Intermittent control: a computational theory of human control

Intermittent control and retinal optic flow when maintaining a curvilinear path

The topic of how humans navigate using vision has been studied for decades. Research has identified the emergent patterns of retinal optic flow from gaze behavior may play an essential role in human curvilinear locomotion. However, the link towards control has been poorly understood. Lately, it has been shown that human locomotor behavior is corrective, formed from intermittent decisions and responses. A simulated virtual reality experiment was conducted where fourteen participants drove through a texture-rich simplistic road environment with left and right curve bends. The goal was to investigate how human intermittent lateral control can be associated with the retinal optic flow-based cues and vehicular heading as sources of information. This work reconstructs dense retinal optic flow using a numerical estimation of optic flow with measured gaze behavior. By combining retinal optic flow with the drivable lane surface, a cross-correlational relation to intermittent steering behavior could be observed. In addition, a novel method of identifying constituent ballistic correction using particle swarm optimization was demonstrated to analyze the incremental correction-based behavior. Through time delay analysis, our results show a human response time of approximately 0.14 s for retinal optic flow-based cues and 0.44 s for heading-based cues, measured from stimulus onset to steering correction onset. These response times were further delayed by 0.17 s when the vehicle-fixed steering wheel was visibly removed. In contrast to classical continuous control strategies, our findings support and argue for the intermittency property in human neuromuscular control of muscle synergies, through the principle of satisficing behavior: to only actuate when there is a perceived need for it. This is aligned with the human sustained sensorimotor model, which uses readily available information and internal models to produce informed responses through evidence accumulation to initiate appropriate ballistic correction, even amidst another correction.

Empowering human-like walking with a bio-inspired gait controller for an under-actuated torque-driven human model

Human gait simulation plays a crucial role in providing insights into various aspects of locomotion, such as diagnosing injuries and impairments, assessing abnormal gait patterns, and developing assistive and rehabilitation technologies. To achieve more realistic gait simulation results, it is essential to use a comprehensive model that accurately replicates the kinematics and kinetics of human movement. Human skeletal models in OpenSim software provide anatomically accurate and anthropomorphic structures, enabling users to create personalized models that accurately replicate individual human behavior. However, these torque-driven models encounter challenges in stabilizing unactuated degree of freedom of pelvis tilt in forward dynamic simulations Adopting a bio-inspired strategy that ensures human balance with a minimized energy expenditure during walking, this paper addresses a gait controller for a torque-driven human skeletal model to achieve stable walking. The proposed controller employs a nonlinear model-based approach to calculate a balance-equivalent control torque and utilizes the hip-ankle strategy to distribute this torque across the lower-limb joints during the stance phase. To optimize the parameters of the trajectory tracking controller and the balance distribution coefficients, we developed a forward dynamic simulation interface established between MATLAB and OpenSim. The simulation results indicated that the torque-driven model achieves a natural gait, with joint torques closely aligning with the experimental data. The robustness of the bio-inspired gait controller was further evaluated by applying a range of external forces on the skeletal model. The robustness analysis demonstrated efficient balance recovery mechanism of the proposed bio-inspired gait controller in response to external disturbances.

Cross-frequency modulation of postural fluctuations and scalp EEG in older adults: error amplification feedback for rapid balance adjustments

Virtual error amplification (VEA) in visual feedback enhances attentive control over postural stability, although the neural mechanisms are still debated. This study investigated the distinct cortical control of unsteady stance in older adults using VEA through cross-frequency modulation of postural fluctuations and scalp EEG. Thirty-seven community-dwelling older adults (68.1 ± 3.6 years) maintained an upright stance on a stabilometer while receiving either VEA or real error feedback. Along with postural fluctuation dynamics, phase-amplitude coupling (PAC) and amplitude-amplitude coupling (AAC) were analyzed for postural fluctuations under 2 Hz and EEG sub-bands (theta, alpha, and beta). The results revealed a higher mean frequency of the postural fluctuation phase (p = .005) and a greater root mean square of the postural fluctuation amplitude (p = .003) with VEA compared to the control condition. VEA also reduced PAC between the postural fluctuation phase and beta-band EEG in the left frontal (p = .009), sensorimotor (p = .002), and occipital (p = .018) areas. Conversely, VEA increased the AAC of posture fluctuation amplitude and beta-band EEG in FP2 (p = .027). Neither theta nor alpha band PAC or AAC were affected by VEA. VEA optimizes postural strategies in older adults during stabilometer stance by enhancing visuospatial attentive control of postural responses and facilitating the transition of motor states against postural perturbations through a disinhibitory process. Incorporating VEA into virtual reality technology is advocated as a valuable strategy for optimizing therapeutic interventions in postural therapy, particularly to mitigate the risk of falls among older adults.

Right-left sEMG burst synchronization of the lumbar erector spinae muscles of seated violin players

Burst-like activation of postural muscles has been previously described and plays a crucial role in elucidating the strategies for postural control adopted by the central nervous system (CNS). A spatio-temporal descriptor of surface electromyographic (sEMG) bursts (STB) is proposed and applied to statistically quantify the burst-like activity of the right and left (R-L) lumbar erector spinae muscle of nine seated violinists playing for two hours. The STB signal is the number of pixels of the high density sEMG (HDsEMG) maps simultaneously showing sEMG amplitude above a given threshold. Burst activity was present in all nine subjects. Four of them met four stringent criteria allowing analysis of frequency, duration, and synchronization between the R-L bursts after 0, 15, 30, 60, 120 min of playing. Mean square coherence between STBs of the two muscles was > 0.75 within ⁓1 Hz bandwidth between 2.2 Hz and 4.5 Hz depending on subject. Non-parametric statistics was applied to compare, in time and space, the R-L features of the bursts. The mean STB width was significantly associated primarily to side and secondarily to time and ranged from 100 to 250 ms. The right STB signals led the left (p < 0.02) by 0 - 160 ms.The inverted pendulum composed by the upper body of a seated violinist is controlled in an intermittent way. The erector spinae of the selected subjects were active, on average, for less than 50% of the time. These findings demonstrate a CNS strategy of intermittent back muscle activation presumably aimed to reducing fatigue during hours of playing in seated violinists.

Attractor dynamics of elite performance: the high bar longswing

Combining biomechanics and motor control, the aim of this study was to investigate the limit cycle dynamics during the high bar longswing across the UK elite gymnastics pathway age groupings. Senior, junior and development gymnasts (N = 30) performed three sets of eight consecutive longswings on the high bar. The centre of mass motion was examined through Poincaré plots and recurrence quantification analysis exploring the limit cycle dynamics of the longswing. Close to one-dimensional limit cycles were displayed for the senior (correlation dimension (CD) = 1.17 ± .08), junior (CD = 1.26 ± .08) and development gymnasts (CD = 1.33 ± .14). Senior elite gymnasts displayed increased recurrence characteristics in addition to longer longswing duration (p < .01) and lower radial angular velocity of the mass centre (p < .01). All groups of gymnasts had highly recurrent and predictable limit cycle characteristics. The findings of this research support the postulation that the further practice, experience and individual development associated with the senior gymnasts contribute to the refinement of the longswing from a nonlinear dynamics perspective. These findings support the idea of functional task decomposition informing the understanding of skill and influencing coaches' decisions around skill development and physical preparation.

