Degrees of freedom and motor planning in purposive movement

This paper presents empirical evidence suggesting that healthy humans can perform a two degree of freedom visuo-motor pursuit tracking task with the same response time delay as a one degree of freedom task. In contrast, the time delay of the response is influenced markedly by the nature of the motor synergy required to produce it. We suggest a conceptual account of this evidence based on adaptive model theory, which combines theories of intermittency from psychology and adaptive optimal control from engineering. The intermittent response planning stage has a fixed period. It possesses multiple optimal trajectory generators such that multiple degrees of freedom can be planned concurrently, without requiring an increase in the planning period. In tasks which require unfamiliar motor synergies, or are deemed to be incompatible, internal adaptive models representing movement dynamics are inaccurate. This means that the actual response which is produced will deviate from the one which is planned. For a given target-response discrepancy, corrective response trajectories of longer duration are planned, consistent with the principle of speed-accuracy trade-off. Compared to familiar or compatible tasks, this results in a longer response time delay and reduced accuracy. From the standpoint of the intermittency approach, the findings of this study help make possible a more integral and predictive account of purposive action.     

Task specificity and the timing of discrete aiming movements

In discrete aiming movements the task criteria of time-minimization to a spatial target (e.g., Fitts, 1954) and time-matching to a spatial-temporal goal (e.g., Schmidt et al., 1979) tend to produce different functions of the speed-accuracy trade-off. Here we examined whether the task-related movement speed-accuracy characteristics were due to differential space-time trade-offs in time-matching, velocity-matching and time-minimizing task goals. Twenty participants performed 100 aiming trials for each of 15 combinations of task-type (3) and space-time condition (5). The prevalence of the primary types of sub-movement (none, pre-peak, post-peak, undershooting and overshooting) was determined from the kinematics of the movement trajectory. There were comparable distributions of trajectory sub-movement profiles and space-time movement outcomes across the three tasks at the short movement duration that became increasingly dissimilar over decreasing movement velocity and increasing movement time conditions. Movement time was the most influential variable in mediating sub-movement characteristics and the spatial/temporal outcome accuracy and variability of discrete aiming tasks – a role that was magnified in the explicit task demands of time-matching. The time-matching and time-minimization task goals in discrete aiming induce qualitatively different control processes that progressively contribute beyond the minimal time conditions to task-specific space-time accuracy and variability characteristics of the respective movement speed-accuracy functions.     

The Cascade Neural Network Model and a Speed-Accuracy Trade-Off of Arm Movement

We propose a hybrid neural network model of aimed arm movements that consists of a feedforward controller and a postural controller. The cascade neural network of Kawato, Maeda, Uno, and Suzuki (1990) was employed as a computational implementation of the feedforward controller. This network computes feedforward motor commands based on a minimum torque-change criterion. If the weighting parameter of the smoothness criterion is fixed and the number of relaxation iterations is rather small, the cascade model cannot calculate the exact torque, and the hand does not reach the desired target by using the feedforward control alone. Thus, one observes an error between the final position and the desired target location. By using a fixed weighting parameter value and a limited iteration number to simulate target-directed arm movements, we found that the cascade model generated a planning time-accuracy trade-off, and a quasi-power-law type of speed-accuracy trade-off. The model provides a candidate neural mechanism to explain the stochastic variability of the time course of the feedforward motor command. Our approach also accounts for several invariant features of multijoint arm trajectories, such as roughly straight hand paths and bell-shaped speed profiles.     

A test of the deadline model for speed-accuracy tradeoffs

Two experiments were conducted to evaluate the deadline model for speed-accuracy tradeoffs. According to the deadline model, participants in speeded-response tasks terminate stimulus discrimination as soon as it has run to completion or as soon as a predetermined time deadline has arrived, whichever comes first. Speed is traded for accuracy by varying the time deadlines; short deadlines yield fast but sometimes inaccurate responses, whereas long deadlines allow for slow, accurate responses. A new prediction of this model, based on a comparison of reaction time distributions, was derived and tested in experiments involving the joint manipulation of speed stress and stimulus discriminability. Clear violations of this prediction were observed when participants made relative brightness judgments (Experiment 1) and when they made lexical decisions (Experiment 2), rejecting both the deadline model and the fast-guess model. Several alternative models for speed-accuracy tradeoffs, including random-walk and accumulator models, are compatible with the results.     

