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

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.

Estimating Human Wrist Stiffness during a Tooling Task

In this work, we propose a practical approach to estimate human joint stiffness during tooling tasks for the purpose of programming a robot by demonstration. More specifically, we estimate the stiffness along the wrist radial-ulnar deviation while a human operator performs flexion-extension movements during a polishing task. The joint stiffness information allows to transfer skills from expert human operators to industrial robots. A typical hand-held, abrasive tool used by humans during finishing tasks was instrumented at the handle (through which both robots and humans are attached to the tool) to assess the 3D force/torque interactions between operator and tool during finishing task, as well as the 3D kinematics of the tool itself. Building upon stochastic methods for human arm impedance estimation, the novelty of our approach is that we rely on the natural variability taking place during the multi-passes task itself to estimate (neuro-)mechanical impedance during motion. Our apparatus (hand-held, finishing tool instrumented with motion capture and multi-axis force/torque sensors) and algorithms (for filtering and impedance estimation) were first tested on an impedance-controlled industrial robot carrying out the finishing task of interest, where the impedance could be pre-programmed. We were able to accurately estimate impedance in this case. The same apparatus and algorithms were then applied to the same task performed by a human operators. The stiffness values of the human operator, at different force level, correlated positively with the muscular activity, measured during the same task.

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.

Hyperstaticity for ergonomie design of a wrist exoskeleton

Increasing the level of transparency in rehabilitation devices has been one of the main goals in robot-aided neurorehabilitation for the past two decades. This issue is particularly important to robotic structures that mimic the human counterpart's morphology and attach directly to the limb. Problems arise for complex joints such as the human wrist, which cannot be accurately matched with a traditional mechanical joint. In such cases, mechanical differences between human and robotic joint cause hyperstaticity (i.e. overconstraint) which, coupled with kinematic misalignments, leads to uncontrolled force/torque at the joint. This paper focuses on the prono-supination (PS) degree of freedom of the forearm. The overall force and torque in the wrist PS rotation is quantified by means of a wrist robot. A practical solution to avoid hyperstaticity and reduce the level of undesired force/torque in the wrist is presented, which is shown to reduce 75% of the force and 68% of the torque.

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.