Interaction of rhythmic and discrete pattern generators in single-joint movements

Automatic detection of foot-strike onsets in a rhythmic forelimb movement

Rhythmic movement is the fundamental motion dynamics characterized by repetitive patterns. Precisely defining onsets in rhythmic movement is essential for a comprehensive analysis of motor functions. Our study introduces an automated method for detecting rat's forelimb foot-strike onsets using deep learning tools. This method demonstrates high accuracy of onset detection by combining two techniques using joint coordinates and behavioral confidence scale. The analysis extends to neural oscillatory responses in the rat's somatosensory cortex, validating the effectiveness of our combined approach. Our technique streamlines experimentation, demanding only a camera and GPU-accelerated computer. This approach is applicable across various contexts and promotes our understanding of brain functions during rhythmic movements.

Dynamic primitives in constrained action: systematic changes in the zero-force trajectory

Humans substantially outperform robotic systems in tasks that require physical interaction, despite seemingly inferior muscle bandwidth and slow neural information transmission. The control strategies that enable this performance remain poorly understood. To bridge that gap, this study examined kinematically constrained motion as an intermediate step between the widely studied unconstrained motions and sparsely studied physical interactions. Subjects turned a horizontal planar crank in two directions (clockwise and counterclockwise) at three constant target speeds (fast, medium, and very slow) as instructed via visual display. With the hand constrained to move in a circle, nonzero forces against the constraint were measured. This experiment exposed two observations that could not result from mechanics alone but may be attributed to neural control composed of dynamic primitives. A plausible mathematical model of interactive dynamics (mechanical impedance) was assumed and used to "subtract" peripheral neuromechanics. This method revealed a summary of the underlying neural control in terms of motion, a zero-force trajectory. The estimated zero-force trajectories were approximately elliptical and their orientation differed significantly with turning direction; that is consistent with control using oscillations to generate an elliptical zero-force trajectory. However, for periods longer than 2-5 s, motion can no longer be perceived or executed as periodic. Instead, it decomposes into a sequence of submovements, manifesting as increased variability. These quantifiable performance limitations support the hypothesis that humans simplify this constrained-motion task by exploiting at least three primitive dynamic actions: oscillations, submovements, and mechanical impedance.NEW & NOTEWORTHY Control using primitive dynamic actions may explain why human performance is superior to robots despite seemingly inferior "wetware"; however, this also implies limitations. For a crank-turning task, this work quantified two such informative limitations. Force was exerted even though it produced no mechanical work, the underlying zero-force trajectory was roughly elliptical, and its orientation differed with turning direction, evidence of oscillatory control. At slow speeds, speed variability increased substantially, indicating intermittent control via submovements.

Human arm endpoint-impedance in rhythmic human-robot interaction exhibits cyclic variations

Estimating the human endpoint-impedance interacting with a physical environment provides insights into goal-directed human movements during physical interactions. This work examined the endpoint-impedance of the upper limb during a hybrid ball-bouncing task with simulated haptic feedback while participants manipulated an admittance-controlled robot. Two experiments implemented a force-perturbation method to estimate the endpoint parameters of 31 participants. Experimental conditions of the ball-bouncing task were simulated in a digital environment. One experiment studied the influence of the target height, while the other explored the impedance at three cyclic phases of the rhythmic movement induced by the task. The participants' performances were analyzed and clustered to establish a potential influence of endpoint impedance on performance in the ball-bouncing task. Results showed that endpoint-impedance parameters ranged from 45 to 445 N/m, 2.2 to 17.5 Ns/m, and 227 to 893 g for the stiffness, damping, and mass, respectively. Results did not support such a critical role of endpoint impedance in performance. Nevertheless, the three endpoint-impedance parameters described significant variations throughout the arm cycle. The stiffness is linked to a quasi-linear increase, with a maximum value reached before the ball impacts. The observed damping and mass cyclic variations seemed to be caused by geometric and kinematic variations. Although this study reveals rapid and within-cycles variations of endpoint-impedance parameters, no direct relationship between endpoint-impedance values and performance levels in ball-bouncing could be found.

Learning to manipulate a whip with simple primitive actions - A simulation study

This simulation study investigated whether a 4-degrees-of-freedom (DOF) arm could strike a target with a 50-DOF whip using a motion profile similar to discrete human movements. The interactive dynamics of the multi-joint arm was modeled as a constant joint-space mechanical impedance, with values derived from experimental measurement. Targets at various locations could be hit with a single maximally smooth motion in joint-space coordinates. The arm movements that hit the targets were identified with fewer than 250 iterations. The optimal actions were essentially planar arm motions in extrinsic task-space coordinates, predominantly oriented along the most compliant direction of both task-space and joint-space mechanical impedances. Of the optimal movement parameters, striking a target was most sensitive to movement duration. This result suggests that the elementary actions observed in human motor behavior may support efficient motor control in interaction with a dynamically complex object.

The contribution of the basal ganglia and cerebellum to motor learning: A neuro-computational approach

Motor learning involves a widespread brain network including the basal ganglia, cerebellum, motor cortex, and brainstem. Despite its importance, little is known about how this network learns motor tasks and which role different parts of this network take. We designed a systems-level computational model of motor learning, including a cortex-basal ganglia motor loop and the cerebellum that both determine the response of central pattern generators in the brainstem. First, we demonstrate its ability to learn arm movements toward different motor goals. Second, we test the model in a motor adaptation task with cognitive control, where the model replicates human data. We conclude that the cortex-basal ganglia loop learns via a novelty-based motor prediction error to determine concrete actions given a desired outcome, and that the cerebellum minimizes the remaining aiming error.

Morphological Computation Increases From Lower- to Higher-Level of Biological Motor Control Hierarchy

Voluntary movements, like point-to-point or oscillatory human arm movements, are generated by the interaction of several structures. High-level neuronal circuits in the brain are responsible for planning and initiating a movement. Spinal circuits incorporate proprioceptive feedback to compensate for deviations from the desired movement. Muscle biochemistry and contraction dynamics generate movement driving forces and provide an immediate physical response to external forces, like a low-level decentralized controller. A simple central neuronal command like "initiate a movement" then recruits all these biological structures and processes leading to complex behavior, e.g., generate a stable oscillatory movement in resonance with an external spring-mass system. It has been discussed that the spinal feedback circuits, the biochemical processes, and the biomechanical muscle dynamics contribute to the movement generation, and, thus, take over some parts of the movement generation and stabilization which would otherwise have to be performed by the high-level controller. This contribution is termed morphological computation and can be quantified with information entropy-based approaches. However, it is unknown whether morphological computation actually differs between these different hierarchical levels of the control system. To investigate this, we simulated point-to-point and oscillatory human arm movements with a neuro-musculoskeletal model. We then quantify morphological computation on the different hierarchy levels. The results show that morphological computation is highest for the most central (highest) level of the modeled control hierarchy, where the movement initiation and timing are encoded. Furthermore, they show that the lowest neuronal control layer, the muscle stimulation input, exploits the morphological computation of the biochemical and biophysical muscle characteristics to generate smooth dynamic movements. This study provides evidence that the system's design in the mechanical as well as in the neurological structure can take over important contributions to control, which would otherwise need to be performed by the higher control levels.

