Optimization of modularity during development to simplify walking control across multiple steps

Introduction

Walking in adults relies on a small number of modules, reducing the number of degrees of freedom that needs to be regulated by the central nervous system (CNS). While walking in toddlers seems to also involve a small number of modules when considering averaged or single-step data, toddlers produce a high amount of variability across strides, and the extent to which this variability interacts with modularity remains unclear.

Methods

Electromyographic activity from 10 bilateral lower limb muscles was recorded in both adults (n = 12) and toddlers (n = 12) over 8 gait cycles. Toddlers were recorded while walking independently and while being supported by an adult. This condition was implemented to assess if motor variability persisted with reduced balance constraints, suggesting a potential central origin rather than reliance on peripheral regulations. We used non-negative matrix factorization to model the underlying modular command with the Space-by-Time Decomposition method, with or without averaging data, and compared the modular organization of toddlers and adults during multiple walking strides.

Results

Toddlers were more variable in both conditions (i.e. independent walking and supported by an adult) and required significantly more modules to account for their greater stride-by-stride variability. Activations of these modules varied more across strides and were less parsimonious compared to adults, even with diminished balance constraints.

Discussion

The findings suggest that modular control of locomotion evolves between toddlerhood and adulthood as the organism develops and practices. Adults seem to be able to generate several strides of walking with less modules than toddlers. The persistence of variability in toddlers when balance constraints were lowered suggests a link with the ability to explore rather than with corrective mechanisms. In conclusion, the capacity of new walkers to flexibly activate their motor command suggests a broader range of possible actions, though distinguishing between modular and non-modular inputs remains challenging.

Human movement modifications induced by different levels of transparency of an active upper limb exoskeleton

Active upper limb exoskeletons are a potentially powerful tool for neuromotor rehabilitation. This potential depends on several basic control modes, one of them being transparency. In this control mode, the exoskeleton must follow the human movement without altering it, which theoretically implies null interaction efforts. Reaching high, albeit imperfect, levels of transparency requires both an adequate control method and an in-depth evaluation of the impacts of the exoskeleton on human movement. The present paper introduces such an evaluation for three different "transparent" controllers either based on an identification of the dynamics of the exoskeleton, or on force feedback control or on their combination. Therefore, these controllers are likely to induce clearly different levels of transparency by design. The conducted investigations could allow to better understand how humans adapt to transparent controllers, which are necessarily imperfect. A group of fourteen participants were subjected to these three controllers while performing reaching movements in a parasagittal plane. The subsequent analyses were conducted in terms of interaction efforts, kinematics, electromyographic signals and ergonomic feedback questionnaires. Results showed that, when subjected to less performing transparent controllers, participants strategies tended to induce relatively high interaction efforts, with higher muscle activity, which resulted in a small sensitivity of kinematic metrics. In other words, very different residual interaction efforts do not necessarily induce very different movement kinematics. Such a behavior could be explained by a natural human tendency to expend effort to preserve their preferred kinematics, which should be taken into account in future transparent controllers evaluation.

Reoptimization of single-joint motor patterns to non-Earth gravity torques induced by a robotic exoskeleton

Gravity is a ubiquitous component of our environment that we have learned to optimally integrate in movement control. Yet, altered gravity conditions arise in numerous applications from space exploration to rehabilitation, thereby pressing the sensorimotor system to adapt. Here, we used a robotic exoskeleton to reproduce the elbow joint-level effects of arbitrary gravity fields ranging from 1g to -1g, passing through Mars- and Moon-like gravities, and tested whether humans can reoptimize their motor patterns accordingly. By comparing the motor patterns of actual arm movements with those predicted by an optimal control model, we show that our participants (N = 61 ) adapted optimally to each gravity-like torque. These findings suggest that the joint-level effects of a large range of gravities can be efficiently apprehended by humans, thus opening new perspectives in arm weight support training in manipulation tasks, whether it be for patients or astronauts.

