Dynamic primitives in constrained action: systematic changes in the zero-force trajectory.

Humans substantially outperform robotic systems in tasks that require physical interaction, despite seemingly inferior muscle bandwidth and slow neural information transmission. The control strategies that enable this performance remain poorly understood. To bridge that gap, this study examined kinematically constrained motion as an intermediate step between the widely studied unconstrained motions and sparsely studied physical interactions. Subjects turned a horizontal planar crank in two directions (clockwise and counterclockwise) at three constant target speeds (fast, medium, and very slow) as instructed via visual display. With the hand constrained to move in a circle, nonzero forces against the constraint were measured. This experiment exposed two observations that could not result from mechanics alone but may be attributed to neural control composed of dynamic primitives. A plausible mathematical model of interactive dynamics (mechanical impedance) was assumed and used to "subtract" peripheral neuromechanics. This method revealed a summary of the underlying neural control in terms of motion, a zero-force trajectory. The estimated zero-force trajectories were approximately elliptical and their orientation differed significantly with turning direction; that is consistent with control using oscillations to generate an elliptical zero-force trajectory. However, for periods longer than 2-5 s, motion can no longer be perceived or executed as periodic. Instead, it decomposes into a sequence of submovements, manifesting as increased variability. These quantifiable performance limitations support the hypothesis that humans simplify this constrained-motion task by exploiting at least three primitive dynamic actions: oscillations, submovements, and mechanical impedance.NEW & NOTEWORTHY Control using primitive dynamic actions may explain why human performance is superior to robots despite seemingly inferior "wetware"; however, this also implies limitations. For a crank-turning task, this work quantified two such informative limitations. Force was exerted even though it produced no mechanical work, the underlying zero-force trajectory was roughly elliptical, and its orientation differed with turning direction, evidence of oscillatory control. At slow speeds, speed variability increased substantially, indicating intermittent control via submovements.

Role of path information in visual perception of joint stiffness.

Humans have an astonishing ability to extract hidden information from the movement of others. In previous work, subjects observed the motion of a simulated stick-figure, two-link planar arm and estimated its stiffness. Fundamentally, stiffness is the relation between force and displacement. Given that subjects were unable to physically interact with the simulated arm, they were forced to make their estimates solely based on observed kinematic information. Remarkably, subjects were able to correctly correlate their stiffness estimates with changes in the simulated stiffness, despite the lack of force information. We hypothesized that subjects were only able to do this because the controller used to produce the simulated arm's movement, composed of oscillatory motions driving mechanical impedances, resembled the controller humans use to produce their own movement. However, it is still unknown what motion features subjects used to estimate stiffness. Human motion exhibits systematic velocity-curvature patterns, and it has previously been shown that these patterns play an important role in perceiving and interpreting motion. Thus, we hypothesized that manipulating the velocity profile should affect subjects' ability to estimate stiffness. To test this, we changed the velocity profile of the simulated two-link planar arm while keeping the simulated joint paths the same. Even with manipulated velocity signals, subjects were still able to estimate changes in simulated joint stiffness. However, when subjects were shown the same simulated path with different velocity profiles, they perceived motions that followed a veridical velocity profile to be less stiff than that of a non-veridical profile. These results suggest that path information (displacement) predominates over temporal information (velocity) when humans use visual observation to estimate stiffness.

Preparing to move: Setting initial conditions to simplify interactions with complex objects.

