as the distributions of the joint angles. We find that the quadratic surfaces fitting the experimental wrist configurations during pointing tasks are characterized by a subject-specific Koenderink shape index and by a bias due to the prono-supination angle distribution. We then introduce a simple postural model using only four parameters to explain these characteristics in a pointing task. The model specifies the redundancy of the pointing task by determining the one-dimensional task-equivalent manifold (TEM), parameterized via wrist torsion. For every pointing direction, the torsion is obtained by the concurrent minimization of an extrinsic cost, which guarantees minimal angle rotations (similar to Listing's law for eye movements) and of an intrinsic cost, which penalizes wrist configurations away from comfortable postures. This allows simulating the sequence of wrist orientations to point at eight peripheral targets, from a central one, passing through intermediate points. The simulation first shows that in contrast to eye movements, which can be predicted by only considering the extrinsic cost (i.e., Listing's law), both costs are necessary to account for the wrist/forearm experimental data. Second, fitting the synthetic Donders' law from the simulated task with a quadratic surface yields similar fitting errors compared to experimental data.

Motor adaptation during redundant tasks with the wrist

This study analyzes motor adaptation during a redundant tasks with the wrist. The goal is threefold: (i) understanding if motor adaptation also occurs when CNS is involved in the solution of the redundancy problem; (ii) addressing whether motor strategies used to solve redundancy (i.e Donders' law) are disrupted or not during adaptation; (iii) verifying if motor strategies remain the same during adaptation and washout or they themselves adapt. First of all, our data confirm that CNS adapts its movements to the perturbation also when it is committed in the execution of a redundant task. Secondly, we showed that motor strategies used to solve redundancy (i.e Donders' law) are not disrupted during adaptation, since absolute values of thickness during the whole protocol remain in the range of physiological values. Lastly, analysis of the curvature of Donders' surfaces suggests that motor strategies, such as Donders' law, remain invariant during motor adaptation in redundant tasks.