Hopf Bifurcations in Complex Multiagent Activity: The Signature of Discrete to Rhythmic Behavioral Transitions

Most human actions are composed of two fundamental movement types, discrete and rhythmic movements. These movement types, or primitives, are analogous to the two elemental behaviors of nonlinear dynamical systems, namely, fixed-point and limit cycle behavior, respectively. Furthermore, there is now a growing body of research demonstrating how various human actions and behaviors can be effectively modeled and understood using a small set of low-dimensional, fixed-point and limit cycle dynamical systems (differential equations). Here, we provide an overview of these dynamical motorprimitives and detail recent research demonstrating how these dynamical primitives can be used to model the task dynamics of complex multiagent behavior. More specifically, we review how a task-dynamic model of multiagent shepherding behavior, composed of rudimentary fixed-point and limit cycle dynamical primitives, can not only effectively model the behavior of cooperating human co-actors, but also reveals how the discovery and intentional use of optimal behavioral coordination during task learning is marked by a spontaneous, self-organized transition between fixed-point and limit cycle dynamics (i.e., via a Hopf bifurcation).

Human control of complex objects: Towards more dexterous robots

Manipulation of objects with underactuated dynamics remains a challenge for robots. In contrast, humans excel at 'tool use' and more insight into human control strategies may inform robotic control architectures. We examined human control of objects that exhibit complex - underactuated, nonlinear, and potentially chaotic dynamics, such as transporting a cup of coffee. Simple control strategies appropriate for unconstrained movements, such as maximizing smoothness, fail as interaction forces have to be compensated or preempted. However, predictive control based on internal models appears daunting when the objects have nonlinear and unpredictable dynamics. We hypothesized that humans learn strategies that make these interactions predictable. Using a virtual environment subjects interacted with a virtual cup and rolling ball using a robotic visual and haptic interface. Two different metrics quantified predictability: stability or contraction, and mutual information between controller and object. In point-to-point displacements subjects exploited the contracting regions of the object dynamics to safely navigate perturbations. Control contraction metrics showed that subjects used a controller that exponentially stabilized trajectories. During continuous cup-and-ball displacements subjects developed predictable solutions sacrificing smoothness and energy efficiency. These results may stimulate control strategies for dexterous robotic manipulators and human-robot interaction.

Separating neural influences from peripheral mechanics: the speed-curvature relation in mechanically constrained actions

While the study of unconstrained movements has revealed important features of neural control, generalizing those insights to more sophisticated object manipulation is challenging. Humans excel at physical interaction with objects, even when those objects introduce complex dynamics and kinematic constraints. This study examined humans turning a horizontal planar crank (radius 10.29 cm) at their preferred and three instructed speeds (with visual feedback), both in clockwise and counterclockwise directions. To explore the role of neuromechanical dynamics, the instructed speeds covered a wide range: fast (near the limits of performance), medium (near preferred speed), and very slow (rendering dynamic effects negligible). Because kinematically constrained movements involve significant physical interaction, disentangling neural control from the influences of biomechanics presents a challenge. To address it, we modeled the interactive dynamics to "subtract off" peripheral biomechanics from observed force and kinematic data, thereby estimating aspects of underlying neural action that may be expressed in terms of motion. We demonstrate the value of this method: remarkably, an approximately elliptical path emerged, and speed minima coincided with curvature maxima, similar to what is seen in unconstrained movements, even though the hand moved at nearly constant speed along a constant-curvature path. These findings suggest that the neural controller takes advantage of peripheral biomechanics to simplify physical interaction. As a result, patterns seen in unconstrained movements persist even when physical interaction prevents their expression in hand kinematics. The reemergence of a speed-curvature relation indicates that it is due, at least in part, to neural processes that emphasize smoothness and predictability.NEW & NOTEWORTHY Physically interacting with kinematic constraints is commonplace in everyday actions. We report a study of humans turning a crank, a circular constraint that imposes constant hand path curvature and hence should suppress variations of hand speed due to the power-law speed-curvature relation widely reported for unconstrained motions. Remarkably, we found that, when peripheral biomechanical factors are removed, a speed-curvature relation reemerges, indicating that it is, at least in part, of neural origin.

Towards an Understanding of Control of Complex Rhythmical "Wavelike" Coordination in Humans

How does the human neurophysiological system self-organize to achieve optimal phase relationships among joints and limbs, such as in the composite rhythms of butterfly and front crawl swimming, drumming, or dancing? We conducted a systematic review of literature relating to central nervous system (CNS) control of phase among joint/limbs in continuous rhythmic activities. SCOPUS and Web of Science were searched using keywords “Phase AND Rhythm AND Coordination”. This yielded 1039 matches from which 23 papers were extracted for inclusion based on screening criteria. The empirical evidence arising from in-vivo, fictive, in-vitro, and modelling of neural control in humans, other species, and robots indicates that the control of movement is facilitated and simplified by innervating muscle synergies by way of spinal central pattern generators (CPGs). These typically behave like oscillators enabling stable repetition across cycles of movements. This approach provides a foundation to guide the design of empirical research in human swimming and other limb independent activities. For example, future research could be conducted to explore whether the Saltiel two-layer CPG model to explain locomotion in cats might also explain the complex relationships among the cyclical motions in human swimming.

Robustness in Human Manipulation of Dynamically Complex Objects through Control Contraction Metrics

Control and manipulation of objects with underactuated dynamics remains a challenge for robots. Due to their typically nonlinear dynamics, it is computationally taxing to implement model-based planning and control techniques. Yet humans can skillfully manipulate such objects, seemingly with ease. More insight into human control strategies may inform how to enhance control strategies in robots. This study examined human control of objects that exhibit complex - underactuated and nonlinear - dynamics. We hypothesized that humans seek to make their trajectories exponentially stable to achieve robustness in the face of external perturbations. A stable trajectory is also robust to the high levels of noise in the human neuromotor system. Motivated by the task of carrying a cup of coffee, a virtual implementation of transporting a cart-pendulum system was developed. Subjects interacted with the virtual system via a robotic manipulandum that provided a haptic and visual interface. Human subjects were instructed to transport this simplified system to a target position as fast as possible without 'spilling coffee', while accommodating different visible perturbations that could be anticipated. To test the hypothesis of exponential convergence, tools from the framework of control contraction metrics were leveraged to analyze human trajectories. Results showed that with practice the trajectories indeed became exponentially stable, selectively around the perturbation. While these findings are agnostic about the involvement of feedback and feedforward control, they do support the hypothesis that humans learn to make trajectories stable, consistent with achieving predictability.