Information processing and movement optimization during development: kinematics of cyclical pointing in 5- to 11-year-old children

The authors studied the development of movement control in speed-accuracy tradeoff conditions in children aged 5-11 years and in adults performing cyclical pointings. Twelve difficulty levels (IDs), ranging from 2 to 6.58 bits, were defined (P. M. Fitts, 1954). Peak and time to peak velocity, acceleration, and deceleration, and acceleration profiles as a function of hand position (Hooke's portraits) were analyzed. Movement time decreased with age and was less affected by ID. Peak velocity and acceleration increased, acceleration and deceleration were decreasingly time consuming, and movement profiles turned to increased harmonicity with age and task easiness. Nevertheless, the developmental trends differed between parameters. Gain in velocity seemed chiefly dependent on improved muscular cooperation patterns before 7 years of age and on improved information processing from age 7 onward; achievement of an optimized strategy in the speed-accuracy tradeoff occurred at age 11 years.     

Speed-accuracy tradeoff functions in choice reaction time: Experimental designs and computational procedures

The existence of tradeoffs between speed and accuracy is an important interpretative problem in choice reaction time (RT) experiments. A recently suggested solution to this problem is the use of complete speed-accuracy tradeoff functions as the primary dependent variable in choice RT ,experiments instead of a single mean RT and error rate. This paper reviews and compares existing procedures for generating empirical speed-accuracy tradeoff, functions for use as dependent variables in choice RT experiments. Two major types of tradeoff function are identified, and their experimental designs and computational procedures are discussed and evaluated. Systematic disparities are demonstrated between the two tradeoff functions in both empirical and computer-simulated data. Although all existing procedures for generating speed-accuracy tradeoff functions involve empirically untested assumptions, one procedure requires less stringent assumptions and is less sensitive to sources of experimental and statistical error. This procedure involves plotting accuracy against RT over a set of experimental conditions in which subjects’ criteria for speed vs. accuracy are systematically varied.     

Effects of average movement velocity on reaction time and spatiotemporal accuracy in single-aiming and rapid-timing movement tasks

The effects of instructed movement speed were investigated in two experiments. First, rapid-timing and single-aiming movement tasks were compared. Unlike rapid timing, single aiming implies spatial accuracy. The aim of the first experiment was twofold: (a) to examine whether the requirement of accurate placement termination in single aiming affects the negative relationship between instructed average velocity and reaction time found in rapid timing, and (b) to test the speed-accuracy relationships predicted by the symmetric impulse variability model of these movement tasks. For this purpose, four average velocities (5, 24, 75, and 140 cm/s) were investigated in both types of movement tasks in a two-choice reaction task. The effects of average velocity on reaction time were similar in both single-aiming and rapid-timing tasks, and the predicted linear relationship between instructed average velocity and spatial accuracy was not found. The results suggest that the movement control mode, that is, open loop or closed loop, interferes with effects of instructed average velocity. The movement control mode explanation was confirmed in the second experiment with respect to the effect of paired velocities on reaction time. It is argued that the type of movement control mode must be considered in the interpretation of effects of instructed average velocity on reaction time and spatiotemporal measures.     

The elusive tradeoff: Speed vs accuracy in visual discrimination tasks

Theoretical models for choice reaction time and discrimination under time pressure must account for Ss’ ability to trade accuracy for increased speed. The fast guess model views these tradeoffs as different mixtures of “all-or-none” strategies, while incremental models assume they reflect different degrees of thoroughness in processing the stimulus. Three experiments sought tradeoffs for difficult visual discriminations, using explicit payoffs to control and manipulate pressures for speed and accuracy. Although guessing was pervasive, the simple fast guess model could be rejected; Experiments II and III obtained tradeoffs even when fast guesses were purged from Ss’ data. Tradeoff functions fit by several formulations revealed: (1) slower rates of increase in accuracy for more similar stimuli, and (2) substantial “dead times” (80–100 msec slower than detection times) before discrimination responses could exceed chance accuracy. Errors were sometimes faster and sometimes slower than correct responses (depending on S’s speed-accuracy trade); the latter effect may reflect a ceiling on S’s achievable accuracy. A final discussion examines implications of the results for models of discrimination under time pressure; it suggests modifications in present models, focusing on the random walk model, and describes an alternative “deadline” model.     

