This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. Experimental observations of human subjects performing voluntary unconstrained movements in a horizontal plane are presented. They confirm the following predictions of the mathematical model: unconstrained point-to-point motions are approximately straight with bell-shaped tangential velocity profiles; curved motions (through an intermediate point or around an obstacle) have portions of low curvature joined by portions of high curvature; at points of high curvature, the tangential velocity is reduced; the durations of the low-curvature portions are approximately equal. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.

https://www.jneurosci.org/content/jneuro/5/7/1688.full.pdf

The coordination of arm movements: an experimentally confirmed mathematical model.

The organization of behavior: A neuropsychological theory

On the basis of computational studies it has been proposed that the central nervous system internally simulates the dynamic behavior of the motor system in planning, control, and learning; the existence and use of such an internal model is still under debate. A sensorimotor integration task was investigated in which participants estimated the location of one of their hands at the end of movements made in the dark and under externally imposed forces. The temporal propagation of errors in this task was analyzed within the theoretical framework of optimal state estimation. These results provide direct support for the existence of an internal model.

http://science.sciencemag.org/content/sci/269/5232/1880.full.pdf

An Internal Model for Sensorimotor Integration

A central problem in motor control is understanding how the many biomechanical degrees of freedom are coordinated to achieve a common goal. An especially puzzling aspect of coordination is that behavioral goals are achieved reliably and repeatedly with movements rarely reproducible in their detail. Existing theoretical frameworks emphasize either goal achievement or the richness of motor variability, but fail to reconcile the two. Here we propose an alternative theory based on stochastic optimal feedback control. We show that the optimal strategy in the face of uncertainty is to allow variability in redundant (task-irrelevant) dimensions. This strategy does not enforce a desired trajectory, but uses feedback more intelligently, correcting only those deviations that interfere with task goals. From this framework, task-constrained variability, goal-directed corrections, motor synergies, controlled parameters, simplifying rules and discrete coordination modes emerge naturally. We present experimental results from a range of motor tasks to support this theory.

/pdf/optimal-feedback-control-as-a-theory-of-motor-coordination-jh26vkl3kk.pdf

Optimal feedback control as a theory of motor coordination.

We investigated how the CNS learns to control movements in different dynamical conditions, and how this learned behavior is represented. In particular, we considered the task of making reaching movements in the presence of externally imposed forces from a mechanical environment. This environment was a force field produced by a robot manipulandum, and the subjects made reaching movements while holding the end-effector of this manipulandum. Since the force field significantly changed the dynamics of the task, subjects' initial movements in the force field were grossly distorted compared to their movements in free space. However, with practice, hand trajectories in the force field converged to a path very similar to that observed in free space. This indicated that for reaching movements, there was a kinematic plan independent of dynamical conditions. The recovery of performance within the changed mechanical environment is motor adaptation. In order to investigate the mechanism underlying this adaptation, we considered the response to the sudden removal of the field after a training phase. The resulting trajectories, named aftereffects, were approximately mirror images of those that were observed when the subjects were initially exposed to the field. This suggested that the motor controller was gradually composing a model of the force field, a model that the nervous system used to predict and compensate for the forces imposed by the environment. In order to explore the structure of the model, we investigated whether adaptation to a force field, as presented in a small region, led to aftereffects in other regions of the workspace. We found that indeed there were aftereffects in workspace regions where no exposure to the field had taken place; that is, there was transfer beyond the boundary of the training data. This observation rules out the hypothesis that the subject's model of the force field was constructed as a narrow association between visited states and experienced forces; that is, adaptation was not via composition of a look-up table. In contrast, subjects modeled the force field by a combination of computational elements whose output was broadly tuned across the motor state space. These elements formed a model that extrapolated to outside the training region in a coordinate system similar to that of the joints and muscles rather than end-point forces. This geometric property suggests that the elements of the adaptive process represent dynamics of a motor task in terms of the intrinsic coordinate system of the sensors and actuators.

