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

Traditional approaches to human information processing tend to deal with perception and action planning in isolation, so that an adequate account of the perception-action interface is still missing On the perceptual side, the dominant cognitive view largely underestimates, and thus fails to account for, the impact of action-related processes on both the processing of perceptual information and on perceptual learning On the action side, most approaches conceive of action planning as a mere continuation of stimulus processing, thus failing to account for the goal-directedness of even the simplest reaction in an experimental task We propose a new framework for a more adequate theoretical treatment of perception and action planning, in which perceptual contents and action plans are coded in a common representational medium by feature codes with distal reference Perceived events (perceptions) and to-be-produced events (actions) are equally represented by integrated, task-tuned networks of feature codes – cognitive structures we call event codes We give an overview of evidence from a wide variety of empirical domains, such as spatial stimulus-response compatibility, sensorimotor synchronization, and ideomotor action, showing that our main assumptions are well supported by the data

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0140525X01000103

The Theory of Event Coding (TEC): a framework for perception and action planning.

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

When we make saccadic eye movements or goal-directed arm movements, there is an infinite number of possible trajectories that the eye or arm could take to reach the target1,2. However, humans show highly stereotyped trajectories in which velocity profiles of both the eye and hand are smooth and symmetric for brief movements3,4. Here we present a unifying theory of eye and arm movements based on the single physiological assumption that the neural control signals are corrupted by noise whose variance increases with the size of the control signal. We propose that in the presence of such signal-dependent noise, the shape of a trajectory is selected to minimize the variance of the final eye or arm position. This minimum-variance theory accurately predicts the trajectories of both saccades and arm movements and the speed–accuracy trade-off described by Fitt's law5. These profiles are robust to changes in the dynamics of the eye or arm, as found empirically6,7. Moreover, the relation between path curvature and hand velocity during drawing movements reproduces the empirical ‘two-thirds power law’8,9. This theory provides a simple and powerful unifying perspective for both eye and arm movement control.

Signal-dependent noise determines motor planning

http://diabeto.enseeiht.fr/download/handwriting/Lacquaniti_1983_Acta-Psychologica.pdf

The law relating the kinematic and figural aspects of drawing movements

Trajectory determines movement dynamics.

The data presented here generalizes the notion of homotetic behavior in the time domain for learned motor sequences, that is, the presence of an invariant structure in such sequences, from typing to handwriting. Furthermore, it extends the principle to the space-time domain for unrestricted, continuous movements. An interpretation of the teleological value of this behavior is provided.

C.A. Terzuolo

Papers

The law relating the kinematic and figural aspects of drawing movements

Trajectory determines movement dynamics.

32 Space-Time Invariance in Learned Motor Skills

Determinants and characteristics of motor patterns used for typing

An algorithm for the generation of curvilinear wrist motion in an arbitrary plane in three-dimensional space.