Knowledge Model for Selecting and Producing Reaching Movements

This article presents a new model of reaching control. The aim of the model is to characterize the computations underlying the selection of coordinated motion patterns among the limb segments. When a spatial target is selected, stored postures are evaluated for the contributions they can make to the task, and a special weighted average (the gaussian average) is taken of the postures to find a single target posture. Movement to the target posture is achieved without explicit planning of the trajectory. Rather, the reaching motion is driven by error correction (reducing the discrepancy between the current and target posture) shaped by inertia. The model solves the degrees-of-freedom problem for reaching. It also allows joints to compensate automatically for reduced mobility of other joints and explains established effects of practice, speed-accuracy trade-off, and kinematics. The model can be extended to other tasks and motor subsystems because of the generality of its underlying concepts.     

Three-dimensional movement trajectories in Fitts' task: Implications for control

According to Fitts (1954), movement time (MT) is a function of the combined effects of movement amplitude and target width (index of difficulty). Aiming movements with the same index of difficulty and MT may have different planning and control processes depending on the specific combination of movement amplitude and target size. Trajectories were evaluated for a broad range of amplitudes and target sizes. A three-dimensional motion recording system (WATSMART) monitored the position of a stylus during aiming movements. MT results replicated Fitts' Law. Analysis of the resultant velocity profiles indicated the following significant effects: As amplitude of movement increased, so did the time to peak resultant velocity; peak resultant velocity increased slightly with target size, and to a greater extent with increases in the amplitude of movement; the time after peak resultant velocity was a function of both amplitude and target size. Resultant velocity profiles were normalized in the time domain to look for scalar relation in the trajectory shape. This revealed that: the resultant velocity profiles were not symmetrical; the proportion of time spent prior to and after peak speed was sensitive to target size only, i.e. as target size decreased, the profiles became more skewed to the right, indicating a longer decelerative phase; for a given target size, a family of curves might be defined and scaled on movement amplitude. These results suggest that a generalized program (base trajectory representation) exists for a given target width and is parameterized or scaled according to the amplitude of movement.     

A linked muscular activation model for movement generation and control

A new model for movement control is presented which incorporates characteristics of impulse-variability and mass-spring models. Movements in the model were controlled with phasic torque impulses in agonist and antagonist muscles and a tonic agonist torque. Characteristics of the phasic agonist and antagonist torque profiles were based on observed properties of movement-related EMGs and muscle isometric torques. Variability of the phasic impulses depended on impulse magnitude as in impulse-variability models. The model therefore predicted a speed-accuracy tradeoff for limb movement. The time of onset and magnitude of the antagonist torque depended on the magnitude of the preceding agonist torque as indicated in studies of movement-related EMGs. This led to the new concept of linkage between the agonist and antagonist muscle forces which was shown to be important for reducing variability of fast movements. Progressive development of linkage during practice could explain the previous findings of decreased movement variability with practice coupled with increased variability of movement-related EMGs. It was concluded that an inherently variable motor system deals with the variability associated with generation of large muscle forces by linking the forces produced by opposing muscles. In this way, variability in net joint torques and in movements can be decreased without the need for the nervous system to closely regulate the individual torques.     

A Linked Muscular Activation Model for Movement Generation and Control

A new model for movement control is presented which incorporates characteristics of impulse-variability and mass-spring models. Movements in the model were controlled with phasic torque impulses in agonist and antagonist muscles and a tonic agonist torque.

Characteristics of the phasic agonist and antagonist torque profiles were based on observed properties of movement-related EMGs and muscle isometric torques. Variability of the phasic impulses depended on impulse magnitude as in impulse-variability models. The model therefore predicted a speed-accuracy tradeoff for limb movement. The time of onset and magnitude of the antagonist torque depended on the magnitude of the preceding agonist torque as indicated in studies of movement-related EMGs. This led to the new concept of linkage between the agonist and antagonist muscle forces which was shown to be important for reducing variability of fast movements. Progressive development of linkage during practice could explain the previous findings of decreased movement variability with practice coupled with increased variability of movement-related EMGs.

