Publisher Correction: Immediate tool incorporation processes determine human motor planning with tools.

This corrects the article DOI: 10.1038/ncomms5524.

Composition and decomposition of internal models in motor learning under altered kinematic and dynamic environments.

The learning process of reaching movements was examined under novel environments whose kinematic and dynamic properties were altered. We used a kinematic transformation (visuomotor rotation), a dynamic transformation (viscous curl field), and a combination of these transformations. When the subjects learned the combined transformation, reaching errors were smaller if the subject first learned the separate kinematic and dynamic transformations. Reaching errors under the kinematic (but not the dynamic) transformation were smaller if subjects first learned the combined transformation. These results suggest that the brain learns multiple internal models to compensate for each transformation and has some ability to combine and decompose these internal models as called for by the occasion.

Possible explanations for trajectory curvature in multijoint arm movements.

Although the straightness of hand paths is a widely accepted feature of human multijoint reaching movement, detailed examinations have revealed slight curvatures in some regions of the workspace. This observation raises the question of whether planned trajectories are straight or curved. If they are straight, 3 possible factors can explain the observed curvatures: (a) imperfect control, (b) visual distortion, or (c) interaction between straight virtual trajectories and the dynamics of the arm. Participants instructed to generate straight movement paths produced movements much straighter than those generated spontaneously. Participants generated spontaneously curved trajectories in the frontoparallel plane, where visual distortion is not expected. Electromyograms suggested that participants generated straighter paths without an increase in arm stiffness. These findings argue against the 3 factors. It follows that planned trajectories are likely to be curved.

A method for measuring endpoint stiffness during multi-joint arm movements.

Current methods for measuring stiffness during human arm movements are either limited to one-joint motions, or lead to systematic errors. The technique presented here enables a simple, accurate and unbiased measurement of endpoint stiffness during multi-joint movements. Using a computer-controlled mechanical interface, the hand is displaced relative to a prediction of the undisturbed trajectory. Stiffness is then computed as the ratio of restoring force to displacement amplitude. Because of the accuracy of the prediction (< 1 cm error after 200 ms) and the quality of the implementation, the movement is not disrupted by the perturbation. This technique requires only 13 as many trials to identify stiffness as the method of Gomi and Kawato (1997, Biological Cybernetics 76, 163-171) and may, therefore, be used to investigate the evolution of stiffness during motor adaptation.

Quantitative examinations for multi joint arm trajectory planning--using a robust calculation algorithm of the minimum commanded torque change trajectory.

In previous research, criteria based on optimal theories were examined to explain trajectory features in time and space in multi joint arm movement. Four criteria have been proposed. They were the minimum hand jerk criterion (by which a trajectory is planned in an extrinsic-kinematic space), the minimum angle jerk criterion (which is planned in an intrinsic-kinematic space), the minimum torque change criterion (where control objects are joint links; it is planned in an intrinsic-dynamic-mechanical space), and the minimum commanded torque change criterion (which is planned in an intrinsic space considering the arm and muscle dynamics). Which of these is proper as a criterion for trajectory planning in the central nervous system has been investigated by comparing predicted trajectories based on these criteria with previously measured trajectories. Optimal trajectories based on the two former criteria can be calculated analytically. In contrast, optimal trajectories based on the minimum commanded torque change criterion are difficult to be calculated, even with numerical methods. In some cases, they can be computed by a Newton-like method or a steepest descent method combined with a penalty method. However, for a realistic physical parameter range, the former becomes unstable quite often and the latter is unreliable about the optimality of the obtained solution. In this paper, we propose a new method to stably calculate optimal trajectories based on the minimum commanded torque change criterion. The method can obtain trajectories satisfying Euler-Poisson equations with a sufficiently high accuracy. In the method, a joint angle trajectory, which satisfies the boundary conditions strictly, is expressed by using orthogonal polynomials. The coefficients of the orthogonal polynomials are estimated by using a linear iterative calculation so as to satisfy the Euler-Poisson equations with a sufficiently high accuracy. In numerical experiments, we show that the optimal solution can be computed in a wide work space and can also be obtained in a short time compared with the previous methods. Finally, we perform supplementary examinations of the experiments by Nakano, Imamizu, Osu, Uno, Gomi, Yoshioka et al. (1999). Estimation of dynamic joint torques and trajectory formation from surface electromyography signals using a neural network model. Biological Cybernetics, 73, 291-300. Their experiments showed that the measured trajectory is the closest to the minimum commanded torque change trajectory by statistical examination of many point-to-point trajectories over a wide range in a horizontal and sagittal work space. We recalculated the minimum commanded torque change trajectory using the proposed method, and performed the same examinations as previous investigations. As a result, it could be reconfirmed that the measured trajectory is closest to the minimum commanded torque change trajectory previously reported.