Synergies reciprocally relate end-effector and joint-angles in rhythmic pointing movements

During rhythmic pointing movements, degrees of freedom (DOF) in the human action system-such as joint-angles in the arm-are assumed to covary to stabilise end-effector movement, e.g. index finger. In this paper, it is suggested that the end-effector movement and the coordination of DOF are reciprocally related in synergies that link DOF so as to produce the end-effector movement. The coordination of DOF in synergies and the relation between end-effector movement and DOF coordination received little attention, though essential to understand the principles of synergy formation. Therefore, the current study assessed how the end-effector movement related to the coordination of joint-angles during rhythmic pointing across target widths and distances. Results demonstrated that joint-angles were linked in different synergies when end-effector movements differed across conditions. Furthermore, in every condition, three joint-angles (shoulder plane of elevation, shoulder inward-outward rotation, elbow flexion-extension) largely drove the end-effector, and all joint-angles contributed to covariation that stabilised the end-effector. Together, results demonstrated synergies that produced the end-effector movement, constrained joint-angles so that they covaried to stabilise the end-effector, and differed when end-effector movement differed. Hence, end-effector and joint-angles were reciprocally related in synergies-indicating that the action system was organised as a complex dynamical system.

The primacy of rhythm: how discrete actions merge into a stable rhythmic pattern

This study examined how humans spontaneously merge a sequence of discrete actions into a rhythmic pattern, even when periodicity is not required. Two experiments used a virtual throwing task, in which subjects performed a long sequence of discrete throwing movements, aiming to hit a virtual target. In experiment 1, subjects performed the task for 11 sessions. Although there was no instruction to perform rhythmically, the variability of the interthrow intervals decreased to a level comparable to that of synchronizing with a metronome; furthermore, dwell times shortened or even disappeared with practice. Floquet multipliers and decreasing variability of the arm trajectories estimated in state space indicated an increasing degree of dynamic stability. Subjects who achieved a higher level of periodicity and stability also displayed higher accuracy in the throwing task. To directly test whether rhythmicity affected performance, experiment 2 disrupted the evolving continuity and periodicity by enforcing a pause between successive throws. This discrete group performed significantly worse and with higher variability in their arm trajectories than the self-paced group. These findings are discussed in the context of previous neuroimaging results showing that rhythmic movements involve significantly fewer cortical and subcortical activations than discrete movements and therefore may pose a computationally more parsimonious solution. Such emerging stable rhythms in neuromotor subsystems may serve as building blocks or dynamic primitives for complex actions. The tendency for humans to spontaneously fall into a rhythm in voluntary movements is consistent with the ubiquity of rhythms at all levels of the physiological system. NEW & NOTEWORTHY When performing a series of throws to hit a target, humans spontaneously merged successive actions into a continuous approximately periodic pattern. The degree of rhythmicity and stability correlated with hitting accuracy. Enforcing irregular pauses between throws to disrupt the rhythm deteriorated performance. Stable rhythmic patterns may simplify control of movement and serve as dynamic primitives for more complex actions. This observation reveals that biological systems tend to exhibit rhythmic behavior consistent with a plethora of physiological processes.

Rhythmic robotic training enhances motor skills of both rhythmic and discrete upper-limb movements after stroke: a longitudinal pilot study

Discrete and rhythmic movements are two fundamental motor primitives being, at least partially, controlled by separate neural circuitries. After a stroke, both primitives may be impaired in the upper limb. Currently, intensive functional movement therapy is recommended after stroke, but it is mainly composed of discrete movements. No recommendation is made for the specific training of rhythmic movements. However, if they form two different primitives, both should receive a specific training to recover the complete motor repertoire, as many daily live movements integrate both of them. This paper reports the effects of a pure unilateral rhythmic movement therapy on motor performance, after stroke. Thirteen patients with chronic stroke participated in this longitudinal pilot study. They were assessed twice before the therapy to validate their chronic state, and twice after the last session to establish the short-term and long-term effects of the therapy. The therapy itself was composed of 12 sessions spread over 1 month. The exercises consisted in performing straight or circular rhythmic movements, while receiving assistance as need through a robotic device. Short-term and long-term improvements were observed in rhythmic movements regarding smoothness, velocity, and harmonicity. More surprisingly, some transfer occurred to the untrained discrete movements. This finding disputes previous studies that reported no transfer from rhythmic to discrete movements with healthy participants.

When Non-Dominant Is Better than Dominant: Kinesiotape Modulates Asymmetries in Timed Performance during a Synchronization-Continuation Task

There is a growing consensus regarding the specialization of the non-dominant limb (NDL)/hemisphere system to employ proprioceptive feedback when executing motor actions. In a wide variety of rhythmic tasks the dominant limb (DL) has advantages in speed and timing consistency over the NDL. Recently, we demonstrated that the application of Kinesio^® Tex (KT) tape, an elastic therapeutic device used for treating athletic injuries, improves significantly the timing consistency of isochronous wrist’s flexion-extensions (IWFEs) of the DL. We argued that the augmented precision of IWFEs is determined by a more efficient motor control during movements due to the extra-proprioceptive effect provided by KT. In this study, we tested the effect of KT on timing precision of IWFEs performed with the DL and the NDL, and we evaluated the efficacy of KT to counteract possible timing precision difference between limbs. Young healthy subjects performed with and without KT (NKT) a synchronization-continuation task in which they first entrained IWFEs to paced auditory stimuli (synchronization phase), and subsequently continued to produce motor responses with the same temporal interval in the absence of the auditory stimulus (continuation phase). Two inter-onset intervals (IOIs) of 550-ms and 800-ms, one within and the other beyond the boundaries of the spontaneous motor tempo, were tested. Kinematics was recorded and temporal parameters were extracted and analyzed. Our results show that limb advantages in performing proficiently rhythmic movements are not side-locked but depend also on speed of movement. The application of KT significantly reduces the timing variability of IWFEs performed at 550-ms IOI. KT not only cancels the disadvantages of the NDL but also makes it even more precise than the DL without KT. The superior sensitivity of the NDL to use the extra-sensory information provided by KT is attributed to a greater competence of the NDL/hemisphere system to rely on sensory input. The findings in this study add a new piece of information to the context of motor timing literature. The performance asymmetries here demonstrated as preferred temporal environments could reflect limb differences in the choice of sensorimotor control strategies for the production of human movement.