On the perception of movement vigour

It is common to get the impression that someone moves rather slowly or quickly in everyday life. In motor control, the natural pace of movement is captured by the concept of vigour, which is often quantified from the speed or duration of goal-directed actions. A common phenomenon, here referred to as the vigour law, is that preferred speed and duration idiosyncratically increase with the magnitude of the motion. According to the direct-matching hypothesis, this vigour law could thus underlie the judgement of someone else's movement vigour. We conducted a series of three experiments (N = 80) to test whether the vigour law also exists in perception and whether it is linked to that of action. In addition to measuring participants' vigour, we also asked them to judge the quickness of stimuli representing horizontal arm reaching movements varying through amplitudes, speeds, and durations. Results showed that speed and duration of movements perceived as neither fast nor slow (i.e., natural pace) increased with amplitude, thereby indicating that the vigour law holds when an observer judges the natural pace of others' movements. Results also revealed that this judgement was population-based (related to the average vigour of all participants) rather than individual-based (participant's own vigour).

The value of time in the invigoration of human movements when interacting with a robotic exoskeleton

Time and effort are thought to be subjectively balanced during the planning of goal-directed actions, thereby setting the vigor of volitional movements. Theoretical models predicted that the value of time should then amount to high levels of effort. However, the time-effort trade-off has so far only been studied for a narrow range of efforts. To investigate the extent to which humans can invest in a time-saving effort, we used a robotic exoskeleton to substantially vary the energetic cost associated with a certain vigor during reaching movements. In this situation, minimizing the time-effort trade-off should lead to high and low human efforts for upward and downward movements, respectively. Consistently, all participants expended substantial amounts of energy upward and remained essentially inactive by harnessing the work of gravity downward, while saving time in both cases. A common time-effort trade-off may therefore determine the vigor of reaching movements for a wide range of efforts.

Generating variability from motor primitives during infant locomotor development

Motor variability is a fundamental feature of developing systems allowing motor exploration and learning. In human infants, leg movements involve a small number of basic coordination patterns called locomotor primitives, but whether and when motor variability could emerge from these primitives remains unknown. Here we longitudinally followed 18 infants on 2-3 time points between birth (~4 days old) and walking onset (~14 months old) and recorded the activity of their leg muscles during locomotor or rhythmic movements. Using unsupervised machine learning, we show that the structure of trial-to-trial variability changes during early development. In the neonatal period, infants own a minimal number of motor primitives but generate a maximal motor variability across trials thanks to variable activations of these primitives. A few months later, toddlers generate significantly less variability despite the existence of more primitives due to more regularity within their activation. These results suggest that human neonates initiate motor exploration as soon as birth by variably activating a few basic locomotor primitives that later fraction and become more consistently activated by the motor system.

From Motivation to Action: Action Cost Better Predicts Changes in Premovement Beta-Band Activity than Speed

Although premovement beta-band event-related desynchronization (β-ERD; 13-30 Hz) from sensorimotor regions is modulated by movement speed, current evidence does not support a strict monotonic association between the two. Given that β-ERD is thought to increase information encoding capacity, we tested the hypothesis that it might be related to the expected neurocomputational cost of movement, here referred to as action cost. Critically, action cost is greater both for slow and fast movements compared with a medium or "preferred" speed. Thirty-one right-handed participants performed a speed-controlled reaching task while recording their EEG. Results revealed potent modulations of beta power as a function of speed, with β-ERD being significantly greater both for movements performed at high and low speeds compared with medium speed. Interestingly, medium-speed movements were more often chosen by participants than low-speed and high-speed movements, suggesting that they were evaluated as less costly. In line with this, modeling of action cost revealed a pattern of modulation across speed conditions that strikingly resembled the one found for β-ERD. Indeed, linear mixed models showed that estimated action cost predicted variations of β-ERD significantly better than speed. This relationship with action cost was specific to beta power, as it was not found when averaging activity in the mu band (8-12 Hz) and gamma band (31-49 Hz) bands. These results demonstrate that increasing β-ERD may not merely speed up movements, but instead facilitate the preparation of high-speed and low-speed movements through the allocation of additional neural resources, thereby enabling flexible motor control.SIGNIFICANCE STATEMENT Heightened beta activity has been associated with movement slowing in Parkinson's disease, and modulations of beta activity are commonly used to decode movement parameters in brain-computer interfaces. Here we show that premovement beta activity is better explained by the neurocomputational cost of the action rather than its speed. Instead of being interpreted as a mere reflection of changes in movement speed, premovement changes in beta activity might therefore be used to infer the amount of neural resources that are allocated for motor planning.

