Pattern Stability and Error Correction During In-Phase and Antiphase Four-Ball Juggling

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants' high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.     

Multiple time scales and subsystem embedding in the learning of juggling

To gain insight into the multiform dynamics and integration of remote yet pertinent subsystems into the performance of complex perceptual-motor skills, we recently conducted a series of longitudinal and cross-sectional experiments on the acquisition of 3-ball cascade juggling in which we measured, next to the ball trajectories, postural sway, eye and head movements and respiration. The aim of the present paper is to review the main results and theoretical implications of these experimental studies for understanding skill acquisition. As regards the evolution of the quality of the juggling itself, we found that only certain aspects of throwing and catching were adjusted, while the goal behavior of sustained juggling (operationalized as the number of consecutive throws) and the degree of frequency and phase locking between the ball trajectories, indexing pattern stability, increased monotonically. The latter three aspects evolved at different rates, reflecting the existence of a temporal hierarchy in learning. Postural sway exhibited initial manifestations of task-specific, possibly mechanically induced, modes of 3:1 and 3:2 frequency locking with the ball trajectories and only few transitions between those modes. Functional stability appeared to be enhanced during practice by minimizing the sway amplitudes rather than by adjusting the sway dynamics itself. Eye and point-of-gaze movements also showed instances of 3:1 and 3:2 frequency locking with the ball trajectories; especially establishing a 3:1 locking (horizontal eye movements) appeared to be important. Expert behavior suggested that extended practice promotes reliance on multiple sources of information, allowing the proficient juggler to switch adaptively between functional organizations involving distinct perceptual systems. No consistent coordination between breathing and juggling was found. It was concluded that multiform dynamics, involving hierarchically ordered time scales, underlie the acquisition of complex skills and that the subsystems subserving realization of the task goal become assembled and embedded in a task- and subsystem-specific manner.     

Intentional switching between patterns of bimanual coordination depends on the intrinsic dynamics of the patterns

Two predictions arising from previous theoretical and empirical work which demonstrated that spontaneous changes of bimanual coordination patterns result from a loss of pattern stability (i.e., a nonequilibrium phase transition) were tested: (a) that the time it takes to intentionally switch from one pattern to another depends on the differential stability of the patterns themselves; and (b) that an intention, defined as an intended behavioral pattern, can change the dynamical characteristics, e.g., the overall stability of the behavioral patterns. Subjects moved both index fingers rhythmically at one of six movement frequencies while performing either an in-phase or antiphase pattern of finger coordination. On cue from an auditory signal, subjects switched from the ongoing pattern to the other pattern. The relative phase of movement between the two fingers was used to characterize the ongoing coordinative pattern. The time taken to switch between patterns, or switching time, and relative phase fluctuations were used to evaluate the modified pattern dynamics resulting from a subject's intention to change patterns. Switching from the in-phase to the antiphase pattern was significantly slower than switching in the opposite direction for all subjects. Both the mean and distribution of switching times in each direction were found to be in agreement with model predictions. movement frequency had little effect on switching time, a finding that is also consistent with the model. Relative phase fluctuations were significantly larger when moving in the antiphase pattern at the highest movement frequencies studied. The results show that, although intentional influences act to modify a coordinative pattern's intrinsic dynamics, the influence of these dynamics on the resulting behavior is always present and is particularly strong at high movement frequencies.     

Intentional Switching Between Patterns of Bimanual Coordination Depends on the Intrinsic Dynamics of the Patterns