How the brain can be trained to achieve an intermittent control strategy for stabilizing quiet stance by means of reinforcement learning

The stabilization of human quiet stance is achieved by a combination of the intrinsic elastic properties of ankle muscles and an active closed-loop activation of the ankle muscles, driven by the delayed feedback of the ongoing sway angle and the corresponding angular velocity in a way of a delayed proportional (P) and derivative (D) feedback controller. It has been shown that the active component of the stabilization process is likely to operate in an intermittent manner rather than as a continuous controller: the switching policy is defined in the phase-plane, which is divided in dangerous and safe regions, separated by appropriate switching boundaries. When the state enters a dangerous region, the delayed PD control is activated, and it is switched off when it enters a safe region, leaving the system to evolve freely. In comparison with continuous feedback control, the intermittent mechanism is more robust and capable to better reproduce postural sway patterns in healthy people. However, the superior performance of the intermittent control paradigm as well as its biological plausibility, suggested by experimental evidence of the intermittent activation of the ankle muscles, leaves open the quest of a feasible learning process, by which the brain can identify the appropriate state-dependent switching policy and tune accordingly the P and D parameters. In this work, it is shown how such a goal can be achieved with a reinforcement motor learning paradigm, building upon the evidence that, in general, the basal ganglia are known to play a central role in reinforcement learning for action selection and, in particular, were found to be specifically involved in postural stabilization.

Learning to stand with sensorimotor delays generalizes across directions and from hand to leg effectors

Humans receive sensory information from the past, requiring the brain to overcome delays to perform daily motor skills such as standing upright. Because delays vary throughout the body and change over a lifetime, it would be advantageous to generalize learned control policies of balancing with delays across contexts. However, not all forms of learning generalize. Here, we use a robotic simulator to impose delays into human balance. When delays are imposed in one direction of standing, participants are initially unstable but relearn to balance by reducing the variability of their motor actions and transfer balance improvements to untrained directions. Upon returning to normal standing, aftereffects from learning are observed as small oscillations in control, yet they do not destabilize balance. Remarkably, when participants train to balance with delays using their hand, learning transfers to standing with the legs. Our findings establish that humans use experience to broadly update their neural control to balance with delays.

An improved intermittent control model of postural sway during quiet standing implemented by a data driven approach

This paper proposes a new intermittent control model during human quiet standing, which is consisted of postulated "regular intervention" and "imminent intervention". The regular intervention is within the main control loop, and its trigger condition is equivalent to the switching frequency of center of pressure (COP) data calculated by wavelet transform. The imminent intervention will only be triggered after the postural sway angle exceeds a certain threshold. In order to prove the effectiveness of the new model, the simulation results of the new model and the model proposed by Asai et al. (2009) are compared with the experimental data. The setting parameters of both models are retrieved by Bayesian regression from the experimental data. The results show that the new model not only could exhibit two power law scaling regimes of power spectral density (PSD) of COP, but also show that indices of the probability density function distance, root mean square (RMS), Total Sway Path, displacement Range, 50% power frequency of center of mass (COP) between the simulation results and the experimental data are closer compared to the existing model. Moreover, the limit cycle oscillations (LCOs) obtained from the simulation results of the new model have a higher degree of matching with those retrieved from the experimental data.

The microstructure of intra- and interpersonal coordination

Movements are naturally composed of submovements, i.e. recurrent speed pulses (2-3 Hz), possibly reflecting intermittent feedback-based motor adjustments. In visuomotor (unimanual) synchronization tasks, partners alternate submovements over time, indicating mutual coregulation. However, it is unclear whether submovement coordination is organized differently between and within individuals. Indeed, different types of information may be variably exploited for intrapersonal and interpersonal coordination. Participants performed a series of bimanual tasks alone or in pairs, with or without visual feedback (solo task only). We analysed the relative timing of submovements between their own hands or between their own hands and those of their partner. Distinct coordinative structures emerged at the submovement level depending on the relevance of visual feedback. Specifically, the relative timing of submovements (between partners/effectors) shifts from alternation to simultaneity and a mixture of both when coordination is achieved using vision (interpersonal), proprioception/efference-copy only (intrapersonal, without vision) or all information sources (intrapersonal, with vision), respectively. These results suggest that submovement coordination represents a behavioural proxy for the adaptive weighting of different sources of information within action-perception loops. In sum, the microstructure of movement reveals common principles governing the dynamics of sensorimotor control to achieve both intra- and interpersonal coordination.

Assessing the influence of cognitive response conflict on balance control: an event-related approach using response-aligned force-plate time series data

Process interference or sharing of attentional resources between cognitive tasks and balance control during upright standing has been well documented. Attentional costs increase with greater balancing demands of a balance activity, for example in standing compared to sitting. The traditional approach for analyzing balance control using posturography with a force plate integrates across relative long trial periods of up to several minutes, which blends any balance adjustments and cognitive operations within this period. In the present study, we pursued an event-related approach to assess if single cognitive operations resolving response selection conflict in the Simon task interfere with concurrent balance control in quiet standing. In addition to traditional outcome measures (response latency, error proportions) in the cognitive Simon task, we investigated the effect of spatial congruency on measures of sway control. We expected that conflict resolution in incongruent trials would alter short-term progression of sway control. Our results demonstrated the expected congruency effect on performance in the cognitive Simon task and the mediolateral variability of balance control within 150 ms before the onset of the manual response was reduced to a greater degree in incongruent compared to congruent trials. In addition, mediolateral variability before and after the manual response was generally reduced compared to variability following target presentation, where no effect of congruency was observed. Assuming that response conflict in incongruent conditions requires suppression of the incorrect response tendencies, our results may imply that mechanisms of cognitive conflict resolution may also carry over to intermittent balance control mechanisms in a direction-specific manner.

Explaining human interactions on the road by large-scale integration of computational psychological theory

When humans share space in road traffic, as drivers or as vulnerable road users, they draw on their full range of communicative and interactive capabilities. Much remains unknown about these behaviors, but they need to be captured in models if automated vehicles are to coexist successfully with human road users. Empirical studies of human road user behavior implicate a large number of underlying cognitive mechanisms, which taken together are well beyond the scope of existing computational models. Here, we note that for all of these putative mechanisms, computational theories exist in different subdisciplines of psychology, for more constrained tasks. We demonstrate how these separate theories can be generalized from abstract laboratory paradigms and integrated into a computational framework for modeling human road user interaction, combining Bayesian perception, a theory of mind regarding others' intentions, behavioral game theory, long-term valuation of action alternatives, and evidence accumulation decision-making. We show that a model with these assumptions-but not simpler versions of the same model-can account for a number of previously unexplained phenomena in naturalistic driver-pedestrian road-crossing interactions, and successfully predicts interaction outcomes in an unseen data set. Our modeling results contribute to demonstrating the real-world value of the theories from which we draw, and address calls in psychology for cumulative theory-building, presenting human road use as a suitable setting for work of this nature. Our findings also underscore the formidable complexity of human interaction in road traffic, with strong implications for the requirements to set on development and testing of vehicle automation.

