Learning the pedalo locomotion task

The authors examined the learning function of a multiple biomechanical degrees of freedom coordination task. Four adult participants practiced the pedalo locomotion task for 350 trials over 7 days. On the basis of the Cauchy theorem, the authors applied a movement pattern difference score that provides a measure of convergence to a fixed point as the criterion for quantifying learning. The findings showed a significant reduction of the movement pattern difference score over practice. Neither an exponential (0.11) nor a power law (0.10) function accommodated a large percentage of the variance of the pattern difference measure on individual learning functions, but the respective fits were higher, although not different, for movement time (.57, .55). Principal components analysis showed a decrease of components over practice; the analysis also showed that 3-5 components were required to accommodate 90% of the variance of the whole-body motion at the end of the final practice session. Those findings on the learning functions for movement and outcome scores are discussed in relation to the redundancy of the biomechanical system in moving to a dynamical stable fixed point in this task.     

Task goals and change in dynamical degrees of freedom with motor learning

In this article, the authors examined the hypothesis that the direction of the change (increase or decrease) in the dynamical degrees of freedom (dimension) regulated as a function of motor learning is task-dependent. Adult participants learned 1 of 2 isometric force-production tasks (Experiment 1: constant force output; Experiment 2: sinusoidal force output) over 5 days of practice and a 6th day with augmented information withdrawal. The results showed that over practice, the task goal induced either an increase (Experiment 1) or a decrease (Experiment 2) in the dimension of force output as performance error was reduced. These findings support the proposition that the observed increase or decrease in dimension with learning is dependent on both the intrinsic dynamics of the system and the short-term change required to realize the task goal.     

Dimensional change in motor learning.

Bernstein (The Co-ordination and Regulation of Movements, Pergamon, London, 1967) outlined a theoretical framework for the degrees of freedom problem in motor control that included a 3-stage approach to the reorganization of the peripheral biomechanical degrees of freedom in motor learning and development. We propose that Bernstein's conception of change through the stages of learning is too narrow in its consideration of the degrees of freedom problem and the actual pathways of change evident in motor learning. It is shown that change in both the organization of the mechanical degrees of freedom and the dimension of the attractor dynamic organizing motor output can either increase or decrease, according to the confluence of constraints imposed on action. The central issue determining directional change in dimension is whether the dimensionality of the task relevant intrinsic dynamic needs to be increased or decreased to realize new task demands.     

Conscious Control Is Associated With Freezing of Mechanical Degrees of Freedom During Motor Learning

This study investigated whether conscious control is associated with freezing of mechanical degrees of freedom during motor learning. Participants practiced a throwing task using either error-strewn or error-reduced practice protocols, which encourage high or low levels of conscious control, respectively. After 24 hr, participants engaged in a series of delayed retention and transfer tests. Furthermore, propensity for conscious control was assessed using participants' ratings and freezing was gauged through movement variability of the throwing arm. Performance was defined by mean radial error. In the error-strewn group, propensity for conscious control was positively associated with both freezing and performance. In the error-reduced group, propensity for conscious control was negatively associated with performance, but not with freezing. These results suggest that conscious control is associated with freezing of mechanical degrees of freedom during motor learning.     

Beyond curve fitting: a dynamical systems account of exponential learning in a discrete timing task

The authors examined the function for learning a discrete timing task from a dynamical systems perspective rather than solely the traditional curve-fitting viewpoint. Adult participants (N = 8) practiced a single-limb angular movement task of 125 ms over 20 degrees for 200 trials. There was no significant difference in percentage of variance accounted for in 3 parameter exponential and power-law nonlinear fits to the individual and averaged data. The percentage of variance increased in both exponential and power-law equations when the data were averaged over participants and trials. Drawing on a dynamical systems approach to time scales in motor learning and on analysis of the distinctive features of exponential and power-law functions, however, the authors conclude that the exponential is the learning function for that task and that level of practice.     

Coordination changes in a discrete multi-articular action as a function of practice

This study investigated how novices re-organized motor system degrees of freedom when practicing a multi-articular discrete kicking task. Four male participants practiced a soccer chipping task to seven different target positions over 12 sessions for 4 weeks. Data from each participant indicated changes in degrees of freedom involvement as a function of practice. Further, each participant showed a different progression of change in levels of joint involvement for hip, knee and ankle in the kicking limb. Cross-correlations between joints in the kicking limb also showed different pathways of coupling and de-coupling with practice. Performance outcome scores improved and variability of intra-limb coordination decreased as a consequence of practice for all participants. Angle-angle plots also showed qualitative changes in intra-limb coordination between early and late practice sessions. Evidence suggested that foot velocity at ball contact was functionally manipulated by participants when kicking to target positions with varying height and distance constraints. Referencing data to a model of learning [Newell, K. M. (1985). Coordination, control and skill. In: Goodman, D., Franks, I., & Wilberg, R.B. (Eds.), Differing perspectives in motor learning, memory, and control. Amsterdam: North-Holland, pp. 295-317] determined that progression through different stages of learning may not be sequential and could alternate between learning stages. The present study highlighted individual differences in acquisition of coordination and control of joint motion even under similar task constraints, showing how degeneracy in movement systems facilitates learning.     