Humans dexterously interact with a variety of objects, including those with complex internal dynamics. Even in the simple action of carrying a cup of coffee, the hand not only applies a force to the cup, but also indirectly to the liquid, which elicits complex reaction forces back on the hand. Due to underactuation and nonlinearity, the object's dynamic response to an action sensitively depends on its initial state and can display unpredictable, even chaotic behavior. With the overarching hypothesis that subjects strive for predictable object-hand interactions, this study examined how subjects explored and prepared the dynamics of an object for subsequent execution of the target task. We specifically hypothesized that subjects find initial conditions that shorten the transients prior to reaching a stable and predictable steady state. Reaching a predictable steady state is desirable as it may reduce the need for online error corrections and facilitate feed forward control. Alternative hypotheses were that subjects seek to reduce effort, increase smoothness, and reduce risk of failure. Motivated by the task of 'carrying a cup of coffee', a simplified cup-and-ball model was implemented in a virtual environment. Human subjects interacted with this virtual object via a robotic manipulandum that provided force feedback. Subjects were encouraged to first explore and prepare the cup-and-ball before initiating a rhythmic movement at a specified frequency between two targets without losing the ball. Consistent with the hypotheses, subjects increased the predictability of interaction forces between hand and object and converged to a set of initial conditions followed by significantly decreased transients. The three alternative hypotheses were not supported. Surprisingly, the subjects' strategy was more effortful and less smooth, unlike the observed behavior in simple reaching movements. Inverse dynamics of the cup-and-ball system and forward simulations with an impedance controller successfully described subjects' behavior. The initial conditions chosen by the subjects in the experiment matched those that produced the most predictable interactions in simulation. These results present first support for the hypothesis that humans prepare the object to minimize transients and increase stability and, overall, the predictability of hand-object interactions.

Mechanical effects of canes on standing posture: beyond perceptual information.

BACKGROUND: Numerous studies showed that postural balance improves through light touch on a stable surface highlighting the importance of haptic information, seemingly downplaying the mechanical contributions of the support. The present study examined the mechanical effects of canes for assisting balance in healthy individuals challenged by standing on a beam. METHODS: Sixteen participants supported themselves with two canes, one in each hand, and applied minimal, preferred, or maximum force onto the canes. They positioned the canes in the frontal plane or in a tripod configuration. Statistical analysis used a linear mixed model to evaluate the effects on the center of pressure and the center of mass. RESULTS: The canes significantly reduced the variability of the center of pressure and the center of mass to the same level as when standing on the ground. Increasing the exerted force beyond the preferred level yielded no further benefits, although in the preferred force condition, participants exploited the altered mechanics by resting their arms on the canes. The tripod configuration allowed for larger variability of the center of pressure in the task-irrelevant anterior-posterior dimension. High forces had a destabilizing effect on the canes: the displacement of the hand on the cane handle increased with the force. CONCLUSIONS: Given this static instability, these results show that using canes can provide not only mechanical benefits but also challenges. From a control perspective, effort can be reduced by resting the arms on the canes and by channeling noise in the task-irrelevant dimensions. However, larger forces exerted onto the canes can also have destabilizing effects and the instability of the canes needs to be counteracted, possibly by arm and shoulder stiffness. Insights into the variety of mechanical effects is important for the design of canes and the instructions of how to use them.

Identifying human postural dynamics and control from unperturbed balance.

BACKGROUND: Upright standing requires control of an inherently unstable multi-joint human body within a small base of support, despite biological motor and / or sensory noise which challenge balance. Without applying perturbations, system identification methods have been regarded as inadequate, because the relevant internal biological noise processes are not accessible to direct measurement. As a result, unperturbed balance studies have been limited to investigation of behavioral patterns rather than possible underlying control strategies. METHODS: In this paper, we present a mathemathically rigorous system identification method that is applicable to study the dynamics and control of unperturbed balance. The method is derived from autocorrelation matrices with non-zero time lags and identifies the system matrix of a discrete-time dynamic system in the presence of unknown noise processes, without requiring any information about the strength of the noise. RESULTS: Unlike reasonable 'least-squares' approaches, the performance of the new method is consistent across a range of different combinations of internal and measurement noise strengths, even when measurement noise is substantial. We present a numerical example of a model that simulates human upright balancing and show that its dynamics can be identified accurately. With a biomechanically reasonable choice of state and input variables, a state feedback controller can also be identified. CONCLUSIONS: This study provides a new method to correctly identify the dynamics of human standing without the need for known external perturbations. The method was numerically validated using simulation that included realistic features of human balance. This method avoids potential issues of adaptation or possible reflex responses evoked by external perturbations, and does not require expensive in-lab, high-precision measurement equipment. It may eventually enable diagnosis and treatment of individuals with impaired balance, and the development of safe and effective assistive and / or rehabilitative technologies.