F = ma. Is the macaque brain Newtonian?

Intuitive Physics, the ability to anticipate how the physical events involving mass objects unfold in time and space, is a central component of intelligent systems. Intuitive physics is a promising tool for gaining insight into mechanisms that generalize across species because both humans and non-human primates are subject to the same physical constraints when engaging with the environment. Physical reasoning abilities are widely present within the animal kingdom, but monkeys, with acute 3D vision and a high level of dexterity, appreciate and manipulate the physical world in much the same way humans do.

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.

On Pinning Linear and Adaptive Synchronization of Multiple Fractional-Order Neural Networks With Unbounded Time-Varying Delays

In this article, the synchronization of multiple fractional-order neural networks with unbounded time-varying delays (FNNUDs) is investigated. By introducing a pinning linear control, sufficient conditions are provided for achieving the synchronization of multiple FNNUDs via an extended Halanay inequality. Moreover, a new effective adaptive control which applies to the fractional differential equations with unbounded time-varying delays is designed, under which sufficient criteria are presented to ensure the synchronization of multiple FNNUDs. The introduced control in this article is also workable in traditional integer-order neural networks. Finally, the validity of obtained results is demonstrated by a numerical example.

Spatial and Temporal Muscle Synergies Provide a Dual Characterization of Low-dimensional and Intermittent Control of Upper-limb Movements

Muscle synergy analysis investigates the neurophysiological mechanisms that the central nervous system employs to coordinate muscles. Several models have been developed to decompose electromyographic (EMG) signals into spatial and temporal synergies. However, using multiple approaches can complicate the interpretation of results. Spatial synergies represent invariant muscle weights modulated with variant temporal coefficients; temporal synergies are invariant temporal profiles that coordinate variant muscle weights. While non-negative matrix factorization allows to extract both spatial and temporal synergies, the comparison between the two approaches was rarely investigated targeting a large set of multi-joint upper-limb movements. Spatial and temporal synergies were extracted from two datasets with proximal (16 subjects, 10M, 6F) and distal upper-limb movements (30 subjects, 21M, 9F), focusing on their differences in reconstruction accuracy and inter-individual variability. We showed the existence of both spatial and temporal structure in the EMG data, comparing synergies with those from a surrogate dataset in which the phases were shuffled preserving the frequency content of the original data. The two models provide a compact characterization of motor coordination at the spatial or temporal level, respectively. However, a lower number of temporal synergies are needed to achieve the same reconstruction R²: spatial and temporal synergies may capture different hierarchical levels of motor control and are dual approaches to the characterization of low-dimensional coordination of the upper-limb. Last, a detailed characterization of the structure of the temporal synergies suggested that they can be related to intermittent control of the movement, allowing high flexibility and dexterity. These results improve neurophysiology understanding in several fields such as motor control, rehabilitation, and prosthetics.

Motor invariants in action execution and perception

The nervous system is sensitive to statistical regularities of the external world and forms internal models of these regularities to predict environmental dynamics. Given the inherently social nature of human behavior, being capable of building reliable predictive models of others' actions may be essential for successful interaction. While social prediction might seem to be a daunting task, the study of human motor control has accumulated ample evidence that our movements follow a series of kinematic invariants, which can be used by observers to reduce their uncertainty during social exchanges. Here, we provide an overview of the most salient regularities that shape biological motion, examine the role of these invariants in recognizing others' actions, and speculate that anchoring socially-relevant perceptual decisions to such kinematic invariants provides a key computational advantage for inferring conspecifics' goals and intentions.

Human Stabilization of Delay-Induced Instability of Haptic Rendering in a Stiffness Discrimination Task

Towards developing a coupled stability theory for haptic systems, we study the interaction of operators with time-delayed force feedback. In this work, we analyzed and validated experimentally the stability boundaries of an uncoupled system - without considering the human. We then designed an experiment in which the participants used a haptic device to interact with virtual elastic force fields in a stiffness discrimination task. We compared the performance and kinematics of users in uncoupled-unstable and uncoupled-stable conditions and characterized the stabilizing contribution of the users. We found that the users were able to perform the task regardless of the uncoupled-stability conditions. In addition, in uncoupled-unstable conditions, users maintained movement characteristics that were important for exploratory mediation, such as depth and duration of the movement, whereas other characteristics were not preserved. The results were reproduced in a simulation of the human controller that combined an inverse model and an optimal feedback controller. Adequate performance under the uncoupled-unstable yet coupled-stable conditions supports the potential benefit of designing for coupled stability of haptic systems. This could lead to the use of less conservative controllers than state-of-the-art solutions in haptic and teleoperation systems, and advance the fidelity of haptic feedback.

Asynchronous Intermittent Regulation of Human Arm Movement with Markovian Jumping Parameters

In this paper, the regulation stability problem of the human arm continuous movement is investigated based on Markovian jumping parameters. In particular, the intermittent control mechanism is adopted in the arm movement regulation procedure to model the human intermittent motor control strategy. Furthermore, by taking into account the Markovian jumping parameters with different modes, the asynchronous regulation issue is proposed to model mode mismatch between the motor control and arm movement. On the basis of model transformation, sufficient stability conditions are established during the arm movements, and the desired regulation gain can be obtained by the convex optimization method. In the end, an illustrative example is presented to show the applicability and effectiveness of our developed model and optimized regulation approach.

What is the contribution of voluntary and reflex processes to sensorimotor control of balance?

The contribution to balance of spinal and transcortical processes including the long-latency reflex is well known. The control of balance has been modelled previously as a continuous, state feedback controller representing, long-latency reflexes. However, the contribution of slower, variable delay processes has not been quantified. Compared with fixed delay processes (spinal, transcortical), we hypothesize that variable delay processes provide the largest contribution to balance and are sensitive to historical context as well as current states. Twenty-two healthy participants used a myoelectric control signal from their leg muscles to maintain balance of their own body while strapped to an actuated, inverted pendulum. We study the myoelectric control signal (u) in relation to the independent disturbance (d) comprising paired, discrete perturbations of varying inter-stimulus-interval (ISI). We fit the closed loop response, u from d, using one linear and two non-linear non-parametric (many parameter) models. Model M1 (ARX) is a generalized, high-order linear-time-invariant (LTI) process with fixed delay. Model M1 is equivalent to any parametric, closed-loop, continuous, linear-time-invariant (LTI), state feedback model. Model M2, a single non-linear process (fixed delay, time-varying amplitude), adds an optimized response amplitude to each stimulus. Model M3, two non-linear processes (one fixed delay, one variable delay, each of time-varying amplitude), add a second process of optimized delay and optimized response amplitude to each stimulus. At short ISI, the myoelectric control signals deviated systematically both from the fixed delay LTI process (M1), and also from the fixed delay, time-varying amplitude process (M2) and not from the two-process model (M3). Analysis of M3 (all fixed delay and variable delay response amplitudes) showed the variable (compared with fixed) delay process 1) made the largest contribution to the response, 2) exhibited refractoriness (increased delay related to short ISI) and 3) was sensitive to stimulus history (stimulus direction 2 relative to stimulus 1). For this whole-body balance task and for these impulsive stimuli, non-linear processes at variable delay are central to control of balance. Compared with fixed delay processes (spinal, transcortical), variable delay processes provided the largest contribution to balance and were sensitive to historical context as well as current states.