Learning to coordinate redundant degrees of freedom in a dynamic balance task

The present study investigated Bernstein's [The co-ordination and regulation of movements, 1967] proposal regarding the three stages of learning in the changing coordination and control of redundant joint-space degrees of freedom. Six participants practiced maintaining balance on a moving platform that was sinusoidally translated in the anterior-posterior direction for 30 trials on day 1 and 10 trials on day 2. At the beginning of practice, the motion of the torso and limb segments was less coherent in the attempt to compensate for the movement of the support surface in retaining a balanced posture. However, with practice, the organization of a compensatory postural coordination mode became highly coherent and also progressively utilized the passive, inertial forces generated by the movement of the support surface. The findings support the propositions that: (a) the pathway of change over time in the coordination pattern of the torso and joint motions depends on the task goal and constraints to action and (b) the changes in limb and torso motion are in support of the learning of a global body center of mass/platform dynamic.     

The dimensionality of movement trajectories and the degrees of freedom problem: A tutorial

A framework for investigating the degrees of freedom problem (how the large number of degrees of freedom (dfs) at micro-levels of analysis are compressed to the smaller number of dfs at the macro-level of behavior) is discussed. The discussion centers around the use of dynamical systems as models of coordinative structures. Dimensionality analysis, a technique for assessing the dfs of an observable behavior, is explained both intuitively and in detail. By measuring the dfs being produced by actors, we can constrain our dynamical models of how actors produce coordinated behavior.     

The organization of multisegmental pulls made by standing humans: I. Near-maximal pulls

Complex multisegmental movements occur when standing subjects exert forceful, impulse-like pulls on a bimanually held handle. The degrees of freedom of this task were analyzed to provide a principled basis for understanding the act's coordination. Body posture was found to be describable by only two degrees of freedom, expressible as the anterior-posterior and vertical coordinates of the center of mass (CM(AP), CM(V)). Kinetic analysis revealed that the two major contributors to pulling force depended only upon CM(AP) motion and the location of the center of the pressure. Kinematic and kinetic data from six well-practiced subjects pulling near their maxima were used to test the prediction of less intersubject variability in CM(AP) than in CM(V) variation led to different movement patterns among subjects. A dynamic model of CM(AP) motion was developed, and manipulation of its three degrees of freedom yielded CM(AP) trajectories that matched the empirical trajectories. It is suggested that the pull might be controlled with reference to these three parameters.     

Free(z)ing Degrees of Freedom in Skill Acquisition

This study reports an empirical investigation into Bernstein's (1967) ideas that in the early stages of the acquisition of a movement skill the coordination problem is reduced by an initial freezing out of degrees of freedom, followed later in the learning process by the release of these degrees of freedom and their incorporation into a dynamic, controllable system. “Freezing” degrees of freedom was made operational both as a rigid fixation of individual degrees of freedom and as the formation of rigid couplings between multiple degrees of freedom. Five subjects practiced slalom-like ski movements on a ski apparatus for 7 consecutive days. Results showed that at the early phases of learning, the joint angles of the lower limbs and torso displayed little movement, as expressed by their standard deviations and ranges of angular motion, whereas joint couplings were high, as shown by the relatively high cross correlations between joint angles. Over practice, angular movement significantly increased in all joint angles of the lower limbs and torso, although the cross correlations decreased. Support for the processes of freezing and releasing degrees of freedom was thus given at both levels of operationalization. In addition, a consistent change from laterally symmetric to laterally asymmetric cross-correlation patterns were observed as a function of practice. Overall, the findings provide empirical support for Bernstein's ideas regarding the mastery of redundant degrees of freedom in the acquisition of coordination.     

Mechanical perturbation of the wrist during one-handed catching

In the present study, the co-ordination of grasp and transport components of one-handed catching was examined following mechanical perturbations applied to the wrist. Six skilled catchers (mean age = 27.5 years) performed 64 trials in which tennis balls were projected at approximately 8 ms-1. The trial blocks consisted of 10 non-perturbed trials (NPTs) (baseline), and a block of 54 trials of which 20 trials were perturbed. The perturbation was in the form of a resistive force (12 N) applied via a piece of cord attached to a mechanical brake. In baseline trials participants reached maximal wrist velocity closer to the time of hand-ball contact (237 ms +/- 68) than in the perturbed (309 ms +/- 61) condition. Furthermore the wrist velocity profile of five out of six participants exhibited a double peak immediately after a perturbation. However, aperture variables such as the relative moment of final hand closure (approximately 70% of overall movement time) were not typically affected. The stability of grasp and transport coupling for one-handed catching was shown to vary from trial to trial. Skilled performers exploited redundant degrees of freedom in the motor system when faced with a sudden, unexpected change in task constraints.     