Frequency-dependent force direction elucidates neural control of balance.

BACKGROUND: Maintaining upright posture is an unstable task that requires sophisticated neuro-muscular control. Humans use foot-ground interaction forces, characterized by point of application, magnitude, and direction to manage body accelerations. When analyzing the directions of the ground reaction forces of standing humans in the frequency domain, previous work found a consistent pattern in different frequency bands. To test whether this frequency-dependent behavior provided a distinctive signature of neural control or was a necessary consequence of biomechanics, this study simulated quiet standing and compared the results with human subject data. METHODS: Aiming to develop the simplest competent and neuromechanically justifiable dynamic model that could account for the pattern observed across multiple subjects, we first explored the minimum number of degrees of freedom required for the model. Then, we applied a well-established optimal control method that was parameterized to maximize physiologically-relevant insight to stabilize the balancing model. RESULTS: If a standing human was modeled as a single inverted pendulum, no controller could reproduce the experimentally observed pattern. The simplest competent model that approximated a standing human was a double inverted pendulum with torque-actuated ankle and hip joints. A range of controller parameters could stabilize this model and reproduce the general trend observed in experimental data; this result seems to indicate a biomechanical constraint and not a consequence of control. However, details of the frequency-dependent pattern varied substantially across tested control parameter values. The set of parameters that best reproduced the human experimental results suggests that the control strategy employed by human subjects to maintain quiet standing was best described by minimal control effort with an emphasis on ankle torque. CONCLUSIONS: The findings suggest that the frequency-dependent pattern of ground reaction forces observed in quiet standing conveys quantitative information about human control strategies. This study's method might be extended to investigate human neural control strategies in different contexts of balance, such as with an assistive device or in neurologically impaired subjects.

Head-Mounted Display-Based Therapies for Adults Post-Stroke: A Systematic Review and Meta-Analysis.

Immersive virtual reality techniques have been applied to the rehabilitation of patients after stroke, but evidence of its clinical effectiveness is scarce. The present review aims to find studies that evaluate the effects of immersive virtual reality (VR) therapies intended for motor function rehabilitation compared to conventional rehabilitation in people after stroke and make recommendations for future studies. Data from different databases were searched from inception until October 2020. Studies that investigated the effects of immersive VR interventions on post-stroke adult subjects via a head-mounted display (HMD) were included. These studies included a control group that received conventional therapy or another non-immersive VR intervention. The studies reported statistical data for the groups involved in at least the posttest as well as relevant outcomes measuring functional or motor recovery of either lower or upper limbs. Most of the studies found significant improvements in some outcomes after the intervention in favor of the virtual rehabilitation group. Although evidence is limited, immersive VR therapies constitute an interesting tool to improve motor learning when used in conjunction with traditional rehabilitation therapies, providing a non-pharmacological therapeutic pathway for people after stroke.

Separating neural influences from peripheral mechanics: the speed-curvature relation in mechanically constrained actions.

While the study of unconstrained movements has revealed important features of neural control, generalizing those insights to more sophisticated object manipulation is challenging. Humans excel at physical interaction with objects, even when those objects introduce complex dynamics and kinematic constraints. This study examined humans turning a horizontal planar crank (radius 10.29 cm) at their preferred and three instructed speeds (with visual feedback), both in clockwise and counterclockwise directions. To explore the role of neuromechanical dynamics, the instructed speeds covered a wide range: fast (near the limits of performance), medium (near preferred speed), and very slow (rendering dynamic effects negligible). Because kinematically constrained movements involve significant physical interaction, disentangling neural control from the influences of biomechanics presents a challenge. To address it, we modeled the interactive dynamics to "subtract off" peripheral biomechanics from observed force and kinematic data, thereby estimating aspects of underlying neural action that may be expressed in terms of motion. We demonstrate the value of this method: remarkably, an approximately elliptical path emerged, and speed minima coincided with curvature maxima, similar to what is seen in unconstrained movements, even though the hand moved at nearly constant speed along a constant-curvature path. These findings suggest that the neural controller takes advantage of peripheral biomechanics to simplify physical interaction. As a result, patterns seen in unconstrained movements persist even when physical interaction prevents their expression in hand kinematics. The reemergence of a speed-curvature relation indicates that it is due, at least in part, to neural processes that emphasize smoothness and predictability.NEW & NOTEWORTHY Physically interacting with kinematic constraints is commonplace in everyday actions. We report a study of humans turning a crank, a circular constraint that imposes constant hand path curvature and hence should suppress variations of hand speed due to the power-law speed-curvature relation widely reported for unconstrained motions. Remarkably, we found that, when peripheral biomechanical factors are removed, a speed-curvature relation reemerges, indicating that it is, at least in part, of neural origin.