It was concluded that an inherently variable motor system deals with the variability associated with generation of large muscle forces by linking the forces produced by opposing muscles. In this way, variability in net joint torques and in movements can be decreased without the need for the nervous system to closely regulate the individual torques.     

A quantitative evaluation of the AVITEWRITE model of handwriting learning

Much sensory-motor behavior develops through imitation, as during the learning of handwriting by children. Such complex sequential acts are broken down into distinct motor control synergies, or muscle groups, whose activities overlap in time to generate continuous, curved movements that obey an inverse relation between curvature and speed. The adaptive vector integration to endpoint handwriting (AVITEWRITE) model of Grossberg and Paine (2000) [A neural model of corticocerebellar interactions during attentive imitation and predictive learning of sequential handwriting movements. Neural Networks, 13, 999-1046] addressed how such complex movements may be learned through attentive imitation. The model suggested how parietal and motor cortical mechanisms, such as difference vector encoding, interact with adaptively-timed, predictive cerebellar learning during movement imitation and predictive performance. Key psychophysical and neural data about learning to make curved movements were simulated, including a decrease in writing time as learning progresses; generation of unimodal, bell-shaped velocity profiles for each movement synergy; size scaling with isochrony, and speed scaling with preservation of the letter shape and the shapes of the velocity profiles; an inverse relation between curvature and tangential velocity; and a two-thirds power law relation between angular velocity and curvature. However, the model learned from letter trajectories of only one subject, and only qualitative kinematic comparisons were made with previously published human data. The present work describes a quantitative test of AVITEWRITE through direct comparison of a corpus of human handwriting data with the model's performance when it learns by tracing the human trajectories. The results show that model performance was variable across the subjects, with an average correlation between the model and human data of 0.89+/-0.10. The present data from simulations using the AVITEWRITE model highlight some of its strengths while focusing attention on areas, such as novel shape learning in children, where all models of handwriting and the learning of other complex sensory-motor skills would benefit from further research.     

Effects of graded doses of alcohol on speed-accuracy tradeoff in choice reaction time

The inconsistency of previous results concerning the effects of alcohol on reaction time (RT) may be related to possible tradeoffs between speed and accuracy. In the present experiment, complete speed-accuracy tradeoff functions were generated for each of five doses of alcohol (0-1.33 ml/kg) in a choice RT task. Such functions permit RT differences resulting from changes in performance efficiency to be distinguished from those due to changes in subjects’ speed accuracy criteria. Increasing doses of alcohol produced a progressive decrease in the slope parameter of linear equations fit to the speed-accuracy data, but did not significantly alter the intercept of the functions with the RT axis. Thus, alcohol reduced performance efficiency by decreasing the rate of growth of accuracy per unit time. A change in speed-accuracy criterion was combined with the decrease in efficiency at the highest alcohol dose.     

Speed-accuracy tradeoff in double stimulation: Effects on the first response

A single-stimulation and two double-stimulation response conditions were compared using explicit payoff matrices to vary speed-accuracy tradeoff. Under accuracy payoff, response latency (RT(1)) to the first stimulus increased as ISI dropped but accuracy remained high and relatively constant. Under speed payoff, RT(1) was only slightly affected by ISI but accuracy dropped as ISI decreased. Transmitted information rates consistently reflected detrimental effects of short ISI. In double stimulation, but not in single stimulation, error response latency exceeded correct response latency. Furthermore, error response latencies were found to be far more variable and more sensitive to changes in speed-accuracy condition than were correct response latencies. Finally, under both speed and accuracy conditions, response latency to the first of two successive stimuli was faster if a response was also required to the second stimulus. Implications of the data for possible models of double-stimulation speed-accuracy tradeoff are considered.     