Immediate tool incorporation processes determine human motor planning with tools.

Human dexterity with tools is believed to stem from our ability to incorporate and use tools as parts of our body. However tool incorporation, evident as extensions in our body representation and peri-personal space, has been observed predominantly after extended tool exposures and does not explain our immediate motor behaviours when we change tools. Here we utilize two novel experiments to elucidate the presence of additional immediate tool incorporation effects that determine motor planning with tools. Interestingly, tools were observed to immediately induce a trial-by-trial, tool length dependent shortening of the perceived limb lengths, opposite to observations of elongations after extended tool use. Our results thus exhibit that tools induce a dual effect on our body representation; an immediate shortening that critically affects motor planning with a new tool, and the slow elongation, probably a consequence of skill related changes in sensory-motor mappings with the repeated use of the tool.

Two is better than one: physical interactions improve motor performance in humans.

How do physical interactions with others change our own motor behavior? Utilizing a novel motor learning paradigm in which the hands of two - individuals are physically connected without their conscious awareness, we investigated how the interaction forces from a partner adapt the motor behavior in physically interacting humans. We observed the motor adaptations during physical interactions to be mutually beneficial such that both the worse and better of the interacting partners improve motor performance during and after interactive practice. We show that these benefits cannot be explained by multi-sensory integration by an individual, but require physical interaction with a reactive partner. Furthermore, the benefits are determined by both the interacting partner's performance and similarity of the partner's behavior to one's own. Our results demonstrate the fundamental neural processes underlying human physical interactions and suggest advantages of interactive paradigms for sport-training and physical rehabilitation.

Feeling the force: returning haptic signals influence effort inference during motor coordination.

Our brain is known to automatically optimize effort expenditure during motor coordination, such that for example, during bimanual braking of a bicycle, a well-oiled brake will automatically be used more than a corroded, heavy brake. But how does our brain infer the effort expenditure? All previous motor coordination models have believed that the effort in a task is known precisely to our brain, solely from the motor commands it generates. Here we show that this belief is incorrect. Through experiments and simulation we exhibit that in addition to the motor commands, the returning haptic signals play a crucial role in the inference of the effort during a force sharing task. Our results thus elucidate a previously unknown sensory-motor association that has major ramifications for our understanding of motor coordination and provides new insights into how sensory modifications due to ergonomics, stroke and disease can affect motor coordination in humans.

Effective utilization of gravity during arm downswing in keystrokes by expert pianists.

The present study investigated a skill-level-dependent interaction between gravity and muscular force when striking piano keys. Kinetic analysis of the arm during the downswing motion performed by expert and novice piano players was made using an inverse dynamic technique. The corresponding activities of the elbow agonist and antagonist muscles were simultaneously recorded using electromyography (EMG). Muscular torque at the elbow joint was computed while excluding the effects of gravitational and motion-dependent interaction torques. During descending the forearm to strike the keys, the experts kept the activation of the triceps (movement agonist) muscle close to the resting level, and decreased anti-gravity activity of the biceps muscle across all loudness levels. This suggested that elbow extension torque was produced by gravity without the contribution of agonist muscular work. For the novices, on the other hand, a distinct activity in the triceps muscle appeared during the middle of the downswing, and its amount and duration were increased with increasing loudness. Therefore, for the novices, agonist muscular force was the predominant contributor to the acceleration of elbow extension during the downswing. We concluded that a balance shift from muscular force dependency to gravity dependency for the generation of a target joint torque occurs with long-term piano training. This shift would support the notion of non-muscular force utilization for improving physiological efficiency of limb movement with respect to the effective use of gravity.