Thinking rhythm objects

The focus of this mini-review is on rhythm objects, defined as strongly coherent chunks of combined sound and body motion in music, typically in the duration range of a few seconds, as may for instance be found in a fragment of dance music, in an energetic drum fill, in a flute ornament, or in a cascade of sounds of a rapid harp glissando. Although there has been much research on rhythm in continuous musical sound and its links with behavior, including the neurocognitive aspects of periodicity, synchrony, and entrainment, there has been much less focus on the generation and perception of singular coherent rhythm objects. This mini-review aims to enhance our understanding of such rhythm objects by pointing to relevant literature on coherence-enhancing elements such as coarticulation, i.e., the fusion of motion events into more extended rhythm objects, and intermittent motor control, i.e., the discontinuous, instant-by-instant control and triggering of rhythm objects.

Interpersonal synchronization of movement intermittency

Most animal species group together and coordinate their behavior in quite sophisticated manners for mating, hunting, or defense purposes. In humans, coordination at a macroscopic level (the pacing of movements) is evident both in daily life (e.g., walking) and skilled (e.g., music and dance) behaviors. By examining the fine structure of movement, we here show that interpersonal coordination is established also at a microscopic – submovement – level. Natural movements appear as marked by recurrent (2–3 Hz) speed breaks, i.e., submovements, that are traditionally considered the result of intermittency in (visuo)motor feedback-based control. In a series of interpersonal coordination tasks, we show that submovements produced by interacting partners are not independent but alternate tightly over time, reflecting online mutual adaptation. These findings unveil a potential core mechanism for behavioral coordination that is based on between-persons synchronization of the intrinsic dynamics of action-perception cycles.

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Movements show intermittent speed pulses occurring at 2–3 Hz, called submovements

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Submovements are actively coordinated in counter-phase by interacting partners

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Submovements coordination depends on spatial alignment but not movement congruency

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Behavioral coordination occurs both at macro- and microscopic movement scales

Human Control Model Estimation in Physical Human-Machine Interaction: A Survey

The study of human-machine interaction as a unique control system was one of the first research interests in the engineering field, with almost a century having passed since the first works appeared in this area. At the same time, it is a crucial aspect of the most recent technological developments made in application fields such as collaborative robotics and artificial intelligence. Learning the processes and dynamics underlying human control strategies when interacting with controlled elements or objects of a different nature has been the subject of research in neuroscience, aerospace, robotics, and artificial intelligence. The cross-domain nature of this field of study can cause difficulties in finding a guiding line that links motor control theory, modelling approaches in physiological control systems, and identifying human-machine general control models in manipulative tasks. The discussed models have varying levels of complexity, from the first quasi-linear model in the frequency domain to the successive optimal control model. These models include detailed descriptions of physiologic subsystems and biomechanics. The motivation behind this work is to provide a complete view of the linear models that could be easily handled both in the time domain and in the frequency domain by using a well-established methodology in the classical linear systems and control theory.

Constraint-Based Sound-Motion Objects in Music Performance

The aim of this paper is to present principles of constraint-based sound-motion objects in music performance. Sound-motion objects are multimodal fragments of combined sound and sound-producing body motion, usually in the duration range of just a few seconds, and conceived, produced, and perceived as intrinsically coherent units. Sound-motion objects have a privileged role as building blocks in music because of their duration, coherence, and salient features and emerge from combined instrumental, biomechanical, and motor control constraints at work in performance. Exploring these constraints and the crucial role of the sound-motion objects can enhance our understanding of generative processes in music and have practical applications in performance, improvisation, and composition.

Quantitative evaluation of posture control in rats with inferior olive lesions

Impairment of inferior olivary neurons (IONs) affects whole-body movements and results in abnormal gait and posture. Because IONs are activated by unpredicted motion rather than regular body movements, the postural dysfunction caused by ION lesions is expected to involve factors other than simple loss of feedback control. In this study, we measured the postural movements of rats with pharmacological ION lesions (IO rats) trained to stand on their hindlimbs. The coordination of body segments as well as the distribution and frequency characteristics of center of mass (COM) motion were analyzed. We determined that the lesion altered the peak properties of the power spectrum density of the COM, whereas changes in coordination and COM distribution were minor. To investigate how the observed properties reflected changes in the control system, we constructed a mathematical model of the standing rats and quantitatively identified the control system. We found an increase in linear proportional control and a decrease in differential and nonlinear control in IO rats compared with intact rats. The dystonia-like changes in body stiffness explain the nature of the linear proportional and differential control, and a disorder in the internal model is one possible cause of the decrease in nonlinear control.

Learning to stand with unexpected sensorimotor delays

Human standing balance relies on self-motion estimates that are used by the nervous system to detect unexpected movements and enable corrective responses and adaptations in control. These estimates must accommodate for inherent delays in sensory and motor pathways. Here, we used a robotic system to simulate human standing about the ankles in the anteroposterior direction and impose sensorimotor delays into the control of balance. Imposed delays destabilized standing, but through training, participants adapted and re-learned to balance with the delays. Before training, imposed delays attenuated vestibular contributions to balance and triggered perceptions of unexpected standing motion, suggesting increased uncertainty in the internal self-motion estimates. After training, vestibular contributions partially returned to baseline levels and larger delays were needed to evoke perceptions of unexpected standing motion. Through learning, the nervous system accommodates balance sensorimotor delays by causally linking whole-body sensory feedback (initially interpreted as imposed motion) to self-generated balance motor commands.

When standing, neurons in the brain send signals to skeletal muscles so we can adjust our movements to stay upright based on the requirements from the surrounding environment. The long nerves needed to connect our brain, muscles and sensors lead to considerable time delays (up to 160 milliseconds) between sensing the environment and the generation of balance-correcting motor signals. Such delays must be accounted for by the brain so it can adjust how it regulates balance and compensates for unexpected movements.

