One-Handed Juggling: A Dynamical Approach to a Rhythmic Movement Task

The skill of rhythmically juggling a ball on a racket was investigated from the viewpoint of nonlinear dynamics. The difference equations that model the dynamical system were analyzed by means of local and nonlocal stability analyses. These analyses showed that the task dynamics offer an economical juggling pattern that is stable even for open-loop actuator motion. For this pattern, two types of predictions were extracted: (a) Stable periodic bouncing is sufficiently characterized by a negative acceleration of the racket at the moment of impact with the ball, and (b) a nonlinear scaling relation maps different juggling trajectories onto one topologically equivalent dynamical system. The relevance of these results for the human control of action was evaluated in an experiment in which subjects (N = 6) performed a comparable task of juggling a ball on a paddle. Task manipulations involved different juggling heights and gravity conditions of the ball. The following predictions were confirmed: (a) For stable rhythmic performance, the paddle's acceleration at impact is negative and fluctuations of the impact acceleration follow predictions from global stability analysis; and (b) for each subject, the realizations of juggling for the different experimental conditions are related by the scaling relation. These results permit one to conclude that humans reliably exploit the stable solutions inherent to the dynamics of the given task and do not overrule these dynamics by other control mechanisms. The dynamical scaling serves as an efficient principle for generating different movement realizations from only a few parameter changes and is discussed as a dynamical formalization of the principle of motor equivalence.     

Task-effector asymmetries in a rhythmic continuation task

Variability in rhythmic movements has been interpreted as a signature of internal or peripheral noise processes. Grounded in an oscillator interpretation, this study hypothesized that period variability and drift arises from the asymmetry between target period and the limb's intrinsic dynamics. Participants synchronized to 7 target periods, swinging 1 of 3 pendulums in a continuation paradigm; 3 periods were longer, 3 shorter, and 1 identical to the preferred period. Results supported 5 predictions: Drift toward the preferred period was observed that scaled with the asymmetry. Variability was lowest for symmetry conditions and increased with the asymmetry. Variability decreased concomitant with the approach toward the preferred period. Periods exponentially approached the preferred period with positive autocorrelations up to 10 cycles.     

Dependence of Finger Flexion Force on the Posture of the Nonperforming Fingers During Key Pressing Tasks

In visuomotor tasks that involve accuracy demands, small directional changes in the trajectories have been taken as evidence of feedback-based error corrections. In the present study variability, or intermittency, in visuomanual tracking of sinusoidal targets was investigated. Two lines of analyses were pursued: First, the hypothesis that humans fundamentally act as intermittent servo-controllers was re-examined, probing the question of whether discontinuities in the movement trajectory directly imply intermittent control. Second, an alternative hypothesis was evaluated: that rhythmic tracking movements are generated by entrainment between the oscillations of the target and the actor, such that intermittency expresses the degree of stability. In 2 experiments, participants (N = 6 in each experiment) swung 1 of 2 different hand-held pendulums, tracking a rhythmic target that oscillated at different frequencies with a constant amplitude. In 1 line of analyses, the authors tested the intermittency hypothesis by using the typical kinematic error measures and spectral analysis. In a 2nd line, they examined relative phase and its variability, following analyses of rhythmic interlimb coordination. The results showed that visually guided corrective processes play a role, especially for slow movements. Intermittency, assessed as frequency and power components of the movement trajectory, was found to change as a function of both target frequency and the manipulandum's inertia. Support for entrainment was found in conditions in which task frequency was identical to or higher than the effector's eigenfrequency. The results suggest that it is the symmetry between task and effector that determines which behavioral regime is dominant.     

Variability, covariation, and invariance with respect to coordinate systems in motor control: reply to Smeets and Louw (2007)

In their comment on the tolerance-noise covariation (TNC) method for decomposing variability by H. Müller and D. Sternad (2003, 2004b), J. B. J. Smeets and S. Louw show that covariation (C), as defined within the TNC method, is not invariant with respect to coordinate transformations and contend that it is, therefore, meaningless. Although the observation is correct, their interpretation is misleading in the following ways: (a) They equate covariation C with the known statistical quantity covariance and noise (N) with standard deviations. The two quantities C and N are conceptually different statistical measures. (b) Dependency on the reference frame is not only a feature of C but of all 3 components. However, such dependency is ubiquitous in motor control. (c) As the frame of reference in biological systems is poorly understood, the TNC method may afford evaluation of different coordinates for control.     