Visual perception of joint stiffness from multijoint motion.

Humans have an astonishing ability to extract hidden information from the movements of others. For example, even with limited kinematic information, humans can distinguish between biological and nonbiological motion, identify the age and gender of a human demonstrator, and recognize what action a human demonstrator is performing. It is unknown, however, whether they can also estimate hidden mechanical properties of another's limbs simply by observing their motions. Strictly speaking, identifying an object's mechanical properties, such as stiffness, requires contact. With only motion information, unambiguous measurements of stiffness are fundamentally impossible, since the same limb motion can be generated with an infinite number of stiffness values. However, we show that humans can readily estimate the stiffness of a simulated limb from its motion. In three experiments, we found that participants linearly increased their rating of arm stiffness as joint stiffness parameters in the arm controller increased. This was remarkable since there was no physical contact with the simulated limb. Moreover, participants had no explicit knowledge of how the simulated arm was controlled. To successfully map nontrivial changes in multijoint motion to changes in arm stiffness, participants likely drew on prior knowledge of human neuromotor control. Having an internal representation consistent with the behavior of the controller used to drive the simulated arm implies that this control policy competently captures key features of veridical biological control. Finding that humans can extract latent features of neuromotor control from kinematics also provides new insight into how humans interpret the motor actions of others. NEW & NOTEWORTHY Humans can visually perceive another's overt motion, but it is unknown whether they can also perceive the hidden dynamic properties of another's limbs from their motions. Here, we show that humans can correctly infer changes in limb stiffness from nontrivial changes in multijoint limb motion without force information or explicit knowledge of the underlying limb controller. Our findings suggest that humans presume others control motor behavior in such a way that limb stiffness influences motion.

Predictability, force, and (anti)resonance in complex object control.

Manipulation of complex objects as in tool use is ubiquitous and has given humans an evolutionary advantage. This study examined the strategies humans choose when manipulating an object with underactuated internal dynamics, such as a cup of coffee. The dynamics of the object renders the temporal evolution complex, possibly even chaotic, and difficult to predict. A cart-and-pendulum model, loosely mimicking coffee sloshing in a cup, was implemented in a virtual environment with a haptic interface. Participants rhythmically manipulated the virtual cup containing a rolling ball; they could choose the oscillation frequency, whereas the amplitude was prescribed. Three hypotheses were tested: 1) humans decrease interaction forces between hand and object; 2) humans increase the predictability of the object dynamics; and 3) humans exploit the resonances of the coupled object-hand system. Analysis revealed that humans chose either a high-frequency strategy with antiphase cup-and-ball movements or a low-frequency strategy with in-phase cup-and-ball movements. Counter to hypothesis 1, they did not decrease interaction force; instead, they increased the predictability of the interaction dynamics, quantified by mutual information, supporting hypothesis 2. To address hypothesis 3, frequency analysis of the coupled hand-object system revealed two resonance frequencies separated by an antiresonance frequency. The low-frequency strategy exploited one resonance, whereas the high-frequency strategy afforded more choice, consistent with the frequency response of the coupled system; both strategies avoided the antiresonance. Hence, humans did not prioritize small interaction forces but rather strategies that rendered interactions predictable. These findings highlight that physical interactions with complex objects pose control challenges not present in unconstrained movements. NEW & NOTEWORTHY Daily actions involve manipulation of complex nonrigid objects, which present a challenge since humans have no direct control of the whole object. We used a virtual-reality experiment and simulations of a cart-and-pendulum system coupled to hand movements with impedance to analyze the manipulation of this underactuated object. We showed that participants developed strategies that increased the predictability of the object behavior by exploiting the resonance structure of the object but did not minimize the hand-object interaction force.