Stability and motor adaptation in human arm movements.

In control, stability captures the reproducibility of motions and the robustness to environmental and internal perturbations. This paper examines how stability can be evaluated in human movements, and possible mechanisms by which humans ensure stability. First, a measure of stability is introduced, which is simple to apply to human movements and corresponds to Lyapunov exponents. Its application to real data shows that it is able to distinguish effectively between stable and unstable dynamics. A computational model is then used to investigate stability in human arm movements, which takes into account motor output variability and computes the force to perform a task according to an inverse dynamics model. Simulation results suggest that even a large time delay does not affect movement stability as long as the reflex feedback is small relative to muscle elasticity. Simulations are also used to demonstrate that existing learning schemes, using a monotonic antisymmetric update law, cannot compensate for unstable dynamics. An impedance compensation algorithm is introduced to learn unstable dynamics, which produces similar adaptation responses to those found in experiments.

Task-dependent viscoelasticity of human multijoint arm and its spatial characteristics for interaction with environments.

Human arm viscoelasticity is important in stabilizing posture, movement, and in interacting with objects. Viscoelastic spatial characteristics are usually indexed by the size, shape, and orientation of a hand stiffness ellipse. It is well known that arm posture is a dominant factor in determining the properties of the stiffness ellipse. However, it is still unclear how much joint stiffness can change under different conditions, and the effects of that change on the spatial characteristics of hand stiffness are poorly examined. To investigate the dexterous control mechanisms of the human arm, we studied the controllability and spatial characteristics of viscoelastic properties of human multijoint arm during different cocontractions and force interactions in various directions and amplitudes in a horizontal plane. We found that different cocontraction ratios between shoulder and elbow joints can produce changes in the shape and orientation of the stiffness ellipse, especially at proximal hand positions. During force regulation tasks we found that shoulder and elbow single-joint stiffness was each roughly proportional to the torque of its own joint, and cross-joint stiffness was correlated with elbow torque. Similar tendencies were also found in the viscosity-torque relationships. As a result of the joint stiffness changes, the orientation and shape of the stiffness ellipses varied during force regulation tasks as well. Based on these observations, we consider why we can change the ellipse characteristics especially in the proximal posture. The present results suggest that humans control directional characteristics of hand stiffness by changing joint stiffness to achieve various interactions with objects.

Multijoint muscle regulation mechanisms examined by measured human arm stiffness and EMG signals.

Stiffness properties of the musculo-skeletal system can be controlled by regulating muscle activation and neural feedback gain. To understand the regulation of multijoint stiffness, we examined the relationship between human arm joint stiffness and muscle activation during static force control in the horizontal plane by means of surface electromyographic (EMG) studies. Subjects were asked to produce a specified force in a specified direction without cocontraction or they were asked to keep different cocontractions while producing or not producing an external force. The stiffness components of shoulder, elbow, and their cross-term and the EMG of six related muscles were measured during the tasks. Assuming that the EMG reflects the corresponding muscle stiffness, the joint stiffness was predicted from the EMG by using a two-link six-muscle arm model and a constrained least-square-error regression method. Using the parameters estimated in this regression, single-joint stiffness (diagonal terms of the joint-stiffness matrix) was decomposed successfully into biarticular and monoarticular muscle components. Although biarticular muscles act on both shoulder and elbow, they were found to covary strongly with elbow monoarticular muscles. The preferred force directions of biarticular muscles were biased to the directions of elbow monoarticular muscles. Namely, the elbow joint is regulated by the simultaneous activation of monoarticular and biarticular muscles, whereas the shoulder joint is regulated dominantly by monoarticular muscles. These results suggest that biarticular muscles are innervated mainly to control the elbow joint during static force-regulation tasks. In addition, muscle regulation mechanisms for static force control tasks were found to be quite different from those during movements previously reported. The elbow single-joint stiffness was always higher than cross-joint stiffness (off-diagonal terms of the matrix) in static tasks while elbow single-joint stiffness is reported to be sometimes as small as cross-joint stiffness during movement. That is, during movements, the elbow monoarticular muscles were occasionally not activated when biarticular muscles were activated. In static tasks, however, monoarticular muscle components in single-joint stiffness were increased considerably whenever biarticular muscle components in single- and cross-joint stiffness increased. These observations suggest that biarticular muscles are not simply coupled with the innervation of elbow monoarticular muscles but also are regulated independently according to the required task. During static force-regulation tasks, covariation between biarticular and elbow monoarticular muscles may be required to increase stability and/or controllability or to distribute effort among the appropriate muscles.