Two predictions arising from previous theoretical and empirical work which demonstrated that spontaneous changes of bimanual coordination patterns result from a loss of pattern stability (i.e., a nonequilibrium phase transition) were tested: (a) that the time it takes to intentionally switch from one pattern to another depends on the differential stability of the patterns themselves; and (b) that an intention, defined as an intended behavioral pattern, can change the dynamical characteristics, e.g., the overall stability of the behavioral patterns. Subjects moved both index fingers rhythmically at one of six movement frequencies while performing either an in-phase or antiphase pattern of finger coordination. On cue from an auditory signal, subjects switched from the ongoing pattern to the other pattern. The relative phase of movement between the two fingers was used to characterize the ongoing coordinative pattern. The time taken to switch between patterns, or switching time, and relative phase fluctuations were used to evaluate the modified pattern dynamics resulting from a subject's intention to change patterns. Switching from the in-phase to the antiphase pattern was significantly slower than switching in the opposite direction for all subjects. Both the mean and distribution of switching times in each direction were found to be in agreement with model predictions. Movement frequency had little effect on switching time, a finding that is also consistent with the model. Relative phase fluctuations were significantly larger when moving in the antiphase pattern at the highest movement frequencies studied. The results show that, although intentional influences act to modify a coordinative pattern's intrinsic dynamics, the influence of these dynamics on the resulting behavior is always present and is particularly strong at high movement frequencies.     

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.     

Temporal stability of rhythmic tapping “on” and “off the beat”: A developmental study

This study, following a dynamic pattern approach, examines age-related differences in the stability of unimanual rhythmic perception-action patterns. Thirty-six children, aged 7, 9, and 11 years, attempted to synchronize their finger tapping to the beats of an auditory metronome, either “on the beat” (i.e., in-phase coordination), or “off the beat” (i.e., antiphase coordination). The temporal stability of these perception- action patterns was measured by the variability of the relative phase between taps and auditory events and by the critical frequency, that is, the frequency at which a loss of stability was observed when the metronome frequency was increased. Age-related differences in stability were found for both relative phase variability and critical frequency. These findings suggest that the relative phase dynamics underlying perception-action coordination patterns change with age in the direction of an increased temporal stability. Received: 29 June 1998 / Accepted: 15 December 1998     

Attentional load associated with performing and stabilizing a between-persons coordination of rhythmic limb movements

This study addressed the issue of intentional stabilization of between-persons coordination patterns (in-phase/isodirectional and anti-phase/non-isodirectional) and the attentional cost incurred by the nervous system in maintaining and further stabilizing these coordination patterns. Five pairs of participants performed in-phase and anti-phase interpersonal coordination patterns in dual-task conditions (coordination+RT task). Results showed that: (1) isodirectional pattern (in-phase) was more stable than non-isodirectional pattern (anti-phase), (2) both iso- and non-isodirectional pattern were stabilized intentionally, (3) RT was lower for the isodirectional pattern (i.e., the most stable), and (4) attentional manipulation led to a trade-off between pattern stability and RT performance. These results suggest that performing between-persons coordination patterns incurs a central cost that depends on the coupling strength between the limbs. These findings are consistent with the previous studies in intrapersonal coordination.     

To Switch or Not to Switch: Recruitment of Degrees of Freedom Stabilizes Biological Coordination

Recruitment and suppression processes were studied in the swinging-pendulum paradigm (cf. P. N. Kugler & M. T. Turvey, 1987). The authors pursued the hypothesis that active recruitment of previously unmeasured degrees of freedom serves to stabilize an antiphase bimanual coordination pattern and thereby obviates the need for pattern switching from an antiphase to an in-phase coordination pattern, a key prediction of the H. Haken, J. A. S. Kelso, and H. Bunz (1985) model. In Experiment 1, 7 subjects swung single hand-held pendulums in time with an auditory metronome whose frequency increased. Pendulum motion changed from planar (2D) to elliptical (3D), and forearm motion (produced by elbow flexion-extension) was recruited with increasing movement rate for cycling frequencies typically above the pendulum's eigenfrequency. In Experiment 2, 7 subjects swung paired pendulums in either an in-phase or an antiphase coordinative mode as movement rate was increased. With the systematic increase in movement rate, the authors attempted to induce transitions from the antiphase to the in-phase coordinative pattern, with loss of stability the key mechanism of pattern change. Transitions from the antiphase to the in-phase coordinative mode were not observed. Pattern stability, as defined by the variability of the phase relation between the pendulums, was affected only a little by increasing movement rate. As in the single-pendulum case, pendulum motion changed from planar to elliptical, and forearm motion was recruited with increasing cycling frequency. Those results reveal a richer dynamics than previously observed in the pendulum paradigm and support the hypothesis that recruitment processes stabilize coordination in biomechanically redundant systems, thereby reducing the need for pattern switching.     