A Trade-Off between Complexity and Interaction Quality for Upper Limb Exoskeleton Interfaces

Exoskeletons are among the most promising devices dedicated to assisting human movement during reeducation protocols and preventing musculoskeletal disorders at work. However, their potential is currently limited, partially because of a fundamental contradiction impacting their design. Indeed, increasing the interaction quality often requires the inclusion of passive degrees of freedom in the design of human-exoskeleton interfaces, which increases the exoskeleton's inertia and complexity. Thus, its control also becomes more complex, and unwanted interaction efforts can become important. In the present paper, we investigate the influence of two passive rotations in the forearm interface on sagittal plane reaching movements while keeping the arm interface unchanged (i.e., without passive degrees of freedom). Such a proposal represents a possible compromise between conflicting design constraints. The in-depth investigations carried out here in terms of interaction efforts, kinematics, electromyographic signals, and subjective feedback of participants all underscored the benefits of such a design. Therefore, the proposed compromise appears to be suitable for rehabilitation sessions, specific tasks at work, and future investigations into human movement using exoskeletons.

Evidence for a cost of time in the invigoration of isometric reaching movements

How the brain determines the vigor of goal-directed movements is a fundamental question in neuroscience. Recent evidence has suggested that vigor results from a trade-off between a cost related to movement production (cost of movement) and a cost related to our brain's tendency to temporally discount the value of future reward (cost of time). However, whether it is critical to hypothesize a cost of time to explain the vigor of basic reaching movements with intangible reward is unclear because the cost of movement may be theoretically sufficient for this purpose. Here we directly address this issue by designing an isometric reaching task whose completion can be accurate and effortless in prefixed durations. The cost of time hypothesis predicts that participants should be prone to spend energy to save time even if the task can be accomplished at virtually no motor cost. Accordingly, we found that all participants generated substantial amounts of force to invigorate task accomplishment, especially when the prefixed duration was long enough. Remarkably, the time saved by each participant was linked to their original vigor in the task and predicted by an optimal control model balancing out movement and time costs. Taken together, these results supports the existence of an idiosyncratic, cognitive cost of time that underlies the invigoration of basic isometric reaching movements.

Decomposing spontaneous sign language into elementary movements: A principal component analysis-based approach

Sign Language (SL) is a continuous and complex stream of multiple body movement features. That raises the challenging issue of providing efficient computational models for the description and analysis of these movements. In the present paper, we used Principal Component Analysis (PCA) to decompose SL motion into elementary movements called principal movements (PMs). PCA was applied to the upper-body motion capture data of six different signers freely producing discourses in French Sign Language. Common PMs were extracted from the whole dataset containing all signers, while individual PMs were extracted separately from the data of individual signers. This study provides three main findings: (1) although the data were not synchronized in time across signers and discourses, the first eight common PMs contained 94.6% of the variance of the movements; (2) the number of PMs that represented 94.6% of the variance was nearly the same for individual as for common PMs; (3) the PM subspaces were highly similar across signers. These results suggest that upper-body motion in unconstrained continuous SL discourses can be described through the dynamic combination of a reduced number of elementary movements. This opens up promising perspectives toward providing efficient automatic SL processing tools based on heavy mocap datasets, in particular for automatic recognition and generation.