Moving slowly is hard for humans: limitations of dynamic primitives

Mounting evidence suggests that human motor control uses dynamic primitives, attractors of dynamic neuromechanical systems that require minimal central supervision. However, advantages for control may be offset by compromised versatility. Extending recent results showing that humans could not sustain discrete movements as duration decreased, this study tested whether smoothly rhythmic movements could be maintained as duration increased. Participants performed horizontal movements between two targets, paced by sounds with intervals that increased from 1 to 6 s by 200 ms per cycle and then decreased again. The instruction emphasized smooth rhythmic movements without interspersed dwell times. We hypothesized that 1) when oscillatory motions slow down, smoothness decreases; 2) slower oscillatory motions are executed as submovements or even discrete movements; and 3) the transition between smooth oscillations and submovements shows hysteresis. An alternative hypothesis was that 4) removing visual feedback restores smoothness, indicative of visually evoked corrections causing the irregularity. Results showed that humans could not perform slow and smooth oscillatory movements. Harmonicity decreased with longer intervals, and dwell times between cycles appeared and became prominent at slower speeds. Velocity profiles showed an increase with cycle duration of the number of overlapping submovements. There was weak evidence of hysteresis in the transition between these two types of movement. Eliminating vision had no effect, suggesting that intermittent visually evoked corrections did not underlie this phenomenon. These results show that it is hard for humans to execute smooth rhythmic motions very slowly. Instead, they "default" to another dynamic primitive and compose motion as a sequence of overlapping submovements.NEW & NOTEWORTHY Complementing a large body of prior work showing advantages of composing primitives to manage the complexity of motor control, this paper uncovers a limitation due to composition of behavior from dynamic primitives: while slower execution frequently makes a task easier, there is a limit and it is hard for humans to move very slowly. We suggest that this remarkable limitation is not due to inadequacies of muscle, nor to slow neural communication, but is a consequence of how the control of movement is organized.

Performance-based robotic assistance during rhythmic arm exercises

Background

Rhythmic and discrete upper-limb movements are two fundamental motor primitives controlled by different neural pathways, at least partially. After stroke, both primitives can be impaired. Both conventional and robot-assisted therapies mainly train discrete functional movements like reaching and grasping. However, if the movements form two distinct neural and functional primitives, both should be trained to recover the complete motor repertoire. Recent studies show that rhythmic movements tend to be less impaired than discrete ones, so combining both movement types in therapy could support the execution of movements with a higher degree of impairment by movements that are performed more stably.

Methods

A new performance-based assistance method was developed to train rhythmic movements with a rehabilitation robot. The algorithm uses the assist-as-needed paradigm by independently assessing and assisting movement features of smoothness, velocity, and amplitude. The method relies on different building blocks: (i) an adaptive oscillator captures the main movement harmonic in state variables, (ii) custom metrics measure the movement performance regarding the three features, and (iii) adaptive forces assist the patient. The patient is encouraged to improve performance regarding these three features with assistance forces computed in parallel to each other. The method was tested with simulated jerky signals and a pilot experiment with two stroke patients, who were instructed to make circular movements with an end-effector robot with assistance during half of the trials.

Results

Simulation data reveal sensitivity of the metrics for assessing the features while limiting interference between them. The assistance’s effectiveness with stroke patients is established since it (i) adapts to the patient’s real-time performance, (ii) improves patient motor performance, and (iii) does not lead the patient to slack. The smoothness assistance was by far the most used by both patients, while it provided no active mechanical work to the patient on average.

Conclusion

Our performance-based assistance method for training rhythmic movements is a viable candidate to complement robot-assisted upper-limb therapies for training a larger motor repertoire.

Implicit guidance to stable performance in a rhythmic perceptual-motor skill

Feedback about error or reward is regarded essential for aiding learners to acquire a perceptual-motor skill. Yet, when a task has redundancy and the mapping between execution and performance outcome is unknown, simple error feedback does not suffice in guiding the learner toward the optimal solutions. The present study developed and tested a new means of implicitly guiding learners to acquire a perceptual-motor skill, rhythmically bouncing a ball on a racket. Due to its rhythmic nature, this task affords dynamically stable solutions that are robust to small errors and noise, a strategy that is independent from actively correcting error. Based on the task model implemented in a virtual environment, a time-shift manipulation was designed to shift the range of ball-racket contacts that achieved dynamically stable solutions. In two experiments, subjects practiced with this manipulation that guided them to impact the ball with more negative racket accelerations, the indicator for the strategy with dynamic stability. Subjects who practiced under normal conditions took longer time to acquire this strategy, although error measures were identical between the control and experimental groups. Unlike in many other haptic guidance or adaptation studies, the experimental groups not only learned, but also maintained the stable solution after the manipulation was removed. These results are a first demonstration that more subtle ways to guide the learner to better performance are needed especially in tasks with redundancy, where error feedback may not be sufficient.

Timing skills and expertise: discrete and continuous timed movements among musicians and athletes

Introduction: Movement-based expertise relies on precise timing of movements and the capacity to predict the timing of events. Music performance involves discrete rhythmic actions that adhere to regular cycles of timed events, whereas many sports involve continuous movements that are not timed in a cyclical manner. It has been proposed that the precision of discrete movements relies on event timing (clock mechanism), whereas continuous movements are controlled by emergent timing. We examined whether movement-based expertise influences the timing mode adopted to maintain precise rhythmic actions.

Materials and Method: Timing precision was evaluated in musicians, athletes and control participants. Discrete and continuous movements were assessed using finger-tapping and circle-drawing tasks, respectively, based on the synchronization-continuation paradigm. In Experiment 1, no auditory feedback was provided in the continuation phase of the trials, whereas in Experiment 2 every action triggered a feedback tone.

Results: Analysis of precision in the continuation phase indicated that athletes performed significantly better than musicians and controls in the circle-drawing task, whereas musicians were more precise than controls in the finger tapping task. Interestingly, musicians were also more precise than controls in the circle-drawing task. Results also showed that the timing mode adopted was dependent on expertise and the presence of auditory feedback.

Discussion: Results showed that movement-based expertise is associated with enhanced timing, but these effects depend on the nature of the training. Expertise was found to influence the timing strategy adopted to maintain precise rhythmic movements, suggesting that event and emergent timing mechanisms are not strictly tied to specific tasks, but can both be adopted to achieve precise timing.

A developmental study of the effect of music training on timed movements

When people clap to music, sing, play a musical instrument, or dance, they engage in temporal entrainment. We examined the effect of music training on the precision of temporal entrainment in 57 children aged 10–14 years (31 musicians, 26 non-musicians). Performance was examined for two tasks: self-paced finger tapping (discrete movements) and circle drawing (continuous movements). For each task, participants synchronized their movements with a steady pacing signal and then continued the movement at the same rate in the absence of the pacing signal. Analysis of movements during the continuation phase revealed that musicians were more accurate than non-musicians at finger tapping and, to a lesser extent, circle drawing. Performance on the finger-tapping task was positively associated with the number of years of formal music training, whereas performance on the circle-drawing task was positively associated with the age of participants. These results indicate that music training and maturation of the motor system reinforce distinct skills of timed movement.

Dynamic primitives of motor behavior

We present in outline a theory of sensorimotor control based on dynamic primitives, which we define as attractors. To account for the broad class of human interactive behaviors-especially tool use-we propose three distinct primitives: submovements, oscillations, and mechanical impedances, the latter necessary for interaction with objects. Owing to the fundamental features of the neuromuscular system-most notably, its slow response-we argue that encoding in terms of parameterized primitives may be an essential simplification required for learning, performance, and retention of complex skills. Primitives may simultaneously and sequentially be combined to produce observable forces and motions. This may be achieved by defining a virtual trajectory composed of submovements and/or oscillations interacting with impedances. Identifying primitives requires care: in principle, overlapping submovements would be sufficient to compose all observed movements but biological evidence shows that oscillations are a distinct primitive. Conversely, we suggest that kinematic synergies, frequently discussed as primitives of complex actions, may be an emergent consequence of neuromuscular impedance. To illustrate how these dynamic primitives may account for complex actions, we briefly review three types of interactive behaviors: constrained motion, impact tasks, and manipulation of dynamic objects.