Aging and neurological disorders can lead to lengthened neural delays, which may result in poorer balance. Computer modeling suggests that we cannot maintain upright balance if delays are longer than 300-340 milliseconds. Directly assessing the destabilizing effects of increased delays in human volunteers can reveal how capable the brain is at adapting to this neurological change.

Using a custom-designed robotic balance simulator, Rasman et al. tested whether healthy volunteers could learn to balance with delays longer than the predicted 300-340 millisecond limit. In a series of experiments, 46 healthy participants stood on the balance simulator which recreates the physical sensations and neural signals for balancing upright based on a computer-driven virtual reality. This unique device enabled Rasman et al. to artificially impose delays by increasing the time between the generation of motor signals and resulting whole-body motion.

The experiments showed that lengthening the delay between motor signals and whole-body motion destabilized upright standing, decreased sensory contributions to balance and led to perceptions of unexpected movements. Over five days of training on the robotic balance simulator, participants regained their ability to balance, which was accompanied by recovered sensory contributions and perceptions of expected standing, despite the imposed delays. When a subset of participants was tested three months later, they were still able to compensate for the increased delay.

The experiments show that the human brain can learn to overcome delays up to 560 milliseconds in the control of balance. This discovery may have important implications for people who develop balance problems because of older age or neurologic diseases like multiple sclerosis. It is possible that robot-assisted training therapies, like the one in this study, could help people overcome their balance impairments.

A feedback information-theoretic transmission scheme (FITTS) for modeling trajectory variability in aimed movements

Trajectories in human aimed movements are inherently variable. Using the concept of positional variance profiles, such trajectories are shown to be decomposable into two phases: In a first phase, the variance of the limb position over many trajectories increases rapidly; in a second phase, it then decreases steadily. A new theoretical model, where the aiming task is seen as a Shannon-like communication problem, is developed to describe the second phase: Information is transmitted from a "source" (determined by the position at the end of the first phase) to a "destination" (the movement's end-point) over a "channel" perturbed by Gaussian noise, with the presence of a noiseless feedback link. Information-theoretic considerations show that the positional variance decreases exponentially with a rate equal to the channel capacity C. Two existing datasets for simple pointing tasks are re-analyzed and observations on real data confirm our model. The first phase has constant duration, and C is found constant across instructions and task parameters, which thus characterizes the participant's performance. Our model provides a clear understanding of the speed-accuracy tradeoff in aimed movements: Since the participant's capacity is fixed, a higher prescribed accuracy necessarily requires a longer second phase resulting in an increased overall movement time. The well-known Fitts' law is also recovered using this approach.

Prolonged Standing Task Affects Adaptability of Postural Control in People With Parkinson's Disease

BACKGROUND

Studies on short-term upright quiet standing tasks have presented contradictory findings about postural control in people with Parkinson's disease (pwPD). Prolonged trial durations might better depict body sway and discriminate pwPD and controls.

OBJECTIVE

The aim of this study was to investigate postural control in pwPD during a prolonged standing task.

METHODS

A total of 26 pwPD and 25 neurologically healthy individuals performed 3 quiet standing trials (60 s) before completing a constrained prolonged standing task for 15 minutes. Motion capture was used to record body sway (Vicon, 100 Hz). To investigate the body sway behavior during the 15 minutes of standing, the analysis was divided into three 5-minute-long phases: early, middle, and late. The following body sway parameters were calculated for the anterior-posterior (AP) and medial-lateral (ML) directions: velocity, root-mean-square, and detrended fluctuations analysis (DFA). The body sway area was also calculated. Two-way ANOVAs (group and phases) and 1-way ANOVA (group) were used to compare these parameters for the prolonged standing and quiet standing, respectively.

RESULTS

pwPD presented smaller sway area (P < .001), less complexity (DFA; AP: P < .009; ML: P < .01), and faster velocity (AP: P < .002; ML: P < .001) of body sway compared with the control group during the prolonged standing task. Although the groups swayed similarly (no difference for sway area) during quiet standing, they presented differences in sway area during the prolonged standing task (P < .001).

CONCLUSIONS

Prolonged standing task reduced adaptability of the postural control system in pwPD. In addition, the prolonged standing task may better analyze the adaptability of the postural control system in pwPD.

Postural instability via a loss of intermittent control in elderly and patients with Parkinson's disease: A model-based and data-driven approach

Postural instability is one of the major symptoms of Parkinson's disease. Here, we assimilated a model of intermittent delay feedback control during quiet standing into postural sway data from healthy young and elderly individuals as well as patients with Parkinson's disease to elucidate the possible mechanisms of instability. Specifically, we estimated the joint probability distribution of a set of parameters in the model using the Bayesian parameter inference such that the model with the inferred parameters can best-fit sway data for each individual. It was expected that the parameter values for three populations would distribute differently in the parameter space depending on their balance capability. Because the intermittent control model is parameterized by a parameter associated with the degree of intermittency in the control, it can represent not only the intermittent model but also the traditional continuous control model with no intermittency. We showed that the inferred parameter values for the three groups of individuals are classified into two major groups in the parameter space: one represents the intermittent control mostly for healthy people and patients with mild postural symptoms and the other the continuous control mostly for some elderly and patients with severe postural symptoms. The results of this study may be interpreted by postulating that increased postural instability in most Parkinson's patients and some elderly persons might be characterized as a dynamical disease.

A bang-bang control model predicts the triphasic muscles activity during hand reaching

There are numerous ways to reach for an apple hanging from a tree. Yet, our motor system uses a specific muscle activity pattern that features activity bursts and silent periods. We suggest that these bursts are an evidence against the common view that the brain controls the commands to the muscles in a smooth continuous manner. Instead, we propose a model in which a motor plan is transformed into a piecewise-constant control signal that is low-pass filtered and transmitted to the muscles with different muscle-specific delays. We use a Markov chain Monte Carlo (MCMC) method to identify transitions in the state of the muscles following initial activation and show that fitting a bang-bang control model to the kinematics of movement predicts these transitions in the state of the muscles. Such a bang-bang controller suggests that the brain reduces the complexity of the problem of ballistic movements control by sending commands to the muscles at sparse times. Identifying this bang-bang controller can be useful to develop efficient controllers for neuroprostheses and other physical human-robot interaction systems.NEW & NOTEWORTHY While ballistic hand reaching movements are characterized by smooth position and velocity signals, the activity of the muscles exhibits bursts and silent periods. Here, we propose that a model based on bang-bang control provides the link between the abrupt changes in the muscle activity and the smooth reaching trajectory. Using bang-bang control instead of continuous control may simplify the design of prostheses and other physical human-robot interaction systems.