Machine Learning of Motion Statistics Reveals the Kinematic Signature of the Identity of a Person in Sign Language

Sign language (SL) motion contains information about the identity of a signer, as does voice for a speaker or gait for a walker. However, how such information is encoded in the movements of a person remains unclear. In the present study, a machine learning model was trained to extract the motion features allowing for the automatic identification of signers. A motion capture (mocap) system recorded six signers during the spontaneous production of French Sign Language (LSF) discourses. A principal component analysis (PCA) was applied to time-averaged statistics of the mocap data. A linear classifier then managed to identify the signers from a reduced set of principal components (PCs). The performance of the model was not affected when information about the size and shape of the signers were normalized. Posture normalization decreased the performance of the model, which nevertheless remained over five times superior to chance level. These findings demonstrate that the identity of a signer can be characterized by specific statistics of kinematic features, beyond information related to size, shape, and posture. This is a first step toward determining the motion descriptors necessary to account for the human ability to identify signers.

Stochastic optimal feedforward-feedback control determines timing and variability of arm movements with or without vision

Human movements with or without vision exhibit timing (i.e. speed and duration) and variability characteristics which are not well captured by existing computational models. Here, we introduce a stochastic optimal feedforward-feedback control (SFFC) model that can predict the nominal timing and trial-by-trial variability of self-paced arm reaching movements carried out with or without online visual feedback of the hand. In SFFC, movement timing results from the minimization of the intrinsic factors of effort and variance due to constant and signal-dependent motor noise, and movement variability depends on the integration of visual feedback. Reaching arm movements data are used to examine the effect of online vision on movement timing and variability, and test the model. This modelling suggests that the central nervous system predicts the effects of sensorimotor noise to generate an optimal feedforward motor command, and triggers optimal feedback corrections to task-related errors based on the available limb state estimate.

A cross-species neural integration of gravity for motor optimization

Recent kinematic results, combined with model simulations, have provided support for the hypothesis that the human brain shapes motor patterns that use gravity effects to minimize muscle effort. Because many different muscular activation patterns can give rise to the same trajectory, here, we specifically investigate gravity-related movement properties by analyzing muscular activation patterns during single-degree-of-freedom arm movements in various directions. Using a well-known decomposition method of tonic and phasic electromyographic activities, we demonstrate that phasic electromyograms (EMGs) present systematic negative phases. This negativity reveals the optimal motor plan's neural signature, where the motor system harvests the mechanical effects of gravity to accelerate downward and decelerate upward movements, thereby saving muscle effort. We compare experimental findings in humans to monkeys, generalizing the Effort-optimization strategy across species.

Stochastic optimal open-loop control as a theory of force and impedance planning via muscle co-contraction

Understanding the underpinnings of biological motor control is an important issue in movement neuroscience. Optimal control theory is a leading framework to rationalize this problem in computational terms. Previously, optimal control models have been devised either in deterministic or in stochastic settings to account for different aspects of motor control (e.g. average behavior versus trial-to-trial variability). While these approaches have yielded valuable insights about motor control, they typically fail in explaining muscle co-contraction. Co-contraction of a group of muscles associated to a motor function (e.g. agonist and antagonist muscles spanning a joint) contributes to modulate the mechanical impedance of the neuromusculoskeletal system (e.g. joint viscoelasticity) and is thought to be mainly under the influence of descending signals from the brain. Here we present a theory suggesting that one primary goal of motor planning may be to issue feedforward (open-loop) motor commands that optimally specify both force and impedance, according to noisy neuromusculoskeletal dynamics and to optimality criteria based on effort and variance. We show that the proposed framework naturally accounts for several previous experimental findings regarding the regulation of force and impedance via muscle co-contraction in the upper-limb. Stochastic optimal (closed-loop) control, preprogramming feedback gains but requiring on-line state estimation processes through long-latency sensory feedback loops, may then complement this nominal feedforward motor command to fully determine the limb’s mechanical impedance. The proposed stochastic optimal open-loop control theory may provide new insights about the general articulation of feedforward/feedback control mechanisms and justify the occurrence of muscle co-contraction in the neural control of movement.