When time becomes personal. Aging and personal identity

Phenomenology and the Cognitive Sciences - Aging is an integral part of human existence. The problem of aging addresses the most fundamental coordinates of our lives but also the ones of the...     

The MRCI with juvenile detainees: optimizing performance or emphasizing ecological validity?

The Miranda Rights Comprehension Instruments (MRCI) are intended to be administered to legally involved youths in a setting free from distractions and stressors with the explicit goal of assessing the examinee's best understanding. However, marked disparities have been observed between juveniles' MRCI performance and their unassisted recall of a representative Miranda warning. We hypothesized that youths' very strong MRCI performance might be partially due to prompts and clarifications used whenever incomplete or ambiguous answers are provided. In this archival study, we systematically re‐scored three MRCI instruments from 231 legally involved youths to evaluate their original responses (i.e., non‐queried scoring). This approach is viewed as more ecologically valid because actual Miranda warnings are typically provided in a routine manner without assistance following each Miranda component. For the large majority of legally involved juveniles, only small differences were noted between standard and non‐queried scoring. However, some dramatic decrements were observed, especially on the Comprehension of Miranda Rights‐II (CMR‐II). More specifically, 15.7% of CMR‐II percentiles dropped precipitously by 60% or more, when using the non‐queried scores. The results are discussed within the context of optimized performances versus ecological validity as applied to Miranda evaluations.     

Moving the Arm at Different Rates: Slow Movements are Avoided

Qualitative and quantitative changes characterize locomotion and rhythmic interlimb coordination at different speeds. Legs and hands do not move more or less quickly; they also adopt different relative coordination patterns. In the present article, the authors asked whether similar transitions occur for unimanual hand movements when speed is slowed below the preferred speed. Participants moved a handheld dowel back and forth between 2 large circular targets in time with a metronome at periods between 370 ms and 1667 ms. The authors analyzed the kinematics of participants’ movements at each period and found that proportional dwell time and number of peaks in the velocity profile increased as driving periods increased. Path lengths and peak velocities remained relatively constant for driving periods exceeding 800 ms. Participants made only gradual changes to their movement parameters, so that they went from a continuous mode to a more discrete mode of behavior for longer driving periods. Thus, unlike for rhythmic bimanual movements or locomotory patterns, there are quantitative but no clear qualitative changes for unimanual movements. The results suggest that participants tried to move close to their preferred tempo at different rates, and that they avoided moving slowly.     

Dynamics of 1:2 Coordination: Temporal Scaling,Latent 1:1, and Bistability

The simplest interlimb multifrequency coordination of 1:2 can be performed at different speeds and in at least two different styles or modes. The effects of speed and mode (in-phase or antiphase) were evaluated in a bimanual 1:2 rhythmic task in which participants (N = 8) oscillated hand-held pendulums with identical or different uncoupled frequencies. A motion equation in relative phase that captures the asymmetries of components and task predicted the 1:2 coordination equilibria resulting from temporal scaling. According to the experimental results, both coordination modes proved to be equally stable. More detailed analyses of individual trials showed signs that the more fundamental 1:1 coordination intruded into the 1:2 coordination.     

Bouncing between model and data: stability, passivity, and optimality in hybrid dynamics

Rhythmically bouncing a ball with a racket is a seemingly simple task, but it poses all the challenges critical for coordinative behavior: perceiving the ball's trajectory to adapt position and velocity of the racket for the next ball contact. To gain insight into the underlying control strategies, the authors conducted a series of studies that tested models with experimental data, with an emphasis on deriving model-based hypotheses and trying to falsify them. Starting with a simple dynamical model of the racket and ball interactions, stability analyses showed that open-loop dynamics affords dynamical stability, such that small perturbations do not require corrections. To obtain this passive stability, the ball has to be impacted with negative acceleration--a strategy that subjects adopted in a variety of conditions at steady state. However, experimental tests that applied perturbations revealed that after perturbations, subjects applied active perceptually guided corrections to reestablish steady state faster than by relying on the passive model's relaxation alone. Hence, the authors derived a model with active control based on optimality principles that considered each impact as a separate reaching-like movement. This model captured some additional features of the racket trajectory but failed to predict more fine-grained aspects of performance. The authors proceed to present a new model that accounts not only for fine-grained behavior but also reconciles passive and active control approaches with new predictions that will be put to test in the next set of experiments.