手的拦截运动的速度伴随效应及影响因素

对手的拦截运动的理论假设、速度伴随效应及其影响因素进行了总结和分析。指出:(1)“速度伴随效应”的机制可能在于补偿反应延迟、维持必需的注视时间、对即时运动信息的利用或时间-准确性权衡;(2)手的拦截运动指标受目标运动方向、先前任务、练习、目标大小、运动表征和策略以及双眼线索等因素的影响;(3)对拦截运动的进一步研究可在统一理论解释的基础上进行,克服研究方法和范围的局限。     

Intentional versus unintentional use of contingencies between perceptual events

In three experiments we studied human ability to use statistical contingencies between visual stimuli (flankers and targets) to improve performance in a letter-digit classification task. We compared the performance of explicitly informed subjects with that of subjects who were told nothing of the contingencies. Simultaneous presentation of flankers and targets (Experiment 1) produced evidence of unintentional contingency use by both informed and uninformed subjects. When stimuli on trialn predicted target stimuli on trialn+1 (Experiment 2) there was no evidence of unintentional processes, but informed subjects showed strong evidence of using intentional prediction strategies. When flanker onset preceded target stimuli presentation (Experiment 3), evidence of contingency use by both informed and uninformed subjects was found, but the data illustrated qualitative differences in response style (e.g., speed-accuracy tradeoffs) between the two groups. Intentional and unintentional uses of contingencies between perceptual events are qualitatively distinct with respect to the time frame in which they can be applied and the performance patterns they produce. Finally, we argue that the unintentional processes studied here are implicit in nature.     

Changes in the variability of movement trajectories with practice

We studied variability in movement phase plane trajectories (velocity-position relation) during movement. Human subjects performed 10 degrees and 30 degrees elbow flexion and extension movements in a visual step tracking paradigm. The area of ellipses with radii equal to one standard deviation in position and velocity was taken as a measure of trajectory variability. Trajectory variability was determined at 10-ms intervals throughout movements. Trajectory variability in both the acceleration and deceleration phases of movement decreased with practice. The average trajectory variability during deceleration was greater than that during acceleration even after extended practice (1000 trials). During practice, subjects usually increased movement speed while maintaining end-position accuracy. Trajectory variability was also related to movement speed when equal amounts of practice were given. Short duration (fast) movements had greater trajectory variability than long duration movements. Thus there is a tradeoff between movement speed and trajectory variability similar to the classical speed-accuracy tradeoff. Trajectory variability increased rapidly during the acceleratory phase of movement. The rate of increase was positively related to both movement amplitude and speed. Thus, the forces producing limb acceleration were variable and this variability was more marked in faster and larger movements. In contrast, trajectory variability increased more slowly or actually decreased during the deceleratory phase of movements. Forces involved in limb deceleration thus appeared to compensate to a greater or lesser degree for the variability in accelerative forces. The experiments indicate that the entire trajectory of simple limb movements is controlled by the central nervous system. Variations in accelerative forces may be compensated for by associated variations in decelerative forces. The linkage between accelerative and decelerative forces is progressively refined with practice resulting in decreased variability of the movement trajectory.     

Predicting Treatment Response for Oppositional Defiant and Conduct Disorder Using Pre-Treatment Adrenal and Gonadal Hormones

Variations in adrenal and gonadal hormone profiles have been linked to increased rates of oppositional defiant disorder (ODD) and conduct disorder (CD). These relationships suggest that certain hormone profiles may be related to how well children respond to psychological treatments for ODD and CD. The current study assessed whether pre-treatment profiles of adrenal and gonadal hormones predicted response to psychological treatment of ODD and CD. One hundred five children, 6–11?years old, participating in a randomized, clinical trial provided samples for cortisol, testosterone, dehydroepiandrosterone, and androstenedione. Diagnostic interviews of ODD and CD were administered up to 3?years post-treatment to track treatment response. Group-based trajectory modeling identified two trajectories of treatment response: (1) a High-response trajectory where children demonstrated lower rates of an ODD or CD diagnosis throughout follow-up, and (2) a Low-response trajectory where children demonstrated higher rates of an ODD or CD diagnosis throughout follow-up. Hierarchical logistic regression predicting treatment response demonstrated that children with higher pre-treatment concentrations of testosterone were four times more likely to be in the Low-response trajectory. No other significant relationship existed between pre-treatment hormone profiles and treatment response. These results suggest that higher concentrations of testosterone are related to how well children diagnosed with ODD or CD respond to psychological treatment over the course of 3?years.