Movement Decomposition in the Primary Motor Cortex

A complex action can be described as the composition of a set of elementary movements. While both kinematic and dynamic elements have been proposed to compose complex actions, the structure of movement decomposition and its neural representation remain unknown. Here, we examined movement decomposition by modeling the temporal dynamics of neural populations in the primary motor cortex of macaque monkeys performing forelimb reaching movements. Using a hidden Markov model, we found that global transitions in the neural population activity are associated with a consistent segmentation of the behavioral output into acceleration and deceleration epochs with directional selectivity. Single cells exhibited modulation of firing rates between the kinematic epochs, with abrupt changes in spiking activity timed with the identified transitions. These results reveal distinct encoding of acceleration and deceleration phases at the level of M1, and point to a specific pattern of movement decomposition that arises from the underlying neural activity. A similar approach can be used to probe the structure of movement decomposition in different brain regions, possibly controlling different temporal scales, to reveal the hierarchical structure of movement composition.

State-space intermittent feedback stabilization of a dual balancing task

Balancing the body in upright standing and balancing a stick on the fingertip are two examples of unstable tasks that, in spite of strong motor and sensory differences, appear to share a similar motor control paradigm, namely a state-space intermittent feedback stabilization mechanism. In this study subjects were required to perform the two tasks simultaneously, with the purpose of highlighting both the coordination between the two skills and the underlying interaction between the corresponding controllers. The experimental results reveal, in particular, that upright standing (the less critical task) is modified in an adaptive way, in order to facilitate the more critical task (stick balancing), but keeping the overall spatio-temporal signature well known in regular upright standing. We were then faced with the following question: to which extent the physical/biomechanical interaction between the two independent intermittent controllers is capable to explain the dual task coordination patterns, without the need to introduce an additional, supervisory layer/module? By comparing the experimental data with the output of a simulation study we support the former hypothesis, suggesting that it is made possible by the intrinsic robustness of both state-space intermittent feedback stabilization mechanisms.

Explaining Parkinsonian postural sway variabilities using intermittent control theory

Postural impairment due to neuro-degenerative disorders such as Parkinson's Disease (PD) leads to restricted gait patterns, fall-related injuries, decreased mobility, and loss of functional independence. Though several clinical and posturographic studies have attempted to reveal the complex pathophysiology involved in PD, the diversity of Parkinsonian population makes them unclear and sometimes even contradictory. For instance, studies related to the Center of Pressure (CoP) sway during quiet stance in PD patients highlight both increase and reduction of magnitude in contrast to age-matched healthy individuals. A possible explanation for this contradiction is presented in this article. While the presence of intermittent control has been observed in postural control in human quiet stance, we hypothesize that one of the factors that affects postural instability in PD might be the increase in intermittency in active feedback control. Using a simulation model representing the Anterior-Posterior dynamics of human quiet standing, the intermittent control strategy is first contrasted against continuous control strategy in terms of stability, energy efficiency and settling time, thus establishing the inherent advantages of an intermittent control strategy. Further, the ability of the intermittent control strategy to explain several clinical observations in PD is demonstrated. An experimental pilot study is also conducted to support the simulation study, and several body sway parameters derived from recordings of CoP are presented. The presented results are in close agreement with reported clinical observations and may also prove useful for the assessment of disease progression and future fall risk.

Policy gradient optimization of controllers for natural dynamic mono-pedal gait

We have previously suggested a biologically-inspired natural dynamic controller for biped locomotion, which applies torque pulses to the different joints at particular phases of an internal phase variable. The parameters of the controller, including the timing and magnitude of the torque pulses and the dynamics of the phase variable, can be kept constant in open loop or adapted to the environment in closed loop. Here we demonstrate the implementation of this approach to a mono-ped robot and the optimization of the controller parameters to enhance robustness via policy gradient. Policy gradient was applied in simulations rather than the actual robot due to safety and hardware considerations. A grounded action transformation (GAT) was learned and used to facilitate the transfer of the learned policy from simulation to hardware. We demonstrate how GAT improves the match between simulations and experiments and how learning enhances the performance and robustness of the mono-ped robot.

Force accuracy rather than high stiffness is associated with faster learning and reduced falls in human balance

Balance requires the centre of mass to be maintained within the base of support. This can be achieved by minimising position sway (stiffness control: SC) or minimising force error (force accuracy control: FAC). Minimising sway reduces exploration of system properties, whereas minimising force error maximizes accurate mapping of the force vs position. We hypothesise that (i) FAC is associated with faster learning and fewer falls whereas (ii) SC is not. Fifteen participants used myoelectric signals from their legs to maintain balance of an actuated, inverted pendulum, to which they were strapped. Using challenging perturbations, participants were trained to maintain balance without falling within five sessions and tested before (PRE) and after (POST) training. We quantified FAC as 'change (POST-PRE) in correlation of force with position' and SC as 'change in sway'. PRE training, five measures (sway, acceleration, co-contraction, effort, falls) showed no correlation with either FAC or SC. POST training, reduced fall rate, effort and acceleration correlated with FAC metric. SC correlated only with reduced sway. Unlike sway minimisation, development of force accuracy was associated with learning and reduced falls. These results support that accurate force estimation allowing movement is more relevant than stiffness to improve balance and prevent falls.

Establishing metrics and control laws for the learning process: ball and beam balancing

Understanding how dexterity improves with practice is a fundamental challenge of motor control and neurorehabilitation. Here we investigate a ball and beam implementation of a dexterity puzzle in which subjects stabilize a ball at the mid-point of a beam by manipulating the angular position of the beam. Stabilizability analysis of different biomechanical models for the ball and beam task with time-delayed proportional-derivative feedback identified the angular position of the beam as the manipulated variable. Consequently, we monitored the changes in the dynamics with learning by measuring changes in the control parameters. Two types of stable motion are possible: node type (nonoscillatory) and spiral type (oscillatory). Both types of motion are observed experimentally and correspond to well-defined regions in the parameter space of the control gains. With practice the control gains for each subject move close to or on the portion of the boundary which separates the node-type and spiral-type solutions and which is associated with the rightmost characteristic exponent of smallest real part. These observations suggest that with learning the control gains for ball and beam balancing change in such a way that minimizes overshoot and the settling time. This study provides an example of how mathematical analysis together with careful experimental observations can shed light onto the early stages of skill acquisition. Since the difficulty of this task depends on the length of the beam, ball and beam balancing tasks may be useful for the rehabilitation of children with dyspraxia and those recovering from a stroke.

LQG framework explains performance of balancing inverted pendulum with incongruent visual feedback

Successful manipulation of objects requires forming internal representations of the object dynamics. To do so, the sensorimotor system uses visual feedback of the object movement allowing us to estimate the object state and build the representation. One way to investigate this mechanism is by introducing a discrepancy between the visual feedback about the object's movement and the actual movement. This causes a decline in the ability to accurately control the object, shedding light about possible factors influencing the performance. In this study, we show that an optimal feedback control framework can account for the performance and kinematic characteristics of balancing an inverted pendulum when visual feedback of pendulum tip did not represent the actual pendulum tip. Our model suggests a possible mechanism for the role of visual feedback on forming internal representation of objects' dynamics.

