Learning feedforward commands to muscles using time-shifted sensory feedback

In adapting to changing forces in the mechanical environment, humans change the force being applied by the limb by reciprocal changes in the activation of antagonistic muscles. However, they also cocontract these muscles when interaction with the environment is mechanically unstable to increase the mechanical impedance of the limb. We have postulated that appropriate patterns of muscle activation could be learned using a simple scheme in which the naturally occurring stretch reflex is used as a template to adjust feedforward commands to muscles. Feedforward commands are modified iteratively by shifting a scaled version of the reflex response forward in time and adding it to the previous feedforward command. We show that such an algorithm can account for the principal features of changes in muscle activation observed when human subjects adapt to instabilities in the mechanical environment. © 2006.

Bipedal walking and running with spring-like biarticular muscles.

Compliant elements in the leg musculoskeletal system appear to be important not only for running but also for walking in human locomotion as shown in the energetics and kinematics studies of spring-mass model. While the spring-mass model assumes a whole leg as a linear spring, it is still not clear how the compliant elements of muscle-tendon systems behave in a human-like segmented leg structure. This study presents a minimalistic model of compliant leg structure that exploits dynamics of biarticular tension springs. In the proposed bipedal model, each leg consists of three leg segments with passive knee and ankle joints that are constrained by four linear tension springs. We found that biarticular arrangements of the springs that correspond to rectus femoris, biceps femoris and gastrocnemius in human legs provide self-stabilizing characteristics for both walking and running gaits. Through the experiments in simulation and a real-world robotic platform, we show how behavioral characteristics of the proposed model agree with basic patterns of human locomotion including joint kinematics and ground reaction force, which could not be explained in the previous models.

Human muscle spindles act as forward sensory models.

Modern theories of motor control incorporate forward models that combine sensory information and motor commands to predict future sensory states. Such models circumvent unavoidable neural delays associated with on-line feedback control. Here we show that signals in human muscle spindle afferents during unconstrained wrist and finger movements predict future kinematic states of their parent muscle. Specifically, we show that the discharges of type Ia afferents are best correlated with the velocity of length changes in their parent muscles approximately 100-160 ms in the future and that their discharges vary depending on motor sequences in a way that cannot be explained by the state of their parent muscle alone. We therefore conclude that muscle spindles can act as "forward sensory models": they are affected both by the current state of their parent muscle and by efferent (fusimotor) control, and their discharges represent future kinematic states. If this conjecture is correct, then sensorimotor learning implies learning how to control not only the skeletal muscles but also the fusimotor system.

Rhythm generation in monkey motor cortex explored using pyramidal tract stimulation.

We investigated whether stimulation of the pyramidal tract (PT) could reset the phase of 15-30 Hz beta oscillations observed in the macaque motor cortex. We recorded local field potentials (LFPs) and multiple single-unit activity from two conscious macaque monkeys performing a precision grip task. EMG activity was also recorded from the second animal. Single PT stimuli were delivered during the hold period of the task, when oscillations in the LFP were most prominent. Stimulus-triggered averaging of the LFP showed a phase-locked oscillatory response to PT stimulation. Frequency domain analysis revealed two components within the response: a 15-30 Hz component, which represented resetting of on-going beta rhythms, and a lower frequency 10 Hz response. Only the higher frequency could be observed in the EMG activity, at stronger stimulus intensities than were required for resetting the cortical rhythm. Stimulation of the PT during movement elicited a greatly reduced oscillatory response. Analysis of single-unit discharge confirmed that PT stimulation was capable of resetting periodic activity in motor cortex. The firing patterns of pyramidal tract neurones (PTNs) and unidentified neurones exhibited successive cycles of suppression and facilitation, time locked to the stimulus. We conclude that PTN activity directly influences the generation of the 15-30 Hz rhythm. These PTNs facilitate EMG activity in upper limb muscles, contributing to corticomuscular coherence at this same frequency. Since the earliest oscillatory effect observed following stimulation was a suppression of firing, we speculate that inhibitory feedback may be the key mechanism generating such oscillations in the motor cortex.

Adaptive control of stiffness to stabilize hand position with large loads.