How the brain generates movement

In this study, we assume that the brain uses a general-purpose pattern generator to transform static commands into basic movement segments. We hypothesize that this pattern generator includes an oscillator whose complete cycle generates a single movement segment. In order to demonstrate this hypothesis, we construct an oscillator-based model of movement generation. The model includes an oscillator that generates harmonic outputs whose frequency and amplitudes can be modulated by external inputs. The harmonic outputs drive a number of integrators, each activating a single muscle. The model generates muscle activation patterns composed of rectilinear and harmonic terms. We show that rectilinear and fundamental harmonic terms account for known properties of natural movements, such as the invariant bell-shaped hand velocity profile during reaching. We implement these dynamics by a neural network model and characterize the tuning properties of the neural integrator cells, the neural oscillator cells, and the inputs to the system. Finally, we propose a method to test our hypothesis that a neural oscillator is a central component in the generation of voluntary movement.

Separate representations of dynamics in rhythmic and discrete movements: evidence from motor learning

Rhythmic and discrete arm movements occur ubiquitously in everyday life, and there is a debate as to whether these two classes of movements arise from the same or different underlying neural mechanisms. Here we examine interference in a motor-learning paradigm to test whether rhythmic and discrete movements employ at least partially separate neural representations. Subjects were required to make circular movements of their right hand while they were exposed to a velocity-dependent force field that perturbed the circularity of the movement path. The direction of the force-field perturbation reversed at the end of each block of 20 revolutions. When subjects made only rhythmic or only discrete circular movements, interference was observed when switching between the two opposing force fields. However, when subjects alternated between blocks of rhythmic and discrete movements, such that each was uniquely associated with one of the perturbation directions, interference was significantly reduced. Only in this case did subjects learn to corepresent the two opposing perturbations, suggesting that different neural resources were employed for the two movement types. Our results provide further evidence that rhythmic and discrete movements employ at least partially separate control mechanisms in the motor system.

Computer simulations of neural mechanisms explaining upper and lower limb excitatory neural coupling

Background

When humans perform rhythmic upper and lower limb locomotor-like movements, there is an excitatory effect of upper limb exertion on lower limb muscle recruitment. To investigate potential neural mechanisms for this behavioral observation, we developed computer simulations modeling interlimb neural pathways among central pattern generators. We hypothesized that enhancement of muscle recruitment from interlimb spinal mechanisms was not sufficient to explain muscle enhancement levels observed in experimental data.

Methods

We used Matsuoka oscillators for the central pattern generators (CPG) and determined parameters that enhanced amplitudes of rhythmic steady state bursts. Potential mechanisms for output enhancement were excitatory and inhibitory sensory feedback gains, excitatory and inhibitory interlimb coupling gains, and coupling geometry. We first simulated the simplest case, a single CPG, and then expanded the model to have two CPGs and lastly four CPGs. In the two and four CPG models, the lower limb CPGs did not receive supraspinal input such that the only mechanisms available for enhancing output were interlimb coupling gains and sensory feedback gains.

Results

In a two-CPG model with inhibitory sensory feedback gains, only excitatory gains of ipsilateral flexor-extensor/extensor-flexor coupling produced reciprocal upper-lower limb bursts and enhanced output up to 26%. In a two-CPG model with excitatory sensory feedback gains, excitatory gains of contralateral flexor-flexor/extensor-extensor coupling produced reciprocal upper-lower limb bursts and enhanced output up to 100%. However, within a given excitatory sensory feedback gain, enhancement due to excitatory interlimb gains could only reach levels up to 20%. Interconnecting four CPGs to have ipsilateral flexor-extensor/extensor-flexor coupling, contralateral flexor-flexor/extensor-extensor coupling, and bilateral flexor-extensor/extensor-flexor coupling could enhance motor output up to 32%. Enhancement observed in experimental data exceeded 32%. Enhancement within this symmetrical four-CPG neural architecture was more sensitive to relatively small interlimb coupling gains. Excitatory sensory feedback gains could produce greater output amplitudes, but larger gains were required for entrainment compared to inhibitory sensory feedback gains.

Conclusions

Based on these simulations, symmetrical interlimb coupling can account for much, but not all of the excitatory neural coupling between upper and lower limbs during rhythmic locomotor-like movements.

Modeling discrete and rhythmic movements through motor primitives: a review

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.

Optimal control of a hybrid rhythmic-discrete task: the bouncing ball revisited

Rhythmically bouncing a ball with a racket is a hybrid task that combines continuous rhythmic actuation of the racket with the control of discrete impact events between racket and ball. This study presents experimental data and a two-layered modeling framework that explicitly addresses the hybrid nature of control: a first discrete layer calculates the state to reach at impact and the second continuous layer smoothly drives the racket to this desired state, based on optimality principles. The testbed for this hybrid model is task performance at a range of increasingly slower tempos. When slowing the rhythm of the bouncing actions, the continuous cycles become separated into a sequence of discrete movements interspersed by dwell times and directed to achieve the desired impact. Analyses of human performance show increasing variability of performance measures with slower tempi, associated with a change in racket trajectories from approximately sinusoidal to less symmetrical velocity profiles. Matching results of model simulations give support to a hybrid control model based on optimality, and therefore suggest that optimality principles are applicable to the sensorimotor control of complex movements such as ball bouncing.

A computational model for rhythmic and discrete movements in uni- and bimanual coordination

Current research on discrete and rhythmic movements differs in both experimental procedures and theory, despite the ubiquitous overlap between discrete and rhythmic components in everyday behaviors. Models of rhythmic movements usually use oscillatory systems mimicking central pattern generators (CPGs). In contrast, models of discrete movements often employ optimization principles, thereby reflecting the higher-level cortical resources involved in the generation of such movements. This letter proposes a unified model for the generation of both rhythmic and discrete movements. We show that a physiologically motivated model of a CPG can not only generate simple rhythmic movements with only a small set of parameters, but can also produce discrete movements if the CPG is fed with an exponentially decaying phasic input. We further show that a particular coupling between two of these units can reproduce main findings on in-phase and antiphase stability. Finally, we propose an integrated model of combined rhythmic and discrete movements for the two hands. These movement classes are sequentially addressed in this letter with increasing model complexity. The model variations are discussed in relation to the degree of recruitment of the higher-level cortical resources, necessary for such movements.