Online feedback and the regulation of degrees of freedom in motor control

We tested the hypothesis that the degree to which online feedback is used to control movement influences the regulation of degrees of freedom in a task. Ten participants performed an isometric force production task with their two index fingers with the goal of matching the total force to a target waveform. The role of online feedback was manipulated by changing three factors - the tracking mode, the profile of the target waveform, and the visual gain. The results showed that the coupling between the finger forces was lower in conditions where participants used online feedback to correct their movements compared to conditions where more feedforward strategies were used. The availability of online feedback is dependent on the nature of the task and this contributes to task-dependent changes in the regulation of the degrees of freedom.     

Anisotropic tracking: evidence for automatic synergy formation in a bimanual task

Investigation of interlimb synergy has become synonymous with the study of coordination dynamics and is largely confined to periodic movement. Based on a computational approach this paper demonstrates a method of investigating the formation of a novel synergy in the context of stochastic, spatially asymmetric movements. Nine right-handed participants performed a two degrees of freedom (2D) "etch-a-sketch" tracking task where the right hand controlled the horizontal position of the response cursor on the display while the left hand controlled the vertical position. In a pre-practice 2D tracking task, measures of phase lag between the irregularly moving target and the response showed that participants controlled left and right hands independently, performance of the right hand being slightly superior to the left. Participants then undertook 4 h 16 min distributed practice of a one degree of freedom etch-a-sketch task where the target was constrained to move irregularly in only the 45 degrees direction on the display. To track such a target accurately participants had to make in-phase coupled stochastic movements of the hands. In a post-practice 2D task, measures of phase lag showed anisotropic improvement in performance, the amount of improvement depending on the direction of motion on the display. Improvement was greatest in the practised 45 degrees and least in the orthogonal 135 degrees direction. Best and worst performances were no longer in the directions associated with right and left hands independently, but in directions requiring coupled movements of the two hands. These data support the proposal that the nervous system can establish a model of novel coupling between the hands and thereby form a task-dependent bimanual synergy for controlling the stochastic coupled movements as an entity.     

Qualitative and quantitative change in the dynamics of motor learning

The experiments examined qualitative and quantitative changes in the dynamics of learning a novel motor skill (roller ball task) as a function of the manipulation of a control parameter (initial ball speed). The focus was on the relation between the rates of change in performance over practice time and the changing time scales of the evolving attractor dynamic. Results showed 3 different learning patterns to the changes in the dynamics as a function of practice that were mediated by the initial ball speed. Only participants who learned the task showed a bifurcation in coordination mode that was preceded by enhanced performance variability. The observed multiple time scales to motor learning are interpreted as the products of the dynamical stability and instability realized from (a) the continually evolving landscape dynamics due to bifurcations between attractor organization and (b) the transient phenomena associated with moving toward and away from fixed-point dynamics.     

Postural coordination modes considered as emergent phenomena.

The coordination of multiple body segments (torso and legs) in the control of standing posture during a suprapostural task was studied. The analysis was motivated by dynamical theories of motor coordination. In 2 experiments it was found that multisegment postural coordination could be described by the relative phase of rotations around the hip and ankle joints. The effective length of the feet, the height of the center of mass, and the amplitude of head motions in a visual tracking task were varied. Across these variations, 2 modes of hip-ankle coordination were observed: in-phase and anti-phase. The emergence of these modes was influenced by constraints imposed by the suprapostural tracking task, supporting the idea that such tasks influence postural control in an adaptive manner. Results are interpreted in terms of a dynamical approach to coordination in which postural coordination modes can be viewed as emergent phenomena.     

The acquisition of movement skills: practice enhances the dynamic stability of bimanual coordination.