Effects of correct and transformed visual feedback on rhythmic visuo-motor tracking: tracking performance and visual search behavior

The effects of correct and transformed visual feedback on rhythmic unimanual visuo-motor tracking were examined, focusing on tracking performance (accuracy and stability) and visual search behavior. Twelve participants (reduced to 9 in the analyses) manually tracked an oscillating visual target signal in phase (by moving the hand in the same direction as the target signal) and in antiphase (by moving the hand in the opposite direction), while the frequency of the target signal was gradually increased to probe pattern stability. Besides a control condition without feedback, correct feedback (representing the actual hand movement) or mirrored feedback (representing the hand movement transformed by 180 degrees) were provided during tracking, resulting in either in-phase or antiphase visual motion of the target and feedback signal, depending on the tracking mode performed. The quality (accuracy and stability) of in-phase tracking was hardly affected by the two forms of feedback, whereas antiphase tracking clearly benefited from mirrored feedback but not from correct feedback. This finding extends previous results indicating that the performance of visuo-motor coordination tasks is aided by visual feedback manipulations resulting in coherently grouped (i.e., in-phase) visual motion structures. Further insights into visuo-motor tracking with and without feedback were garnered from the visual search patterns accompanying task performance. Smooth pursuit eye movements only occurred at lower oscillation frequencies and prevailed during in-phase tracking and when target and feedback signal moved in phase. At higher frequencies, point-of-gaze was fixated at a location that depended on the feedback provided and the resulting visual motion structures. During in-phase tracking the mirrored feedback was ignored, which explains why performance was not affected in this condition. Point-of-gaze fixations at one of the end-points were accompanied by reduced motor variability at this location, reflecting a form of visuo-motor anchoring that may support the pick up of discrete information as well as the control of hand movements to a desired location.     

Acquisition and Automatization of a Complex Task: An Examination of Three-Ball Cascade Juggling

The learning patterns of 3-ball cascade juggling from acquisition until automaticity were examined in 10 participants. On the basis of outcome measures derived from 26 practice sessions and 4 periodic probe sessions, the authors differentiated participants into 3 distinct learning types: a proficient group, an emerging group, and a single late learner. The proficient group was distinguished by how rapidly they learned and automatized performance. Most interesting, an inverse response cost (i.e., performance boost) on the secondary task was found in the majority of proficient group members during the dual-task condition. The present results are discussed in relation to the P. L. Ackerman model (1987, 1988) of complex skill acquisition as is the significance of the inverse response cost finding.     

The metabolic and cognitive energy costs of stabilising a high-energy interlimb coordination task

Kinematic (relative phase error), metabolic (oxygen consumption, heart rate) and attentional (baseline and cycling reaction times) variables were measured while participants practised a high energy-demanding, intrinsically unstable 90 degrees relative phase coordination pattern on independent bicycle ergometers. The variables were found to be strongly inter-correlated, suggesting a link between emerging performance stability with practice and minimal metabolic and attentional cost. The effects of practice of 90 degrees relative phase coordination on the performance of in-phase (0 degrees-phase) and antiphase (180 degrees-phase) coordination were investigated by measuring the relative phase attractor layouts and recording the metabolic and attentional cost of the three coordination patterns before and after practice. The attentional variables did not differ significantly between coordination patterns and did not change with practice. Before practice, the coordination performance was most accurate and stable for in-phase cycling, with antiphase next and 90 degrees-phase the poorest. However, metabolic cost was lower for antiphase than either in-phase or 90 degrees-phase cycling, and the pre-practice attractor layout deviated from that predicted on the basis of dynamic stability as an attractor state, revealing an attraction to antiphase cycling. After practice of 90 degrees-phase cycling, in-phase cycling remained the most accurate and stable, with 90 degrees-phase next and antiphase the poorest, but antiphase retained the lowest metabolic energy cost. The attractor layout had changed, with new attractors formed at the practised 90 degrees-phase pattern and its symmetrical partner of 270 degrees-phase. Considering both the pre- and post-practice results, attractors were formed at either a low metabolic energy cost but less stable (antiphase) pattern or at a more stable but higher metabolic energy cost (90 degrees-phase) pattern, but in neither case at the most stable and accurate (in-phase) pattern. The results suggest that energetic factors affect coordination dynamics and that coordination modes lower in metabolic energy expenditure may compete with dynamically stable modes.     