Altered Gravity Highlights Central Pattern Generator Mechanisms

In many nonprimate species, rhythmic patterns of activity such as locomotion or respiration are generated by neural networks at the spinal level. These neural networks are called central pattern generators (CPGs). Under normal gravitational conditions, the energy efficiency and the robustness of human rhythmic movements are due to the ability of CPGs to drive the system at a pace close to its resonant frequency. This property can be compared with oscillators running at resonant frequency, for which the energy is optimally exchanged with the environment. However, the ability of the CPG to adapt the frequency of rhythmic movements to new gravitational conditions has never been studied. We show here that the frequency of a rhythmic movement of the upper limb is systematically influenced by the different gravitational conditions created in parabolic flight. The period of the arm movement is shortened with increasing gravity levels. In weightlessness, however, the period is more dependent on instructions given to the participants, suggesting a decreased influence of resonant frequency. Our results are in agreement with a computational model of a CPG coupled to a simple pendulum under the control of gravity. We demonstrate that the innate modulation of rhythmic movements by CPGs is highly flexible across gravitational contexts. This further supports the involvement of CPG mechanisms in the achievement of efficient rhythmic arm movements. Our contribution is of major interest for the study of human rhythmic activities, both in a normal Earth environment and during microgravity conditions in space.

Robotics and neuroscience: a rhythmic interaction

At the crossing between motor control neuroscience and robotics system theory, the paper presents a rhythmic experiment that is amenable both to handy laboratory implementation and simple mathematical modeling. The experiment is based on an impact juggling task, requiring the coordination of two upper-limb effectors and some phase-locking with the trajectories of one or several juggled objects. We describe the experiment, its implementation and the mathematical model used for the analysis. Our underlying research focuses on the role of sensory feedback in rhythmic tasks. In a robotic implementation of our experiment, we study the minimum feedback that is required to achieve robust control. A limited source of feedback, measuring only the impact times, is shown to give promising results. A second field of investigation concerns the human behavior in the same impact juggling task. We study how a variation of the tempo induces a transition between two distinct control strategies with different sensory feedback requirements. Analogies and differences between the robotic and human behaviors are obviously of high relevance in such a flexible setup.

On rhythmic and discrete movements: reflections, definitions and implications for motor control

At present, rhythmic and discrete movements are investigated by largely distinct research communities using different experimental paradigms and theoretical constructs. As these two classes of movements are tightly interlinked in everyday behavior, a common theoretical foundation spanning across these two types of movements would be valuable. Furthermore, it has been argued that these two movement types may constitute primitives for more complex behavior. The goal of this paper is to develop a rigorous taxonomic foundation that not only permits better communication between different research communities, but also helps in defining movement types in experimental design and thereby clarifies fundamental questions about primitives in motor control. We propose formal definitions for discrete and rhythmic movements, analyze some of their variants, and discuss the application of a smoothness measure to both types that enables quantification of discreteness and rhythmicity. Central to the definition of discrete movement is their separation by postures. Based on this intuitive definition, certain variants of rhythmic movement are indistinguishable from a sequence of discrete movements, reflecting an ongoing debate in the motor neuroscience literature. Conversely, there exist rhythmic movements that cannot be composed of a sequence of discrete movements. As such, this taxonomy may provide a language for studying more complex behaviors in a principled fashion.

Effects of movement frequency and joint kinetics on the joint coordination underlying bimanual circle drawing

Ten healthy participants performed bimanual symmetric and asymmetric circle drawing at 4 frequencies. The authors partitioned the variance of the joint configuration across repetitions into 1 component representing equivalent joint configurations with respect to achieving stability of the mean hand path (i.e., goal-equivalent variance, GEV) and 1 component leading to a variable hand path (non-goal-equivalent variance, NGEV) across cycles. Higher frequencies led to increased NGEV related to control of the nondominant hand and to the relative position and orientation between the hands during asymmetric drawing. The results were related to differences in muscle and interaction moments between the arms, and they suggest a possible relationship between the ability to use intersegmental forces and the stability of interlimb synergy.

Target width scaling in a repetitive aiming task: switching between cyclical and discrete units of action

An aiming task was used to identify the processes whereby the motor system adapted a repetitive aiming action to systematic changes in ID (ID = log(2 )(2A/W), Fitts in J Exp Psychol 47:381-391, 1954) within a single trial. Task ID was scaled in a trial by moving the outside edge of two stationary targets to produce nine different target IDs in a trail. The ID within a trial was scaled in one of two directions: (1) an increasing ID condition, starting with an ID = 3.07 and ending with an ID = 5.91; and (2) a decreasing ID condition, starting with an ID = 5.91 and ending with an ID = 3.07. An index of movement harmonicity (Guiard in Acta Psychol 82:139-159, 1993) revealed that the repetitive aiming action was harmonic in nature when task ID was 3.07, and consisted of a series of discrete segments when task ID was 5.91. This finding provides evidence for the existence of discrete and cyclical units of action that are irreducible and that may be employed independently to assemble longer continuous actions. The scaling of ID within a trial promoted a transition in repetitive aiming motions assembled from discrete and cyclical units of action. A variety of kinematic measures (e.g., movement harmonicity, time spent accelerating the limb) revealed a critical ID (ID(c)) region (4.01-4.91) separating aiming motions governed by the different units of action. Enhancement of fluctuations before the transition were found in the movement harmonicity data and in the distance traveled to peak velocity data, with variability in these measures highest in the ID(c) region. The enhancement of fluctuations indicates that loss of stability in the limb's motion acted as a key mechanism underlying the transition between units of action. The loss of stability was associated with the transition from cyclical to discrete actions and with the transition from discrete to cyclical actions. The transition between units of action may be conceptualized as a transition from a limit cycle attractor (cyclical unit of action) to a shift between two fixed-point attractors (discrete unit of action) when ID was increased, with the transition occurring in the opposite direction when ID was decreased.

Intermanual interactions during initiation and production of rhythmic and discrete movements in individuals lacking a corpus callosum

Three individuals lacking a corpus callosum, two due to callosotomy and one agenesis, and three age-matched healthy controls were tested on a bimanual task in which a discrete or rhythmic arm movement was initiated following a visual signal while the other arm produced continuous, rhythmic movements. The control participants initiated the secondary, rhythmic movement in phase with the ongoing rhythmic base movement and the two limbs were coupled in an inphase mode across the duration of the trial. In contrast, the acallosal individuals failed to show phase entrainment at the initiation of the secondary, rhythmic movements. Moreover, the callosotomy patients exhibited weak coupling between the rhythmically moving limbs while the individual with callosal agenesis consistently synchronized in an antiphase mode. The control participants exhibited increased perturbation of the ongoing base movement when initiating a discrete movement; for the acallosal participants, the base movement was similarly perturbed in both secondary movement conditions. These results are consistent with the hypothesis that intermanual interactions observed during bimanual movements arise from various levels of control, and that these are distinct for discrete and rhythmic movements. Temporal coupling during rhythmic movements arises in large part from transcallosal interactions between the two hemispheres. The imposition of a secondary movement may transiently disrupt an ongoing rhythmic movement even in the absence of the corpus callosum. This may reflect subcortical interactions associated with response initiation, or, due to dual task demands, a transient shift in attentional resources.