Stability and predictability in human control of complex objects.

Previous research on movement control suggested that humans exploit stability to reduce vulnerability to internal noise and external perturbations. For interactions with complex objects, predictive control based on an internal model of body and environment is needed to preempt perturbations and instabilities due to delays. We hypothesize that stability can serve as means to render the complex dynamics of the body and the task more predictable and thereby simplify control. However, the assessment of stability in complex interactions with nonlinear and underactuated objects is challenging, as for existent stability analyses the system needs to be close to a (known) attractor. After reviewing existing methods for stability analysis of human movement, we argue that contraction theory provides a suitable approach to quantify stability or convergence in complex transient behaviors. To test its usefulness, we examined the task of carrying a cup of coffee, an object with internal degrees of freedom. A simplified model of the task, a cart with a suspended pendulum, was implemented in a virtual environment to study human control strategies. The experimental task was to transport this cart-and-pendulum on a horizontal line from rest to a target position as fast as possible. Each block of trials presented a visible perturbation, which either could be in the direction of motion or opposite to it. To test the hypothesis that humans exploit stability to overcome perturbations, the dynamic model of the free, unforced system was analyzed using contraction theory. A contraction metric was obtained by numerically solving a partial differential equation, and the contraction regions with respect to that metric were computed. Experimental results showed that subjects indeed moved through the contraction regions of the free, unforced system. This strategy attenuated the perturbations, obviated error corrections, and made the dynamics more predictable. The advantages and shortcomings of contraction analysis are discussed in the context of other stability analyses.

Treadmill vs. overground walking: different response to physical interaction.

Rehabilitation of human motor function is an issue of growing significance, and human-interactive robots offer promising potential to meet the need. For the lower extremity, however, robot-aided therapy has proven challenging. To inform effective approaches to robotic gait therapy, it is important to better understand unimpaired locomotor control: its sensitivity to different mechanical contexts and its response to perturbations. The present study evaluated the behavior of 14 healthy subjects who walked on a motorized treadmill and overground while wearing an exoskeletal ankle robot. Their response to a periodic series of ankle plantar flexion torque pulses, delivered at periods different from, but sufficiently close to, their preferred stride cadence, was assessed to determine whether gait entrainment occurred, how it differed across conditions, and if the adapted motor behavior persisted after perturbation. Certain aspects of locomotor control were exquisitely sensitive to walking context, while others were not. Gaits entrained more often and more rapidly during overground walking, yet, in all cases, entrained gaits synchronized the torque pulses with ankle push-off, where they provided assistance with propulsion. Furthermore, subjects entrained to perturbation periods that required an adaption toward slower cadence, even though the pulses acted to accelerate gait, indicating a neural adaptation of locomotor control. Lastly, during 15 post-perturbation strides, the entrained gait period was observed to persist more frequently during overground walking. This persistence was correlated with the number of strides walked at the entrained gait period (i.e., longer exposure), which also indicated a neural adaptation.NEW & NOTEWORTHY We show that the response of human locomotion to physical interaction differs between treadmill and overground walking. Subjects entrained to a periodic series of ankle plantar flexion torque pulses that shifted their gait cadence, synchronizing ankle push-off with the pulses (so that they assisted propulsion) even when gait cadence slowed. Entrainment was faster overground and, on removal of torque pulses, the entrained gait period persisted more prominently overground, indicating a neural adaptation of locomotor control.

Moving slowly is hard for humans: limitations of dynamic primitives.