Biceps Brachii Muscle Synergy and Target Reaching in a Virtual Environment

A muscular synergy is a theory suggesting that the central nervous system uses few commands to activate a group of muscles to produce a given movement. Here, we investigate how a muscle synergy extracted from a single muscle can be at the origin of different signals which could facilitate the control of modern upper limb myoelectric prostheses with many degrees of freedom. Five pairs of surface electrodes were positioned across the biceps of 12 normal subjects and electromyographic (EMG) signals were collected while their upper limbs were in eight different static postures. Those signals were used to move, within a virtual cube, a small red sphere toward different targets. With three muscular synergies extracted from the five EMG signals, a classifier was trained to identify which synergy pattern was associated with a given static posture. Later, when a posture was recognized, the result was a displacement of a red sphere toward a corner of a virtual cube presented on a computer screen. The axes of the cube were assigned to the shoulder, elbow and wrist joint while each of its the corners was associated with a static posture. The goal for subjects was to reach, one at a time, the four targets positioned at different locations and heights in the virtual cube with different sequences of postures. The results of 12 normal subjects indicate that with the muscular synergies of the biceps brachii, it was possible, but not easy for an untrained person, to reach a target on each trial. Thus, as a proof of concept, we show that features of the biceps muscular synergy have the potential to facilitate the control of upper limb myoelectric prostheses. To our knowledge, this has never been shown before.

A systems-theoretic analysis of low-level human motor control: application to a single-joint arm model

Continuous control using internal models appears to be quite straightforward explaining human motor control. However, it demands both, a high computational effort and a high model preciseness as the whole trajectory needs to be converted. Intermittent control shows great promise for avoiding these drawbacks of continuous control, at least to a certain extent. In this contribution, we study intermittency at the motoneuron level. We ask: how many different, but constant muscle stimulation sets are necessary to generate a stable movement for a specific motor task? Intermittent control, in our perspective, can be assumed only if the number of transitions is relatively small. As application case, a single-joint arm movement is considered. The muscle contraction dynamics is described by a Hill-type muscle model, for the muscle activation dynamics both Hatze's and Zajac's approach are considered. To actuate the lower arm, up to four muscle groups are implemented. A systems-theoretic approach is used to find the smallest number of transitions between constant stimulation sets. A method for a stability analysis of human motion is presented. A Lyapunov function candidate is specified. Thanks to sum-of-squares methods, the presented procedure is generally applicable and computationally feasible. The region-of-attraction of a transition point, and the number of transitions necessary to perform stable arm movements are estimated. The results support the intermittent control theory on this level of motor control, because only very few transitions are necessary.

Effects of model inaccuracies on reaching movements with intermittent control

Background and objectives

Human motor control (HMC) has been hypothesized to involve state estimation, prediction and feedback control to overcome noise, delays and disturbances. However, the nature of communication between these processes, and, in particular, whether it is continuous or intermittent, is still an open issue. Depending on the nature of communication, the resulting control is referred to as continuous control (CC) or intermittent control (IC). While standard HMC theories are based on CC, IC has been argued to be more viable since it reduces computational and communication burden and agrees better with some experimental results. However, to be a feasible model for HMC, IC has to cope well with inaccurately modeled plants, which are common in daily life, as when lifting lighter than expected loads. While IC may involve event-driven triggering, it is generally assumed that refractory mechanisms in HMC set a lower limit on the interval between triggers. Hence, we focus on periodic IC, which addresses this lower limit and also facilitates analysis.

Theoretical methods and results

Theoretical stability criteria are derived for CC and IC of inaccurately modeled linear time-invariant systems with and without delays. Considering a simple muscle-actuated hand model with inaccurately modeled load, both CC and IC remain stable over most of the investigated range, and may become unstable only when the actual load is much smaller than expected, usually smaller than the minimum set by the actual mass of the forearm and hand. Neither CC nor IC is consistently superior to the other in terms of the range of loads over which the system remains stable.

Numerical methods and results

Numerical simulations of time-delayed reaching movements are presented and analyzed to evaluate the effects of model inaccuracies when the control and observer gains are time-dependent, as is assumed to occur in HMC. Both IC and CC agree qualitatively with previously published experimental results with inaccurately modeled plants. Thus, our study suggests that IC copes well with inaccurately modeled plants and is indeed a viable model for HMC.

Direct estimation of the parameters of a delayed, intermittent activation feedback model of postural sway during quiet standing

Human postural sway during quiet standing has been characterized as a proportional-integral-derivative controller with intermittent activation. In the model, patterns of sway result from both instantaneous, passive, mechanical resistance and delayed, intermittent resistance signaled by the central nervous system. A Kalman-Filter framework was designed to directly estimate from experimental data the parameters of the model’s stochastic delay differential equations with discrete dynamic switching conditions. Simulations showed that all parameters could be estimated over a variety of possible data-generating configurations with varying degrees of bias and variance depending on their empirical identification. Applications to experimental data reveal distributions of each parameter that correspond well to previous findings, suggesting that many useful, physiological measures may be extracted from sway data. Individuals varied in degree and type of deviation from theoretical expectations, ranging from harmonic oscillation to non-equilibrium Langevin dynamics.

Balance control systems in Parkinson's disease and the impact of pedunculopontine area stimulation

Impaired balance is a major contributor to falls and diminished quality of life in Parkinson’s disease, yet the pathophysiology is poorly understood. Here, we assessed if patients with Parkinson’s disease and severe clinical balance impairment have deficits in the intermittent and continuous control systems proposed to maintain upright stance, and furthermore, whether such deficits are potentially reversible, with the experimental therapy of pedunculopontine nucleus deep brain stimulation. Two subject groups were assessed: (i) 13 patients with Parkinson’s disease and severe clinical balance impairment, implanted with pedunculopontine nucleus deep brain stimulators; and (ii) 13 healthy control subjects. Patients were assessed in the OFF medication state and blinded to two conditions; off and on pedunculopontine nucleus stimulation. Postural sway data (deviations in centre of pressure) were collected during quiet stance using posturography. Intermittent control of sway was assessed by calculating the frequency of intermittent switching behaviour (discontinuities), derived using a wavelet-based transformation of the sway time series. Continuous control of sway was assessed with a proportional–integral–derivative (PID) controller model using ballistic reaction time as a measure of feedback delay. Clinical balance impairment was assessed using the ‘pull test’ to rate postural reflexes and by rating attempts to arise from sitting to standing. Patients with Parkinson’s disease demonstrated reduced intermittent switching of postural sway compared with healthy controls. Patients also had abnormal feedback gains in postural sway according to the PID model. Pedunculopontine nucleus stimulation improved intermittent switching of postural sway, feedback gains in the PID model and clinical balance impairment. Clinical balance impairment correlated with intermittent switching of postural sway (rho = − 0.705, P < 0.001) and feedback gains in the PID model (rho = 0.619, P = 0.011). These results suggest that dysfunctional intermittent and continuous control systems may contribute to the pathophysiology of clinical balance impairment in Parkinson’s disease. Clinical balance impairment and their related control system deficits are potentially reversible, as demonstrated by their improvement with pedunculopontine nucleus deep brain stimulation.