The goal of this work was to investigate stability in relation to the magnitude and direction of forces applied by the hand. The endpoint stiffness and joint stiffness of the arm were measured during a postural task in which subjects exerted up to 30% maximum voluntary force in each of four directions while controlling the position of the hand. All four coefficients of the joint stiffness matrix were found to vary linearly with both elbow and shoulder torque. This contrasts with the results of a previous study, which employed a force control task and concluded that the joint stiffness coefficients varied linearly with either shoulder or elbow torque but not both. Joint stiffness was transformed into endpoint stiffness to compare the effect on stability as endpoint force increased. When the joint stiffness coefficients were modeled as varying with the net torque at only one joint, as in the previous study, we found that hand position became unstable if endpoint force exceeded about 22 N in a specific direction. This did not occur when the joint stiffness coefficients were modeled as varying with the net torque at both joints, as in the present study. Rather, hand position became increasingly more stable as endpoint force increased for all directions of applied force. Our analysis suggests that co-contraction of biarticular muscles was primarily responsible for the increased stability. This clearly demonstrates how the central nervous system can selectively adapt the impedance of the arm in a specific direction to stabilize hand position when the force applied by the hand has a destabilizing effect in that direction.

Adaptation to stable and unstable dynamics achieved by combined impedance control and inverse dynamics model.

This study compared adaptation in novel force fields where trajectories were initially either stable or unstable to elucidate the processes of learning novel skills and adapting to new environments. Subjects learned to move in a null force field (NF), which was unexpectedly changed either to a velocity-dependent force field (VF), which resulted in perturbed but stable hand trajectories, or a position-dependent divergent force field (DF), which resulted in unstable trajectories. With practice, subjects learned to compensate for the perturbations produced by both force fields. Adaptation was characterized by an initial increase in the activation of all muscles followed by a gradual reduction. The time course of the increase in activation was correlated with a reduction in hand-path error for the DF but not for the VF. Adaptation to the VF could have been achieved solely by formation of an inverse dynamics model and adaptation to the DF solely by impedance control. However, indices of learning, such as hand-path error, joint torque, and electromyographic activation and deactivation suggest that the CNS combined these processes during adaptation to both force fields. Our results suggest that during the early phase of learning there is an increase in endpoint stiffness that serves to reduce hand-path error and provides additional stability, regardless of whether the dynamics are stable or unstable. We suggest that the motor control system utilizes an inverse dynamics model to learn the mean dynamics and an impedance controller to assist in the formation of the inverse dynamics model and to generate needed stability.

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.

Reflex contributions to the directional tuning of arm stiffness

It has been shown that during arm movement, humans selectively change the endpoint stiffness of their arm to compensate for the instability in an unstable environment. When the direction of the instability is rotated with respect to the direction of movement, it was found that humans modify the antisymmetric component of their endpoint stiffness. The antisymmetric component of stiffness arises due to reflex responses suggesting that the subjects may have tuned their reflex responses as part of the feedforward adaptive control. The goal of this study was to examine whether the CNS modulates the gain of the reflex response for selective tuning of endpoint impedance. Subjects performed reaching movements in three unstable force fields produced by a robotic manipulandum, each field differing only in the rotational component. After subjects had learned to compensate for the field, allowing them to make unperturbed movements to the target, the endpoint stiffness of the arm was estimated in the middle of the movements. At the same time electromyographic activity (EMG) of six arm muscles was recorded. Analysis of the EMG revealed differences across force fields in the reflex gain of these muscles consistent with stiffness changes. This study suggests that the CNS modulates the reflex gain as part of the adaptive feedforward command in which the endpoint impedance is selectively tuned to overcome environmental instability. © 2008 Springer-Verlag Berlin Heidelberg.

Impedance control is selectively tuned to multiple directions of movement

Humans are able to learn tool-handling tasks, such as carving, demonstrating their competency to make movements in unstable environments with varied directions. When faced with a single direction of instability, humans learn to selectively co-contract their arm muscles tuning the mechanical stiffness of the limb end point to stabilize movements. This study examines, for the first time, subjects simultaneously adapting to two distinct directions of instability, a situation that may typically occur when using tools. Subjects learned to perform reaching movements in two directions, each of which had lateral instability requiring control of impedance. The subjects were able to adapt to these unstable interactions and switch between movements in the two directions; they did so by learning to selectively control the end-point stiffness counteracting the environmental instability without superfluous stiffness in other directions. This finding demonstrates that the central nervous system can simultaneously tune the mechanical impedance of the limbs to multiple movements by learning movement-specific solutions. Furthermore, it suggests that the impedance controller learns as a function of the state of the arm rather than a general strategy. © 2011 the American Physiological Society.