Mounting evidence suggests that human motor control uses dynamic primitives, attractors of dynamic neuromechanical systems that require minimal central supervision. However, advantages for control may be offset by compromised versatility. Extending recent results showing that humans could not sustain discrete movements as duration decreased, this study tested whether smoothly rhythmic movements could be maintained as duration increased. Participants performed horizontal movements between two targets, paced by sounds with intervals that increased from 1 to 6 s by 200 ms per cycle and then decreased again. The instruction emphasized smooth rhythmic movements without interspersed dwell times. We hypothesized that 1) when oscillatory motions slow down, smoothness decreases; 2) slower oscillatory motions are executed as submovements or even discrete movements; and 3) the transition between smooth oscillations and submovements shows hysteresis. An alternative hypothesis was that 4) removing visual feedback restores smoothness, indicative of visually evoked corrections causing the irregularity. Results showed that humans could not perform slow and smooth oscillatory movements. Harmonicity decreased with longer intervals, and dwell times between cycles appeared and became prominent at slower speeds. Velocity profiles showed an increase with cycle duration of the number of overlapping submovements. There was weak evidence of hysteresis in the transition between these two types of movement. Eliminating vision had no effect, suggesting that intermittent visually evoked corrections did not underlie this phenomenon. These results show that it is hard for humans to execute smooth rhythmic motions very slowly. Instead, they "default" to another dynamic primitive and compose motion as a sequence of overlapping submovements.NEW & NOTEWORTHY Complementing a large body of prior work showing advantages of composing primitives to manage the complexity of motor control, this paper uncovers a limitation due to composition of behavior from dynamic primitives: while slower execution frequently makes a task easier, there is a limit and it is hard for humans to move very slowly. We suggest that this remarkable limitation is not due to inadequacies of muscle, nor to slow neural communication, but is a consequence of how the control of movement is organized.

Brownian processes in human motor control support descending neural velocity commands.

The motor neuroscience literature suggests that the central nervous system may encode some motor commands in terms of velocity. In this work, we tackle the question: what consequences would velocity commands produce at the behavioral level? Considering the ubiquitous presence of noise in the neuromusculoskeletal system, we predict that velocity commands affected by stationary noise would produce "random walks", also known as Brownian processes, in position. Brownian motions are distinctively characterized by a linearly growing variance and a power spectral density that declines in inverse proportion to frequency. This work first shows that these Brownian processes are indeed observed in unbounded motion tasks e.g., rotating a crank. We further predict that such growing variance would still be present, but bounded, in tasks requiring a constant posture e.g., maintaining a static hand position or quietly standing. This hypothesis was also confirmed by experimental observations. A series of descriptive models are investigated to justify the observed behavior. Interestingly, one of the models capable of accounting for all the experimental results must feature forward-path velocity commands corrupted by stationary noise. The results of this work provide behavioral support for the hypothesis that humans plan the motion components of their actions in terms of velocity.

The Study of Complex Manipulation via Kinematic Hand Synergies: The Effects of Data Pre-Processing.

The study of kinematic hand synergies through matrix decomposition techniques, such as singular value decomposition, supports the theory that humans might control a subspace of predefined motions during manipulation tasks. These subspaces are often referred to as synergies. However, different data pre-processing methods lead to quantitatively different conclusions about these synergies. In this work, we shed light on the role of data pre-processing on the study of hand synergies by analyzing both numerical simulation and real kinematic data from a complex manipulation task, i.e., piano playing. The results obtained suggest that centering the data, by removing the mean, appears to be the most appropriate preprocessing technique for studying kinematic hand synergies.

Learning to manipulate a whip with simple primitive actions - A simulation study.

This simulation study investigated whether a 4-degrees-of-freedom (DOF) arm could strike a target with a 50-DOF whip using a motion profile similar to discrete human movements. The interactive dynamics of the multi-joint arm was modeled as a constant joint-space mechanical impedance, with values derived from experimental measurement. Targets at various locations could be hit with a single maximally smooth motion in joint-space coordinates. The arm movements that hit the targets were identified with fewer than 250 iterations. The optimal actions were essentially planar arm motions in extrinsic task-space coordinates, predominantly oriented along the most compliant direction of both task-space and joint-space mechanical impedances. Of the optimal movement parameters, striking a target was most sensitive to movement duration. This result suggests that the elementary actions observed in human motor behavior may support efficient motor control in interaction with a dynamically complex object.