The role of different submovement types during pointing to a target

The present study extends our previous findings in challenging the traditional interpretation of irregularities in the velocity profile of pointing movements as corrective submovements performed to improve accuracy of target achievement. The study is driven by a hypothesis that pointing includes at least two subtasks, accurate target achievement and motion termination, each of which can cause submovements (Dounskaia et al. Exp Brain Res 164:505-516, 2005). To investigate submovements associated with these subtasks, two tasks were performed in the experiment. Task 1 was used to examine the contribution of the two subtasks on submovement production by comparing submovements in discrete movements that include motion termination and in cyclic movements during which motion termination is not performed. Target size manipulations emphasized submovements related to the accuracy subtask. The results confirmed that both subtasks included in pointing cause submovements. Gross types of submovements (types 1 and 2) were associated with motion termination and fine submovements (type 3) with accuracy regulation. Task 2 further investigated sources of the accuracy-associated type 3 submovements by including only cyclic movements performed at two levels of frequency. Most (97.6%) of the submovements in task 2 were of type 3. Submovement incidence was strongly (inversely) associated with cyclic frequency, and it was independent of target size. This result questions the accuracy subtask as a primary source for type 3 submovements, and it raises the possibility that these submovements are an inherent property of low-speed movements. Together, results of the two tasks support our previous finding that gross submovements are not necessarily related to accuracy regulation. They also provide evidence that challenges the interpretation of fine submovements as corrections performed voluntarily to improve pointing accuracy. Alternative interpretations of accuracy regulation mechanisms, such as regulation of muscle stiffness and of the muscle co-contraction level are discussed in light of the present results.

Influence of biomechanical factors on substructure of pointing movements

Irregularities in the velocity profile near the end of pointing movements have been interpreted as corrective submovements whose purpose is to provide accuracy of pointing to the target. The purpose of the present study was to investigate whether two additional factors related to biomechanical properties of the arm also cause submovements. First, motion termination and stabilization of the limb in the final position required by a discrete pointing task may contribute to submovements. Second, inaccurate regulation of interactive torque at the joints may also cause submovements. To investigate the contributions of these two biomechanical factors and the traditionally considered factor of pointing accuracy, the incidence of submovements was analyzed during three types of experimental manipulations. In addition to target size manipulations (small and large targets), conditions for motion termination were manipulated by examining discrete movements (which terminated at the target) and reciprocal movements (which reversed direction without dwelling on the target). Interaction torques were varied by using targets that require different shoulder-elbow coordination patterns. Submovements were detected in 41% of all analyzed movements. Data supported influences from the accuracy and motion termination factors but not from the interactive torque regulation factor on submovement incidence. Gross submovements were associated with motion termination; fine submovements primarily with accuracy demands. These findings and the analysis of temporal movement characteristics suggest that motion termination is an extra movement component that makes control of discrete movements different to control of reciprocal movements. Implications of the findings to a noise-related interpretation of Fitts' law are discussed. The study emphasizes the influence of arm biomechanics on endpoint kinematics.

From parallel sequence representations to calligraphic control: a conspiracy of neural circuits

Calligraphic writing presents many challenges for motor control, including: learning and recall of stroke sequences; critical timing of stroke onsets and durations; fine control of grip and contact forces; and letterform invariance under size scaling, which entails fine control of stroke directions and amplitudes during recruitment and derecruitment of musculoskeletal degrees of freedom. Experimental and computational studies in behavioral neuroscience have progressed toward explaining the learning, planning, and control exercised in tasks that share features with calligraphic writing and drawing. This article highlights component operations ranging from parallel sequence representations to fine force control. Treated in succession are: competitive queuing models of sequence representation, performance, learning, and recall; letter size scaling and motor equivalence; cursive handwriting models in which sensory-motor transformations are performed by circuits that learn inverse differential kinematic mappings; and fine-grained control of timing and transient forces by circuit models that learn to solve inverse dynamics problems.

The Excitator as a Minimal Model for the Coordination Dynamics of Discrete and Rhythmic Movement Generation

The authors identify a class of excitable two-dimensional model systems, the excitators, that provide an entry point to the understanding of the mechanisms of discrete and rhythmic movement generation and a variety of related phenomena, such as false starts and the geometry of phase space trajectories. The starting point of their analysis is the topological properties of the phase flow. In particular, the phenomenon of false starts provides a characteristic structural condition for the phase flow, the separatrix, which partitions the phase space. Threshold phenomena, which are characteristic of excitable systems, as well as stable and unstable fixed points and periodic orbits, are discussed. Stable manifolds in the proximity of fixed points, resulting in an overshoot and a slow return phase after movement execution, are predicted in the analysis. To investigate coordination phenomena, the authors discuss the effects of two types of couplings, the sigmoidal coupling and a truncated version thereof, known as the Haken-Kelso-Bunz (HKB) coupling. They show analytically and numerically that the sigmoidal coupling leads to convergence phenomena in phase space, whereas the HKB coupling displays convergent as well as divergent behaviors. The authors suggest a specific representation of the excitator that allows the quantification of the predictions.

Discrete and cyclical movements: unified dynamics or separate control?

In the literature on motor control, three theoretical perspectives on the relation between discrete and cyclical movements may be discerned: (a) cyclical movements are concatenated discrete movements; (b) discrete movements are a limiting case of cyclical movements, and (c) discrete and cyclical movements are motor primitives that may be combined but are irreducible to each other. To examine the tenability of these perspectives, 16 participants performed cyclical and discrete (flexion and extension) reaching movements of various amplitudes to differently sized targets. The kinematic properties of the recorded movements were analyzed and compared in detail. The cyclical, ongoing movements differed markedly from the discrete movements as well as from the first and last half-cycles of a bout of cyclical movements, especially in terms of their symmetry ratio. These effects were largely independent of amplitude, target size and movement direction (flexion-extension). The results obtained ruled out perspective (a) and, in principle, left open perspectives (b) and (c). However, the observed kinematic features were not readily accounted for by the specific dynamical models that have been proposed under perspectives (b) and (c). Future modeling attempts should explicate the dynamics of initiation and abortion of both discrete and cyclical movements.

Bimanual Coordination: An Unbalanced Field of Research

Using more than one limb to perform functional, goal-directed actions is arguably one of the most important abilities that human beings possess. In many everyday tasks, the hands, in particular, must be used to accomplish all manner of goals. From buttoning a shirt to opening a jam jar and driving to work, good bimanual coordination is of great utility. In addition to the tasks mentioned above, there are also other tasks involving the functional use of more than one limb, including walking or cycling and typing a report. With a little thought, it becomes apparent that there is at least one important difference between these categories of coordination tasks. On one hand, in some tasks the effectors must perform markedly different motor outputs that are bound together in some functionally defined and usually object-oriented manner (e.g., buttoning a shirt) yet, in others, the effectors produce very similar motor outputs but in a specific temporal order, which may or may not repeat itself periodically (e.g., walking and cycling compared to typing or drumming). In this short article, I will argue that the second category of coordination task and, in particular, cyclical coordination, has been studied extensively and, at least at the level of behavior, is relatively well understood. In contrast the former category of bimanual task is seldom studied and, even at the descriptive level, is rather poorly understood. One of the reasons for this may be the complexity of such tasks and the technical difficulties involved in attempting to study them. By highlighting some key studies, I hope to illustrate that such tasks can be fruitfully studied in the laboratory. Last, since the neural control processes underlying both classes of coordination task are not yet well known, I aim to draw attention to the potential value of the interventional technique of Transcranial Magnetic Stimulation (TMS) as a tool for investigating the functions of brain regions contributing to bimanual coordination.