Measuring stiffness during arm movements in various dynamic environments

The technique presented in this paper enables a simple, accurate and unbiased measurement of hand stiffness during human arm movements. Using a computer-controlled mechanical interface, the hand is shifted relative to a prediction of the undisturbed trajectory. Stiffness is then computed as the restoring force divided by the position amplitude of the perturbation. A precise prediction algorithm insures the measurement quality. We used this technique to measure stiffness in free movements and after adaptation to a linear velocity dependent force field. The subjects compensated for the external force by co-contracting muscles selectively. The stiffness geometry changed with learning and stiffness tended to increase in the direction of the external force.

Transducer and base compliance alter the in situ 6 dof force measured from muscle during an isometric contraction in a multi-joint limb.

Although musculoskeletal models are commonly used, validating the muscle actions predicted by such models is often difficult. In situ isometric measurements are a possible solution. The base of the skeleton is immobilized and the endpoint of the limb is rigidly attached to a 6-axis force transducer. Individual muscles are stimulated and the resulting forces and moments recorded. Such analyses generally assume idealized conditions. In this study we have developed an analysis taking into account the compliances due to imperfect fixation of the skeleton, imperfect attachment of the force transducer, and extra degrees of freedom (dof) in the joints that sometimes become necessary in fixed end contractions. We use simulations of the rat hindlimb to illustrate the consequences of such compliances. We show that when the limb is overconstrained, i.e., when there are fewer dof within the limb than are restrained by the skeletal fixation, the compliances of the skeletal fixation and of the transducer attachment can significantly affect measured forces and moments. When the limb dofs and restrained dofs are matched, however, the measured forces and moments are independent of these compliances. We also show that this framework can be used to model limb dofs, so that rather than simply omitting dofs in which a limb does not move (e.g., abduction at the knee), the limited motion of the limb in these dofs can be more realistically modeled as a very low compliance. Finally, we discuss the practical implications of these results to experimental measurements of muscle actions.

Self-organization of reflexive behavior from spontaneous motor activity.

In mammals, the development of reflexes is often regarded as an innate process. However, recent findings show that fetuses are endowed with favorable conditions for ontogenetic development. In this article, we hypothesize that the circuitry of at least some mammalian reflexes can be self-organized from the sensory and motor interactions brought forth in a musculoskeletal system. We focus mainly on three reflexes: the myotatic reflex, the reciprocal inhibition reflex, and the reverse myotatic reflex. To test our hypothesis, we conducted a set of experiments on a simulated musculoskeletal system using pairs of agonist and antagonist muscles. The reflex connectivity is obtained by producing spontaneous motor activity in each muscle and by correlating the resulting sensor and motor signals. Our results show that, under biologically plausible conditions, the reflex circuitry thus obtained is consistent with that identified in relation to the analogous mammalian reflexes. In addition, they show that the reflex connectivity obtained depends on the morphology of the musculoskeletal system as well as on the environment that it is embedded in.

Self-organization of spinal reflexes involving homonymous, antagonist and synergistic interactions

Recent results in spinal research are challenging the historical view that the spinal reflexes are mostly hardwired and fixed behaviours. In previous work we have shown that three of the simplest spinal reflexes could be self-organised in an agonist-antagonist pair of muscles. The simplicity of these reflexes is given from the fact that they entail at most one interneuron mediating the connectivity between afferent inputs and efferent outputs. These reflexes are: the Myotatic, the Reciprocal Inibition and the Reverse Myotatic reflexes. In this paper we apply our framework to a simulated 2D leg model actuated by six muscles (mono- and bi-articular). Our results show that the framework is successful in learning most of the spinal reflex circuitry as well as the corresponding behaviour in the more complicated muscle arrangement. © 2012 Springer-Verlag.