Neuromuscular-skeletal origins of predominant patterns of coordination in rhythmic two-joint arm movement

The authors tested for predominant patterns of coordination in the combination of rhythmic flexion-extension (FE) and supination- (SP) at the elbow-joint complex. Participants (N=10) spontaneously established in-phase (supination synchronized with flexion) and antiphase (pronation synchronized with flexion) patterns. In addition, the authors used a motorized robot arm to generate involuntary SP movements with different phase relations with respect to voluntary FE. The involuntarily induced in-phase pattern was accentuated and was more consistent than other patterns. The result provides evidence that the predominance of the in-phase pattern originates in the influence of neuromuscular-skeletal constraints rather than in a preference dictated by perceptual-cognitive factors implicated in voluntary control. Neuromuscular-skeletal constraints involved in the predominance of the in-phase and the antiphase patterns are discussed.     

Acquisition and automatization of a complex task: an examination of three-ball cascade juggling

The learning patterns of 3-ball cascade juggling from acquisition until automaticity were examined in 10 participants. On the basis of outcome measures derived from 26 practice sessions and 4 periodic probe sessions, the authors differentiated participants into 3 distinct learning types: a proficient group, an emerging group, and a single late learner. The proficient group was distinguished by how rapidly they learned and automatized performance. Most interesting, an inverse response cost (i.e., performance boost) on the secondary task was found in the majority of proficient group members during the dual-task condition. The present results are discussed in relation to the P. L. Ackerman model (1987, 1988) of complex skill acquisition as is the significance of the inverse response cost finding.     

Human Energy Expenditure and Postural Coordination on the Mechanical Horse

The authors investigated and compared the energy expenditure and postural coordination of two groups of healthy subjects on a mechanical horse at 4 increasing oscillation frequencies. Energy expenditure was assessed from the oxygen consumption, respiratory quotient, and heart rate values, and postural coordination was characterized by relative phase computations between subjects (elbow, head, trunk) and horse. The results showed that the postural coordination of the riders was better adapted (i.e., maintenance of in-phase and antiphase) than that of the nonriders, but the energy expenditure remains the same. Likewise, we observed an energy system shifting only for nonriders (from aerobic to lactic anaerobic mode). Finally, cross-correlations showed a link between energy expenditure and postural coordination in the riders (i.e., effectiveness).     

The effect of volition on the stability of bimanual coordination

The authors investigated how the intention to passively perform a behavior and the intention to persist with a behavior impact upon the spatial and temporal properties of bimanual coordination. Participants (N = 30) were asked to perform a bimanual coordination task that demanded the continuous rhythmic extension-flexion of the wrists. The frequency of movement was scaled by an auditory metronome beat from 1.5 Hz, increasing to 3.25 Hz in.25-Hz increments. The task was further defined by the requirement that the movements be performed initially in a prescribed pattern of coordination (in-phase or antiphase) while the participants assumed one of two different intentional states: stay with the prescribed pattern should it become unstable or do not intervene should the pattern begin to change. Transitions away from the initially prescribed pattern were observed only in trials conducted in the antiphase mode of coordination. The time at which the antiphase pattern of coordination became unstable was not found to be influenced by the intentional state. In addition, the do-not-intervene set led to a switch to an in-phase pattern of coordination whereas the stay set led to phase wandering. Those findings are discussed within the framework of a dynamic account of bimanual coordination.     