Rhythmic and discrete elements in multi-joint coordination

Everyday actions invariably consist of a combination of discrete and rhythmic elements within or across joints. The study investigated constraints arising from the co-occurrence of the two actions in a two-joint task and how endpoint trajectories are shaped due to these action elements at the joint level. The task consisted of an elbow oscillation in the plane that was to be merged with a fast discrete adduction or abduction in the shoulder triggered by an auditory signal. The task was performed with and without explicit instruction about the joint involvement. Two hypotheses were tested: (1) kinematic constraints for the coupling of discrete and rhythmic elements arise at the neuro-muscular level, such that EMG bursts of the discrete and rhythmic movement have a tendency to synchronize. This effect was documented previously in a comparable single-joint task. (2) The merging of the two elements is constrained by intersegmental torques such that initiation and performance of the discrete movement utilizes interaction torques. This hypothesis rests on the assumption that the CNS has an internal model of the limb dynamics and exploits passive torques. Key results support hypothesis 1: (i) the discrete action's initiation at the shoulder was constrained to a preferred phase of the ongoing elbow oscillation. (ii) The rhythmic elbow movement showed a systematic phase advance during the discrete shoulder shift, similar to those reported for the single-joint variant of the task. Reaction times of the discrete movement were longer and peak velocities slower than reported for isolated discrete movements, due to the simultaneous presence of the oscillation. (iii) Interaction torques acting from the elbow onto the shoulder joint were not selectively exploited for the acceleration of the discrete shoulder movement. Indirectly however, hypothesis 2 also found support: torques at the elbow generated compensatory muscle activity in the shoulder that stabilized the stationary joint. It was this rhythmic activity that posed the direct constraints on the initiation of the discrete movement.

Interaction between discrete and rhythmic movements: reaction time and phase of discrete movement initiation during oscillatory movements

This study investigates a task in which discrete and rhythmic movements are combined in a single-joint elbow rotation. Previous studies reported a tendency for the EMG burst associated with the discrete movement to occur around the expected burst associated with the rhythmic movement (e.g., [Exp. Brain Res. 99 (1994) 325; J. Neurol. Neurosurg. Psychiatry 40 (1977) 1129; Hum. Mov. Sci. 19 (2000) 627]). We document this interaction between discrete and rhythmic movements in different task variations and suggest a model consisting of rhythmic and discrete pattern generators that reproduces the major results. In the experiment, subjects performed single-joint elbow oscillatory movements (2 Hz). Upon a signal, they initiated a movement that consisted of a shift in the midpoint of the oscillation (MID), a shift in the amplitude of the oscillation (AMP), or a combination of both (MID + AMP). These shifting movements were performed either in a reaction time or in a self-paced fashion. The tendency for the EMG bursts associated with the discrete and rhythmic movements to synchronize was found similarly in all three tasks and instruction conditions, but the synchronization was most pronounced in the self-initiated discrete movement. Reaction time was increased for the combined task (MID + AMP), indicating higher control demands due to a combination of discrete and rhythmic components. This EMG burst synchronization was reproduced in a model based on a half-center oscillator with activation signals that produce either rhythmic or discrete activity. This activity was interpreted as torques driving a simple limb model. Summation of discrete and rhythmic activation signals of the pattern generators was sufficient to simulate the EMG burst synchronization. Further, simulation data reproduced the modulation of the reaction time as a function of the phase of the discrete movement.

Discrete and cyclical units of action in a mixed target pair aiming task

Two experiments addressed the issue of discrete and cyclical units as possible basic units of action that might be used to construct complex actions based on task constraints. The experiments examined the influence of low and high accuracy constraints on the end-effector's motion in rhythmical aiming movements. Both experiments utilized a Fitts-type task under three accuracy constraints: (1) big target pairing-low index of movement difficulty (ID), (2) small target pairing-high ID, and (3) mixed target pairing-one target high ID and the other target low ID. Experiment I was a 1-degree-of-freedom ( df) task that required subjects to crossover the inside edge of targets in a target pair using elbow flexion-extension motions. Experiment II used a 2- df task that required subjects to tap back and forth between targets in a target pair using a hand-held stylus. In both experiments, end-effector motion in the low ID condition was cyclical with the end-effector's motion consistent with a limit-cycle attractor description, while in the high ID condition end-effector motion was discrete and consistent with a fixed-point attractor description. The mixed target pairing produced both discrete and cyclical features in the end-effector's dynamics that suggested a functional linking of discrete and cyclical units of action as the optimal movement solution. Evidence supporting the above statements was found in the kinematic measures of movement time (MT), dwell time, proportion of MT accelerating and decelerating, and in a measure of harmonicity (Guiard 1993, Acta Psychol 82:139-159; Guiard 1997, Hum Mov Sci 16:97-131). Extended practice in the mixed target condition revealed a bias towards cyclical motion with practice. The results demonstrate that discrete and cyclical motion, represented as limit-cycle and fixed-point attractors, are basic units of action that the motor system uses in constructing more complex action sequences. The results are discussed with reference to coordinative structures and the generalized motor program as basic units of action. Issues pertaining to visual feedback processing and movement braking in rapid aiming tasks are also discussed.

Interactions between Rhythmic and Discrete Components in a Bimanual Task

An asymmetric bimanual task was investigated in which participants performed a rhythmic movement with their dominant arm and initiated a second movement with their nondominant arm at a random phase of the continued oscillations. The objective was to examine whether different constraints existed between rhythmic and discrete movements and, more generally, whether rhythmic and discrete movements can be regarded as two different movement primitives. Participants performed rhythmic forearm rotations at 1 of 4 prescribed metronome periods. After a random interval, a trigger signaled to initiate either a discrete or rhythmic movement with the left forearm as fast as possible while continuing the oscillations. Analyses extracted the mutual influences that the two movements exerted on each other and contrasted discrete-rhythmic and rhythmic-rhythmic coupling. (a) The initiation of the rhythmic movement was constrained to occur in-phase with the ongoing rhythmic movement, while the discrete movement could be initiated at any arbitrary phase. (b) Reaction time of the initiated rhythmic movement scaled with the oscillation period, while the discrete movement's reaction time was invariant across periods. (c) Peak velocity of the initiated movement scaled with the oscillatory period in both tasks but more strongly in the discrete movement. (d) Synchronization of EMG bursts of both arm flexors was evident in both tasks but more strongly in the rhythmic-rhythmic combination. The results are interpreted as support for the hypothesis that discrete and rhythmic actions are two different control regimes, and coupling occurs at a higher level in the central nervous system.