Stiffness, not inertial coupling, determines path curvature of wrist motions.

When humans rotate their wrist in flexion-extension, radial-ulnar deviation, and combinations, the resulting paths (like the path of a laser pointer on a screen) exhibit a distinctive pattern of curvature. In this report we show that the passive stiffness of the wrist is sufficient to account for this pattern. Simulating the dynamics of wrist rotations using a demonstrably realistic model under a variety of conditions, we show that wrist stiffness can explain all characteristics of the observed pattern of curvature. We also provide evidence against other possible causes. We further demonstrate that the phenomenon is robust against variations in human wrist parameters (inertia, damping, and stiffness) and choice of model inputs. Our findings explain two previously observed phenomena: why faster wrist rotations exhibit more curvature and why path curvature rotates with pronation-supination of the forearm. Our results imply that, as in reaching, path straightness is a goal in the planning and control of wrist rotations. This requires humans to predict and compensate for wrist dynamics, but, unlike reaching, nonlinear inertial coupling (e.g., Coriolis acceleration) is insignificant. The dominant term to be compensated is wrist stiffness.

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.

Dynamic primitives of motor behavior.

We present in outline a theory of sensorimotor control based on dynamic primitives, which we define as attractors. To account for the broad class of human interactive behaviors-especially tool use-we propose three distinct primitives: submovements, oscillations, and mechanical impedances, the latter necessary for interaction with objects. Owing to the fundamental features of the neuromuscular system-most notably, its slow response-we argue that encoding in terms of parameterized primitives may be an essential simplification required for learning, performance, and retention of complex skills. Primitives may simultaneously and sequentially be combined to produce observable forces and motions. This may be achieved by defining a virtual trajectory composed of submovements and/or oscillations interacting with impedances. Identifying primitives requires care: in principle, overlapping submovements would be sufficient to compose all observed movements but biological evidence shows that oscillations are a distinct primitive. Conversely, we suggest that kinematic synergies, frequently discussed as primitives of complex actions, may be an emergent consequence of neuromuscular impedance. To illustrate how these dynamic primitives may account for complex actions, we briefly review three types of interactive behaviors: constrained motion, impact tasks, and manipulation of dynamic objects.

Gait Entrainment to Torque Pulses From a Hip Exoskeleton Robot.

Robot-aided locomotor rehabilitation has proven challenging. To facilitate progress, it is important to first understand the neuro-mechanical dynamics and control of unimpaired human locomotion. Our previous studies found that human gait entrained to periodic torque pulses at the ankle when the pulse period was close to preferred stride duration. Moreover, synchronized gait exhibited a constant phase relation with the pulses so that the robot provided mechanical assistance. To test the generality of mechanical gait entrainment, this study characterized unimpaired human subjects' responses to periodic torque pulses during overground walking. The intervention was applied by a hip exoskeleton robot, Samsung GEMS-H. Gait entrainment was assessed based on the time-course of the phase at which torque pulses occurred within each stride. Experiments were conducted for two consecutive days to evaluate whether the second day elicited more entrainment. Whether entrainment was affected by the difference between pulse period and preferred stride duration was also assessed. Results indicated that the intervention evoked gait entrainment that occurred more often when the period of perturbation was closer to subjects' preferred stride duration, but the difference between consecutive days was insignificant. Entrainment was accompanied by convergence of pulse phase to a similar value across all conditions, where the robot maximized mechanical assistance. Clear evidence of motor adaptation indicated the potential of the intervention for rehabilitation. This study quantified important aspects of the nonlinear neuro-mechanical dynamics underlying unimpaired human walking, which will inform the development of effective approaches to robot-aided locomotor rehabilitation, exploiting natural dynamics in a minimally-encumbering way.