Anchoring strategies for learning a bimanual coordination pattern

Anchoring has been defined as synchronizing a point in a movement cycle with an external stimulus (W. D. Byblow, R. G. Carson, & D. Goodman, 1994). Previously, investigators have examined anchoring during in-phase and antiphase movements. The present authors examined anchoring during acquisition of a novel bimanual coordination pattern. Participants performed a 90 degrees pattern at 1 Hz, with a 2- or 4-Hz metronome. No group differences were found in pattern performance; however, the 4-Hz group developed more consistent anchoring relative to the metronome. Mechanical anchor-point variability differed by hand, position (midpoint vs. endpoint), and direction (flexion vs. extension) but not by metronome frequency. Those results support and extend previous findings but leave unanswered questions regarding the benefits and effectiveness of anchoring during a 90 degrees pattern.     

Metabolic and attentional energy costs of interlimb coordination

The authors investigated metabolic and attentional energy costs as participants (N = 6) practiced in-phase, antiphase, and 90 degrees -phase cycling (order counterbalanced) on independent bicycle ergometers, with resistance (40 W/ergometer) and frequency (40 rpm) held constant. Coordination stabilized and became more accurate for all 3 cycling modes, as shown by measures of relative phase, but that collective variable could not account for other relevant attributes of the multifaceted motor behavior observed across the 3 coordination modes. In-phase and antiphase cycling were similar in stability and accuracy, but antiphase had the lowest metabolic and attentional energy costs. Because both homologous muscle action and perceptually symmetrical oscillations coincided in the in-phase mode, the absence of predominance of the inphase pattern showed that neither of those musculoskeletal and perceptual factors exclusively determined the strongest attractor of the coordination dynamics. Both metabolic and attentional costs declined with practice, consistent with the hypothesis that adaptive motor behavior is guided by sensory information concerning the energy demands of the task. Attentional cost was influenced not only by the information-processing demands of kinematic stability but also by the metabolic energy demands. Metabolic energy cost appeared to be the crucial determinant of the preferred solution for this coordination task.     

Coordination changes in the early stages of learning to cascade juggle

The experiment was setup to examine the coordination changes in assembling the movement form of 3-ball cascade juggling. Eight adult participants learned to juggle over 4 weeks of practice. Juggling scores were recorded at each session and performance was videotaped at eight selected sessions for purposes of movement analysis. Once the basic spatial and temporal constraints on cascade juggling were satisfied, and the figure-8 juggling mode was established, temporal modulations of the relative motions of the hands were emphasized. All participants learned to juggle and the increase over practice in the number of consecutive balls caught was best fit with a power law. The non-proportional rate of performance increment was consistent with the qualitative changes in the form of the hand and ball movement kinematics that occurred over practice.     

Phase Transitions and Critical Fluctuations in Rhythmic Coordination of Ipsilateral Hand and Foot

Four subjects performed rhythmic movements of the ankle and the wrist in time with an auditory metronome, in two modes of coordination, antiphase and in-phase. The forearm was placed in either a prone or a supine position. When movements were prepared in the antiphase mode, spontaneous transitions to the in-phase mode, or to phase wandering were observed as metronome frequency was increased. When prepared in the in-phase mode, transitions between in-phase modes or to phase wandering were occasionally observed. Predicted signature features of nonequilbrium phase transitions were noted, including loss of stability and critical fluctuations. The stability of the movement patterns was determined by spatial (dependent upon the direction of movement) rather than anatomical (dependent on the coupling of specific muscle groups) constraints. The position of the forearm had no consistent bearing upon the variability of the phase relations between the limbs, the frequency of phase transitions, or the time of onset of transitions. These results are discussed with reference to the coordination dynamics (e.g., multistability, loss of stability) of multijoint movements.     

Effects of attentional prioritisation on the temporal and spatial components of an interlimb circle-drawing task

This study aimed to examine the effects of directing attention to the spatial dimension of the circle-drawing task on interlimb coordination patterns across limbs. Eighteen participants performed a circle-drawing task involving in-phase and antiphase coordination modes under upper limb, contralateral and ipsilateral limb combinations. Results indicated that (a) coordination pattern stability co-varied with central cost when attentional focus was directed to the spatial dimensions of the interlimb circle-drawing task; (b) attentional focus on the spatial components modified the inherent performance asymmetries between the limbs; (c) finally, attention to the spatial components of the interlimb circle-drawing task modulated movement trajectories and at the same time the stability of temporal coordination.