David W. Franklin

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 skilful and energy-efficient strategy of selective control of impedance geometry.

Computational Mechanisms of Sensorimotor Control

In order to generate skilled and efficient actions, the motor system must find solutions to several problems inherent in sensorimotor control, including nonlinearity, nonstationarity, delays, redundancy, uncertainty, and noise. We review these problems and five computational mechanisms that the brain may use to limit their deleterious effects: optimal feedback control, impedance control, predictive control, Bayesian decision theory, and sensorimotor learning. Together, these computational mechanisms allow skilled and fluent sensorimotor behavior.

Endpoint Stiffness of the Arm Is Directionally Tuned to Instability in the Environment

It has been shown that humans are able to selectively control the endpoint impedance of their arms when moving in an unstable environment. However, directional instability was only examined for the case in which the main contribution was from coactivation of biarticular muscles. The goal of this study was to examine whether, in general, the CNS activates the sets of muscles that contribute to selective control of impedance in particular directions. Subjects performed reaching movements in three differently oriented unstable environments generated by a robotic manipulandum. After subjects had learned to make relatively straight reaching movements in the unstable force field, the endpoint stiffness of the limb was measured at the midpoint of the movements. For each force field, the endpoint stiffness increased in a specific direction, whereas there was little change in stiffness in the orthogonal direction. The increase in stiffness was oriented along the direction of instability in the environment, which caused the major axis of the stiffness ellipse to rotate toward the instability in the environment. This study confirms that the CNS is able to control the endpoint impedance of the limbs and selectively adapt it to the environment. Furthermore, it supports the idea that the CNS incorporates an impedance controller that acts to ensure stability, reduce movement variability, and reduce metabolic cost.

CNS Learns Stable, Accurate, and Efficient Movements Using a Simple Algorithm

We propose a new model of motor learning to explain the exceptional dexterity and rapid adaptation to change, which characterize human motor control. It is based on the brain simultaneously optimizing stability, accuracy and efficiency. Formulated as a V-shaped learning function, it stipulates precisely how feedforward commands to individual muscles are adjusted based on error. Changes in muscle activation patterns recorded in experiments provide direct support for this control scheme. In simulated motor learning of novel environmental interactions, muscle activation, force and impedance evolved in a manner similar to humans, demonstrating its efficiency and plausibility. This model of motor learning offers new insights as to how the brain controls the complex musculoskeletal system and iteratively adjusts motor commands to improve motor skills with practice.

Functional significance of stiffness in adaptation of multijoint arm movements to stable and unstable dynamics

This study compared the mechanisms of adaptation to stable and unstable dynamics from the perspective of changes in joint mechanics. Subjects were instructed to make point to point movements in force fields generated by a robotic manipulandum which interacted with the arm in either a stable or an unstable manner. After subjects adjusted to the initial disturbing effects of the force fields they were able to produce normal straight movements to the target. In the case of the stable interaction, subjects modified the joint torques in order to appropriately compensate for the force field. No change in joint torque or endpoint force was required or observed in the case of the unstable interaction. After adaptation, the endpoint stiffness of the arm was measured by applying displacements to the hand in eight different directions midway through the movements. This was compared to the stiffness measured similarly during movements in a null force field. After adaptation, the endpoint stiffness under both the stable and unstable dynamics was modified relative to the null field. Adaptation to unstable dynamics was achieved by selective modification of endpoint stiffness in the direction of the instability. To investigate whether the change in endpoint stiffness could be accounted for by change in joint torque or endpoint force, we estimated the change in stiffness on each trial based on the change in joint torque relative to the null field. For stable dynamics the change in endpoint stiffness was accurately predicted. However, for unstable dynamics the change in endpoint stiffness could not be reproduced. In fact, the predicted endpoint stiffness was similar to that in the null force field. Thus, the change in endpoint stiffness seen after adaptation to stable dynamics was directly related to changes in net joint torque necessary to compensate for the dynamics in contrast to adaptation to unstable dynamics, where a selective change in endpoint stiffness occurred without any modification of net joint torque.

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.

Specificity of Reflex Adaptation for Task-Relevant Variability

The motor system responds to perturbations with reflexes, such as the vestibulo-ocular reflex or stretch reflex, whose gains adapt in response to novel and fixed changes in the environment, such as magnifying spectacles or standing on a tilting platform. Here we demonstrate a reflex response to shifts in the hands visual location during reaching, which occurs before the onset of voluntary reaction time, and investigate how its magnitude depends on statistical properties of the environment. We examine the change in reflex response to two different distributions of visuomotor discrepancies, both of which have zero mean and equal variance across trials. Critically one distribution is task relevant and the other task irrelevant. The task-relevant discrepancies are maintained to the end of the movement, whereas the task-irrelevant discrepancies are transient such that no discrepancy exists at the end of the movement. The reflex magnitude was assessed using identical probe trials under both distributions. We find opposite directions of adaptation of the reflex response under these two distributions, with increased reflex magnitudes for task-relevant variability and decreased reflex magnitudes for task-irrelevant variability. This demonstrates modulation of reflex magnitudes in the absence of a fixed change in the environment, and shows that reflexes are sensitive to the statistics of tasks with modulation depending on whether the variability is task relevant or task irrelevant.

