Key aspects of how brains control movement remain unclear and may even appear to be contradictory. Simple arm movements appear to involve a puzzling mixture of discrete and continuous processes. They depend on mechanical physics and peripheral neural feedback processes that appear to be fundamentally continuous-time phenomena; yet they exhibit behaviors that appear to be characteristic of symbolic or logical processes that operate on fundamentally discrete entities. This paper will review some observations of arm movement intermittency (fluctuations in limb kinematics that cannot be explained by low-level mechanics and dynamics) as evidence that fundamentally discrete processes underlie movement production; discuss some physiological origins of the phenomena, especially their relation to visual feedback; and discuss how they may relate to the fundamentally continuous processes required to interact with the physical world.
In this paper, we review research that we and our colleagues have done on the cognitive substrates of the planning and control of voluntary movements, especially movements of the hands and arms. We begin with a phenomenon observed in a natural setting and then brought into the laboratory—the end-state comfort effect. This is a tendency to sacrifice initial comfort in reach-and-grasp tasks for final comfort or stability. The phenomenon can be traced to knowledge of the biomechanical advantages of occupying the middle of the range of motion for a joint. Next, we discuss three computational models that we and our colleagues have developed to address the problem of selecting particular movement patterns when an infinite number of movement patterns allow a task to be achieved. According to the first model—the optimal selection model—effectors contribute to tasks in proportion to their goodness of fit to task demands. This model is successful in many ways but fails when a task cannot be accomplished by any one of the effectors acting alone. A second model—the Knowledge model—solves this problem and displays some important competencies, including immediate compensation for reduced mobility of joints. The Knowledge model does not allow for high, equal emphasis on more than one task requirement, however, and requires a number of ad hoc assumptions. These limitations are overcome in a new model which, besides achieving everything that the earlier models could, also allows for effective reaching around obstacles and related abilities, including grasping of objects in realistic ways. The computational mechanisms we have devised may be applicable in domains outside motor control.
Human arm movements display characteristic patterns in their trajectories, the torques at the joints and in the EMG patterns in the various muscles. The relationship between the torques and the kinematics is described by physics but the relationship between these properties and the activation of the muscles that produce both is complex and far from well understood. The paper discusses some of the motor control theories that help us understand why we perform our movements in the way we do and how the central nervous system activates the muscles towards those ends. This paper argues that in spite of the well known regularities that are found in simple movement kinematics, an understanding of how muscles are activated will emerge from studying the regularities of the joint torques. However, because of the complex anatomical relations by which muscle forces are converted into joint torques, a full understanding of how the patterns of muscle activation are created may emerge only from the study of the EMG patterns themselves.
Various approaches have been followed to date in the theoretical analysis and modeling of human motor functions. Most notable are notions taken from the fields of control engineering, information theory, and various computational approaches. However, several aspects of motor behaviour have not been dealt with in a satisfactory way so far. For example, the spaces of motor degrees of freedom are customarily considered to be linear even when they are not, and their geometric structure is often ignored. In order to address these issues we apply some general and powerful tools from Differential Geometry. We demonstrate their usefulness to the field by examining several questions that have arisen in the study of the oculomotor system and smooth movements of the hand. In particular, we have achieved the following results: the clarification of aspects relating to eye rotations and the control strategy known as Donders' law and Listing's law; the identification of binocular motor space as the Lie algebra so (4); reproduction of binocular fixation point trajectories in the horizontal plane of regard using a simple kinematic model; by viewing the trajectories traced by the hand as curves in the affine plane, an empirical relation between the geometry and kinematics of smooth hand motion has been shown to imply that the hand moves at approximately constant affine speed; from this behavioural relation we further derived a constraint on neural cortical dynamics under the hypothesis of neural population vector coding. All in all, the geometric methods described here have enabled us to analyse and elucidate several aspects of motor performance, planning and control, and their possible corresponding representations in the brain. We expect that such geometric methods will be increasingly used and that they will have an important role in future research of human motor control.
Sequential movements are characterized by the partially defined states of dynamical systems. A mathematical model for the control of human sequential movements is formulated by defining an objective function, using the same strategy as the previous investigations on simple point-to-point motion and locomotion. The problem of indeterminacy is solved using the dynamical optimization theory. In moving from an initial to a final position in a given time, the objective function is in the form of a quadratic integral whose integrand is a weighted sum of two terms. The first term is the square of the change in torque, and the second is the square of the angular velocity. The model predicts the measured trajectories in planar, multijoint arm movements, leading us to a conclusion that in sequential movements, both the “energy” consumption of the muscles and the motion of the musculoskeletal system are approximately optimum. The optimization approach is discussed on the basis of the previous studies on point-to-point movements and the present study on sequential movements.
Dexterous hitting movement, which requires continuous and variable input-output transformation, was examined from the viewpoints of preprogrammed control and a dynamical system with external temporal input as a continuous control model. The movements of forehand and backhand tennis strokes were observed kinematically under two conditions: when the same input pattern was repeated, and when two different input patterns were switched stochastically. Analysis of the time when movement was initiated and the relative timing revealed that different outputs corresponded to the same input under the switching input condition. This result does not seem to support a preprogrammed control model. On the other hand, the analysis based on a dynamical system confirmed two different excited attractors corresponding to two inputs under the periodic condition, and the transition between these two attractors under the switching input condition. This suggests that dexterity can be understood as a dynamical system with external temporal input.
Recent studies in the field of nonlinear dynamics have shown that the motion of a damped, driven pendulum transits between non-chaotic and chaotic states. This has raised an important question to the field of human movement control: why are human rhythmical movements apparently capable of avoiding chaos? In the present study, it is hypothesized that readjustment of the stiffness with increasing movement frequency in human rhythmical movement is necessary to maintain the order of rhythmical movement avoiding chaotic states. In other words, movement-generated afferent signals are used for readjustment of the stiffness so as to maintain the order of rhythmical movement. The stiffness change with increasing movement frequency was checked experimentally using EMG signals. Subjects extended and flexed their elbow joints rhythmically at frequency ranging from 1.0 to 3.0 Hz in step of 0.5 Hz. It was found that the joint stiffness was readjusted with increasing forcing frequency. A simulation study of the elbow joint motions confirmed that if the readjustment of the joint stiffness was not done the stability of rhythmical movement was lost. These experimental data and simulation data supported the hypothesis.
The simple recurrent network (SRN or Elman net) was shown to be able to learn disposition of syntactic categories of complex sentences with relative clauses in declarative sentences (Elman, 1991). However, it has not been known whether SRN can learn disposition of syntactic categories of more complex sentence grammer like interrogative sentences and recognize case of the words in the sentences. In this paper, we show the recurrent network is able to predict the next word in interrogative sentence and assign the case of nouns.
Most of the studies on visual attention using the cueing paradigm have examined the influence of spatial relationships between cues and targets on the target processing. In the present study, the congruity of non-spatial properties (colors) between cues and targets was incorporated to the general cueing procedure and three steps of the cue lead time (CLT) were provided in order to investigate the dynamic characteristics of the visual attention affected by the spatial and the non-spatial stimulus information. The probability of the non-spatial (color) congruity between cues and targets was set at 50%. In spite of the equal probability, the facilitation of the RT was found on the color congruity condition, and the inhibition was revealed on the incongruity condition. These results suggested that visual attention could be captured by the non-spatial property of the stimulus. By the cost-benefit analysis, it was found that the inhibitory effect was larger than the facilitation effect and more rapidly decreased with the increase of CLT. Furthermore, the results indicated that the attentional capture by the non-spatial property occurred only when the cue and the target had the spatial congruity.