During bimanual movements, two relatively stable "inherent" patterns of coordination (in-phase and anti-phase) are displayed (e.g., Kelso, Am. J. Physiol. 246 (1984) R1000). Recent research has shown that new patterns of coordination can be learned. For example, following practice a 90 degrees out-of-phase pattern can emerge as an additional, relatively stable, state (e.g., Zanone & Kelso, J. Exp. Psychol.: Human Performance and Perception 18 (1992) 403). On this basis, it has been concluded that practice leads to the evolution and stabilisation of the newly learned pattern and that this process of learning changes the entire attractor layout of the dynamic system. A general feature of such research has been to observe the changes of the targeted pattern's stability characteristics during training at a single movement frequency. The present study was designed to examine how practice affects the maintenance of a coordinated pattern as the movement frequency is scaled. Eleven volunteers were asked to perform a bimanual forearm pronation-supination task. Time to transition onset was used as an index of the subjects' ability to maintain two symmetrically opposite coordinated patterns (target task - 90 degrees out-of-phase - transfer task - 270 degrees out-of-phase). Their ability to maintain the target task and the transfer task were examined again after five practice sessions each consisting of 15 trials of only the 90 degrees out-of-phase pattern. Concurrent performance feedback (a Lissajous figure) was available to the participants during each practice trial. A comparison of the time to transition onset showed that the target task was more stable after practice (p=0.025). These changes were still observed one week (p=0.05) and two months (p=0.075) after the practice period. Changes in the stability of the transfer task were not observed until two months after practice (p=0.025). Notably, following practice, transitions from the 90 degrees pattern were generally to the anti-phase (180 degrees ) pattern, whereas, transitions from the 270 degrees pattern were to the 90 degrees pattern. These results suggest that practice does improve the stability of a 90 degrees pattern, and that such improvements are transferable to the performance of the unpractised 270 degrees pattern. In addition, the anti-phase pattern remained more stable than the practised 90 degrees pattern throughout.     

Compressing movement information via principal components analysis (PCA): Contrasting outcomes from the time and frequency domains

PCA has become an increasingly used analysis technique in the movement domain to reveal patterns in data of various kinds (e.g., kinematics, kinetics, EEG, EMG) and to compress the dimension of the multivariate data set recorded. It appears that virtually all movement related PCA analyses have, however, been conducted in the time domain (PCA_t). This standard approach can be biased when there are lead-lag (phase-related) properties to the multivariate time series data. Here we show through theoretical derivation and analysis of simulated and experimental postural kinematics data sets that PCA_t and, PCA in the frequency domain (PCA_f), can lead to contrasting determinations of the dimension of a data set, with the tendency of PCA_t to overestimate the number of components. PCA_f also provides the possibility of obtaining amplitude and phase-difference spectra for each principal component that are uniquely suitable to reveal control mechanisms of the system. The bias in the PCA_t estimate of the number of components can have significant implications for the veracity of the interpretations drawn in regard to the dynamical degrees of freedom of the perceptual-motor system.     

Dimensionality and the dynamics of human unstable equilibrium

Maintaining an unstable equilibrium requires that multiple joints be coordinated so that the center of mass is kept above the base of support. The authors' aim in the present study was to discover the underlying dynamics of local (foot, hip, or head) and global (center of mass) components involved in balance control and how those dynamics are affected by changes in the available information. Participants (N = 6) had to maintain their balance on an unstable platform. Using dimensional analyses (largest Lyapunov exponent and correlation dimension), the authors examined the active degrees of freedom involved in balance control. Results indicated a similarity in dimension between local (joints) and global (center of mass) components, between a fixed point and a limit cycle. The behavior of the center of mass was found to be more predictable than the behavior of its local constituents. In addition, the available visual information affected the predictability of the postural behavior, which suggests that vision is used in the stabilization of the low-dimensional dynamics underlying balance control.     

The Provenance and Control of Behavior: Simplistic Answers Are Doomed to Fail

This study examined the movement coordination in an exceptional tetraplegic individual who has practiced Japanese calligraphy with a mouth-held brush for over 25 years to reach master level. In the experiment, the calligrapher wrote the same Chinese character on a sheet of ink paper multiple times. The uncontrolled manifold analysis revealed the forms of covariation among joint degrees of freedom so as to keep the brush pressure, brush angle, and upright head posture invariant over different realizations of the task while allowing for joint configuration fluctuations that do not affect these task variables. The fact that the 3 task variables were simultaneously controlled further suggested that the acquisition of the skill was not only a matter of learning to control each of the task variables but also a matter of learning to nest different layers of activities that control the multiple functional relationships to the environment in such a way as not to be dysfunctional for one layer to another.     

Monocular optical constraints on collision control

A simulated ball-hitting task was used to explore the optical basis for collision control. Ball speed and size were manipulated in Experiments 1 and 2. Results showed a tendency for participants to respond earlier to slower and larger balls. Early in practice, participants would consistently miss the slowest and largest balls. Experiments 3 and 4 examined performance as a function of the range of speeds. Performance for identical speeds differed depending on whether the speeds were fastest or slowest within a range. Asymmetric transfer between the 2 ranges of speeds showed that those trained with slow speeds were very successful when tested with a faster range of speeds. Those trained with fast speeds did not do as well when tested on slower speeds. The pattern of results across 4 experiments suggests that participants were using optical angle and expansion rate as separate degrees of freedom for solving the collision task.