Extrinsic and intrinsic dynamics in movement intermittency

What determines how we move in the world? Motor neuroscience often focusses either on intrinsic rhythmical properties of motor circuits or extrinsic sensorimotor feedback loops. Here we show that the interplay of both intrinsic and extrinsic dynamics is required to explain the intermittency observed in continuous tracking movements. Using spatiotemporal perturbations in humans, we demonstrate that apparently discrete submovements made 2-3 times per second reflect constructive interference between motor errors and continuous feedback corrections that are filtered by intrinsic circuitry in the motor system. Local field potentials in monkey motor cortex revealed characteristic signatures of a Kalman filter, giving rise to both low-frequency cortical cycles during movement, and delta oscillations during sleep. We interpret these results within the framework of optimal feedback control, and suggest that the intrinsic rhythmicity of motor cortical networks reflects an internal model of external dynamics, which is used for state estimation during feedback-guided movement.

Editorial note

This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

Stabilization of a Cart Inverted Pendulum: Improving the Intermittent Feedback Strategy to Match the Limits of Human Performance

Stabilization of the CIP (Cart Inverted Pendulum) is an analogy to stick balancing on a finger and is an example of unstable tasks that humans face in everyday life. The difficulty of the task grows exponentially with the decrease of the length of the stick and a stick length of 32 cm is considered as a human limit even for well-trained subjects. Moreover, there is a cybernetic limit related to the delay of the multimodal sensory feedback (about 230 ms) that supports a feedback stabilization strategy. We previously demonstrated that an intermittent-feedback control paradigm, originally developed for modeling the stabilization of upright standing, can be applied with success also to the CIP system, but with values of the critical parameters far from the limiting ones (stick length 50 cm and feedback delay 100 ms). The intermittent control paradigm is based on the alternation of on-phases, driven by a proportional/derivative delayed feedback controller, and off-phases, where the feedback is switched off and the motion evolves according to the intrinsic dynamics of the CIP. In its standard formulation, the switching mechanism consists of a simple threshold operator: the feedback control is switched off if the current (delayed) state vector is closer to the stable than to the unstable manifold of the off-phase and is switched on in the opposite case. Although this simple formulation is effective for explaining upright standing as well as CIP balancing, it fails in the most challenging configuration of the CIP. In this work we propose a modification of the standard intermittent control policy that focuses on the explicit selection of switching times and is based on the phase reset of the estimated state vector at each switching time and on the simulation of an approximated internal model of CIP dynamics. We demonstrate, by simulating the modified intermittent control policy, that it can match the limits of human performance, while operating near the edge of instability.

Exponential Synchronization for Delayed Dynamical Networks via Intermittent Control: Dealing With Actuator Saturations

Over the past two decades, the synchronization problem for dynamical networks has drawn significant attention due to its clear practical insight in biological systems, social networks, and neuroscience. In the case where a dynamical network cannot achieve the synchronization by itself, the feedback controller should be added to drive the network toward a desired orbit. On the other hand, the time delays may often occur in the nodes or the couplings of a dynamical network, and the existence of time delays may induce some undesirable dynamics or even instability. Moreover, in the course of implementing a feedback controller, the inevitable actuator limitations could downgrade the system performance and, in the worst case, destabilize the closed-loop dynamics. The main purpose of this paper is to consider the synchronization problem for a class of delayed dynamical networks with actuator saturations. Each node of the dynamical network is described by a nonlinear system with a time-varying delay and the intermittent control strategy is proposed. By using a combination of novel sector conditions, piecewise Lyapunov-like functionals and the switched system approach, delay-dependent sufficient conditions are first obtained under which the dynamical network is locally exponentially synchronized. Then, the explicit characterization of the controller gains is established by means of the feasibility of certain matrix inequalities. Furthermore, optimization problems are formulated in order to acquire a larger estimate of the set of initial conditions for the evolution of the error dynamics when designing the intermittent controller. Finally, two examples are given to show the benefits and effectiveness of the developed theoretical results.

Toward a motor signature in autism: Studies from human-machine interaction

BACKGROUND

Autism spectrum disorder (ASD) is a heterogeneous group of neurodevelopmental disorders which core symptoms are impairments in socio-communication and repetitive symptoms and stereotypies. Although not cardinal symptoms per se, motor impairments are fundamental aspects of ASD. These impairments are associated with postural and motor control disabilities that we investigated using computational modeling and developmental robotics through human-machine interaction paradigms.

METHOD

First, in a set of studies involving a human-robot posture imitation, we explored the impact of 3 different groups of partners (including a group of children with ASD) on robot learning by imitation. Second, using an ecological task, i.e. a real-time motor imitation with a tightrope walker (TW) avatar, we investigated interpersonal synchronization, motor coordination and motor control during the task in children with ASD (n=29), TD children (n=39) and children with developmental coordination disorder (n=17, DCD).

RESULTS

From the human-robot experiments, we evidenced that motor signature at both groups' and individuals' levels had a key influence on imitation learning, posture recognition and identity recognition. From the more dynamic motor imitation paradigm with a TW avatar, we found that interpersonal synchronization, motor coordination and motor control were more impaired in children with ASD compared to both TD children and children with DCD. Taken together these results confirm the motor peculiarities of children with ASD despite imitation tasks were adequately performed.

DISCUSSION

Studies from human-machine interaction support the idea of a behavioral signature in children with ASD. However, several issues need to be addressed. Is this behavioral signature motoric in essence? Is it possible to ascertain that these peculiarities occur during all motor tasks (e.g. posture, voluntary movement)? Could this motor signature be considered as specific to autism, notably in comparison to DCD that also display poor motor coordination skills? We suggest that more work comparing the two conditions should be implemented, including analysis of kinematics and movement smoothness with sufficient measurement quality to allow spectral analysis.

A computational scheme for internal models not requiring precise system parameters

Utilization by humans of a precise and adaptable internal model of the dynamics of the body in generating movements is a well-supported concept. The prevailing opinion is that such an internal model ceaselessly develops through long-term repetition and accumulation in the central nervous system (CNS). However, a long-term learning process would not be absolutely necessary for the formation of internal models. It is possible to estimate the dynamics of the system by using a motor command and its resulting output, instead of constructing a model of the dynamics with precise parameters. In this study, a computational model is proposed that uses a motor command and its corresponding output to estimate the dynamics of the system and it is examined whether the proposed model is capable of describing a series of empirical movements. The proposed model was found to be capable of describing humans' fast movements which require compensation for system dynamics as well as sensory delays. In addition, the proposed model shows equifinality under inertial perturbations as seen in several experimental studies. This satisfactory reproducibility of the proposed computation raises the possibility that humans make a movement by estimating the system dynamics with a copy of motor command and sensory output on a momentary basis, without the need to identify precise system parameters.