/pdf/adaptive-representation-of-dynamics-during-learning-of-a-1oq3qvqyla.pdf

Adaptive representation of dynamics during learning of a motor task

Simple arm movements involving forward projection of the hand toward a target were studied by measuring simultaneous wrist position in three-dimensional space and changes in elbow angle. An attempt was made to identify those features of the movement which exhibit invariant characteristics under the hypothesis that such invariances may reflect the operations by which central processes participate in the organization of the movement. The first such invariance to be identified was that the trajectory in space is independent of movement speed. Secondly, the movement can be viewed as consisting of two phases, an acceleratory phase and a deceleratory one, with the movement during the acceleratory phase being so organized as to maintain the ratio of elbow angular velocity to shoulder angular velocity invariant with respect to target location in the deceleratory phase. It is suggested that proprioceptive information is used to control the movement and that the latter invariance may result from a negative feedback of force involving tendon organ afferents.

https://www.jneurosci.org/content/jneuro/1/7/710.full.pdf

Invariant characteristics of a pointing movement in man

1. The accuracy with which subjects pointed to targets in extrapersonal space was assessed under a variety of experimental conditions. 2. When subjects pointed in the dark to remembered target locations, they made substantial errors. Errors in distance, measured from the shoulder to the target, were sometimes as much as 15 cm. Errors in direction, also measured from the shoulder, were smaller. 3. An analysis of the information transmitted by the location of the subject's finger about the location of the target showed that the information about the target's distance was consistently lower than the information about its direction. 4. The errors in distance persisted when subjects had their arm in view and pointed in the light to remembered target locations. 5. The errors were much smaller when subjects used a pointer to point to the target or when they were asked to reproduce the position of their finger after it had been passively moved to the target. 6. From these findings we conclude that subjects have a reasonably accurate visual representation of target location and are able to effectively use kinesthetically derived information about target location. We therefore suggest that errors in pointing result from errors in the sensorimotor transformation from the visual representation of the target location to the kinematic representation of the arm movement.

http://www.ece.uvic.ca/~bctill/papers/mocap/Soechting_Flanders_1989a.pdf

Sensorimotor representations for pointing to targets in three-dimensional space

We present a model for several early stages of the sensorimotor transformations involved in targeted arm movement. In psychophysical experiments, human subjects pointed to the remembered locations of randomly placed targets in three-dimensional space. They made consistent errors in distance, and from these errors stages in the sensorimotor transformation were deduced. When subjects attempted to move the right index finger to a virtual target they consistently undershot the distance of the more distal targets. Other experiments indicated that the error was in the sensorimotor transformation rather than in the perception of distance. The error was most consistent when evaluated using a spherical coordinate system based at the right shoulder, indicating that the neural representation of target parameters is transformed from a retinocentric representation to a shoulder-centered representation. According to the model, the error in distance results from the neural implementation of a linear approximation in the algorithm to transform shoulder-centered target parameters into a set of arm orientations appropriate for placing the finger on the target. The transformation to final arm orientations places visually derived information into a frame of reference where it can readily be combined with kinesthetically derived information about initial arm orientations. The combination of these representations of initial and final arm orientations could give rise to the representation of movement direction recorded in the motor cortex by Georgopoulos and his colleagues. Later stages, such as the transformation from kinematic (position) to dynamic (force) parameters, or to levels of muscle activation, are beyond the scope of the present model.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0140525X00068813

Early stages in a sensorimotor transformation

1. We define an extrinsic frame of reference to represent the location of a point in extrapersonal space relative to a human subject's shoulder, and we define an intrinsic frame of reference to rep...

/pdf/errors-in-pointing-are-due-to-approximations-in-sensorimotor-1vy75emoj5.pdf

Errors in pointing are due to approximations in sensorimotor transformations

The effects of constraints related to movement accuracy on the spatial and temporal characteristics of pointing movements of the arm to a target were investigated. It was found that movement time increased, even at slow speeds, when target size decreased. Spatial variability of the trajectory of the index finger was also reduced, but only in proximity to the target, when higher accuracy was demanded while variability of motion at the wrist showed little change. The effect of varying the angular orientation of the target on the trajectories of the wrist and finger was also investigated. The data support the hypothesis that motion at the shoulder and elbow joints, which is closely linked, is determined primarily by target position while motion at the wrist joint, which is only loosely coupled to the motion at the more proximal joints, is related principally to the angular orientation of the target in space. The data also suggest that wrist motion is controlled separately from motion at the more proximal joints.

John F. Soechting

Papers

Invariant characteristics of a pointing movement in man

Sensorimotor representations for pointing to targets in three-dimensional space

Early stages in a sensorimotor transformation

Errors in pointing are due to approximations in sensorimotor transformations

Effect of Target Size on Spatial and Temporal Characteristics of a Pointing Movement in Man