Impedance Control Reduces Instability That Arises from Motor Noise

There is ample evidence that humans are able to control the endpoint impedance of their arms in response to active destabilizing force fields. However, such fields are uncommon in daily life. Here, we examine whether the CNS selectively controls the endpoint impedance of the arm in the absence of active force fields but in the presence of instability arising from task geometry and signal-dependent noise (SDN) in the neuromuscular system. Subjects were required to generate forces, in two orthogonal directions, onto four differently curved rigid objects simulated by a robotic manipulandum. The endpoint stiffness of the limb was estimated for each object curvature. With increasing curvature, the endpoint stiffness increased mainly parallel to the object surface and to a lesser extent in the orthogonal direction. Therefore, the orientation of the stiffness ellipses did not orient to the direction of instability. Simulations showed that the observed stiffness geometries and their pattern of change with instability are the result of a tradeoff between maximizing the mechanical stability and minimizing the destabilizing effects of SDN. Therefore, it would have been suboptimal to align the stiffness ellipse in the direction of instability. The time course of the changes in stiffness geometry suggests that modulation takes place both within and across trials. Our results show that an increase in stiffness relative to the increase in noise can be sufficient to reduce kinematic variability, thereby allowing stiffness control to improve stability in natural tasks.

Impedance control and internal model use during the initial stage of adaptation to novel dynamics in humans

This study investigated the neuromuscular mechanisms underlying the initial stage of adaptation to novel dynamics. A destabilizing velocity‐dependent force field (VF) was introduced for sets of three consecutive trials. Between sets a random number of 4–8 null field trials were interposed, where the VF was inactivated. This prevented subjects from learning the novel dynamics, making it possible to repeatedly recreate the initial adaptive response. We were able to investigate detailed changes in neural control between the first, second and third VF trials. We identified two feedforward control mechanisms, which were initiated on the second VF trial and resulted in a 50% reduction in the hand path error. Responses to disturbances encountered on the first VF trial were feedback in nature, i.e. reflexes and voluntary correction of errors. However, on the second VF trial, muscle activation patterns were modified in anticipation of the effects of the force field. Feedforward cocontraction of all muscles was used to increase the viscoelastic impedance of the arm. While stiffening the arm, subjects also exerted a lateral force to counteract the perturbing effect of the force field. These anticipatory actions indicate that the central nervous system responds rapidly to counteract hitherto unfamiliar disturbances by a combination of increased viscoelastic impedance and formation of a crude internal dynamics model.

Inability to activate muscles maximally during cocontraction and the effect on joint stiffness

In order to determine the maximum joint stiffness that could be produced by cocontraction of wrist flexor and extensor muscles, experiments were conducted in which healthy human subjects stabilized a wrist manipulandum that was made mechanically unstable by using positive position feedback to create a load with the characteristics of a negative spring. To determine a subjects limit of stability, the negative stiffness of the manipulandum was increased by increments until the subject could no longer reliably stabilize the manipulandum in a 1° target window. Static wrist stiffness was measured by applying a 3° rampand-hold displacement of the manipulandum, which stretched the wrist flexor muscles. As the load stiffness was made more and more negative, subjects responded by increasing the level of cocontraction of flexor and extensor muscles to increase the stiffness of the wrist. The stiffness measured at a subjects limit of stability was taken as the maximum stiffness that the subject could achieve by cocontraction of wrist flexor and extensor muscles. In almost all cases, this value was as large or larger than that measured when the subject was asked to cocontract maximally to stiffen the wrist in the absence of any load. Static wrist stiffness was also measured when subjects reciprocally activated flexor or extensor muscles to hold the manipulandum in the target window against a load generated by a stretched spring. We found a strong linear correlation between wrist stiffness and flexor torque over the range of torques used in this study (20–80% maximal voluntary contraction). The maximum stiffness achieved by cocontraction of wrist flexor and extensor muscles was less than 50% of the maximum value predicted from the joint stiffness measured during matched reciprocal activation of flexor and extensor muscles. EMG recorded from either wrist flexor or extensor muscles during maximal cocontraction confirmed that this reduced stiffness was due to lower levels of activation during cocontraction of flexor and extensor muscles than during reciprocal contraction.