The central nervous system stabilizes unstable dynamics by learning optimal impedance.

To manipulate objects or to use tools we must compensate for any forces arising from interaction with the physical environment. Recent studies indicate that this compensation is achieved by learning an internal model of the dynamics, that is, a neural representation of the relation between motor command and movement. In these studies interaction with the physical environment was stable, but many common tasks are intrinsically unstable. For example, keeping a screwdriver in the slot of a screw is unstable because excessive force parallel to the slot can cause the screwdriver to slip and because misdirected force can cause loss of contact between the screwdriver and the screw. Stability may be dependent on the control of mechanical impedance in the human arm because mechanical impedance can generate forces which resist destabilizing motion. Here we examined arm movements in an unstable dynamic environment created by a robotic interface. Our results show that humans learn to stabilize unstable dynamics using the skillful and energy-efficient strategy of selective control of impedance geometry.

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model.

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. A number of invariant features of multijoint planar reaching movements have been observed in measured hand trajectories. These features include roughly straight hand paths and bell-shaped speed profiles where the trajectory curvatures between transverse and radial movements have been found to be different. For quantitative and statistical investigations, we obtained a large amount of trajectory data within a wide range of the workspace in the horizontal and sagittal planes (400 trajectories for each subject). A pair of movements within the horizontal and sagittal planes was set to be equivalent in the elbow and shoulder flexion/extension. The trajectory curvatures of the corresponding pair in these planes were almost the same. Moreover, these curvatures can be accurately reproduced with a linear regression from the summation of rotations in the elbow and shoulder joints. This means that trajectory curvatures systematically depend on the movement location and direction represented in the intrinsic body coordinates. We then examined the following four candidates as planning spaces and the four corresponding computational models for trajectory planning. The candidates were as follows: the minimum hand jerk model in an extrinsic-kinematic space, the minimum angle jerk model in an intrinsic-kinematic space, the minimum torque change model in an intrinsic-dynamic-mechanical space, and the minimum commanded torque change model in an intrinsic-dynamic-neural space. The minimum commanded torque change model, which is proposed here as a computable version of the minimum motor command change model, reproduced actual trajectories best for curvature, position, velocity, acceleration, and torque. The model's prediction that the longer the duration of the movement the larger the trajectory curvature was also confirmed. Movements passing through via-points in the horizontal plane were also measured, and they converged to those predicted by the minimum commanded torque change model with training. Our results indicated that the brain may plan, and learn to plan, the optimal trajectory in the intrinsic coordinates considering arm and muscle dynamics and using representations for motor commands controlling muscle tensions.

How are internal models of unstable tasks formed?

The results of recent studies suggest that humans can form internal models that they use in a feedforward manner to compensate for both stable and unstable dynamics. To examine how internal models are formed, we performed adaptation experiments in novel dynamics, and measured the endpoint force, trajectory and EMG during learning. Analysis of reflex feedback and change of feedforward commands between consecutive trials suggested a unified model of motor learning, which can coherently unify the learning processes observed in stable and unstable dynamics and reproduce available data on motor learning. To our knowledge, this algorithm, based on the concurrent minimization of (reflex) feedback and muscle activation, is also the first nonlinear adaptive controller able to stabilize unstable dynamics.