This study presents a novel computational theory to explain the planning of force and impedance (e.g. viscoelasticity) in the neural control of movement. It assumes that one main goal of motor planning is to elaborate feedforward motor commands that determine both the force and the impedance required for the task at hand. These feedforward motor commands (i.e. that are defined prior to movement execution) are designed to minimize effort and variance costs considering the uncertainty arising from sensorimotor or environmental noise. A major outcome of this mathematical framework is the explanation of muscle co-contraction (i.e. the concurrent contraction of a group of muscles involved in a motor function). Muscle co-contraction has been shown to occur in many situations but previous modeling works struggled to account for it. Although effortful, co-contraction contributes to increase the robustness of motor behavior (e.g. small variance) upstream of sophisticated optimal closed-loop control processes that require state estimation from delayed sensory feedback to function. This work may have implications regarding our understanding of the neural control of movement in computational terms. It also provides a theoretical ground to explain how to optimally plan force and impedance within a general and versatile framework.

Modularity underlying the performance of unusual locomotor tasks inspired by developmental milestones

Motor behaviors are often hypothesized to be set up from the combination of a small number of modules encoded in the central nervous system. These modules are thought to combine such that a variety of motor tasks can be realized, from reproducible tasks such as walking to more unusual locomotor tasks that typically exhibit more step-by-step variability. We investigated the impact of step-by-step variability on the modular architecture of unusual tasks compared with walking. To this aim, 20 adults had to perform walking and two unusual modes of locomotion inspired by developmental milestones (cruising and crawling). Sixteen surface electromyography (EMG) signals were recorded to extract both spatial and temporal modules. Modules were extracted from both averaged and nonaveraged (i.e., single step) EMG signals to assess the significance of step-to-step variability when participants practiced such unusual locomotor tasks. The number of modules extracted from averaged data was similar across tasks, but a higher number of modules was required to reconstruct nonaveraged EMG data of the unusual tasks. Although certain walking modules were shared with cruising and crawling, task-specific modules were necessary to account for the muscle patterns underlying these unusual locomotion modes. These results highlight a more complex modularity (e.g., more modules) for cruising and crawling compared with walking, which was only apparent when the step-to-step variability of EMG patterns was considered. This suggests that considering nonaveraged data is relevant when muscle modularity is studied, especially in motor tasks with high variability as in motor development.NEW & NOTEWORTHY This study addresses the general question of modularity in locomotor control. We demonstrate for the first time the importance of intraindividual variability in the muscle modularity of unusual locomotor behaviors that exhibit greater step-by-step variability than standard walking. Crawling and cruising, the unusual locomotor modes considered, are based on a more complex modular organization than walking. More spatial and temporal modules, task specific or shared with walking modules, are needed to reconstruct muscle patterns.

Vigor of reaching, walking, and gazing movements: on the consistency of interindividual differences

Movement vigor is an important feature of motor control that is thought to originate from cortico-basal ganglia circuits and processes shared with decision-making, such as temporal reward discounting. Accordingly, vigor may be related to one's relationship with time, which may, in turn, reflect a general trait-like feature of individuality. While significant interindividual differences of vigor have been typically reported for isolated motor tasks, little is known about the consistency of such differences across tasks and movement effectors. Here, we assessed interindividual consistency of vigor across reaching (both dominant and nondominant arm), walking, and gazing movements of various distances within the same group of 20 participants. Given distinct neural pathways and biomechanical specificities of each movement modality, a significant consistency would corroborate the trait-like aspect of vigor. Vigor scores for dominant and nondominant arm movements were found to be highly correlated across individuals. Vigor scores of reaching and walking were also significantly correlated across individuals, indicating that people who reach faster than others also tend to walk faster. At last, vigor scores of saccades were uncorrelated with those of reaching and walking, reaffirming that the vigor of stimulus-elicited eye saccades is distinct. These findings highlight the trait-like aspect of vigor for reaching movements with either arms and, to a lesser extent, walking.NEW & NOTEWORTHY Robust interindividual differences of movement vigor have been reported for arm reaching and saccades. Beyond biomechanics, personality trait-like characteristics have been proposed to account for those differences. Here, we examined for the first time the consistency of interindividual differences of vigor during dominant/nondominant arm reaching, walking, and gazing to assess the trait-like aspect of vigor. We found a significant consistency of vigor within our group of individuals for all tested tasks/effectors except saccades.

Space-by-Time Modular Decomposition Effectively Describes Whole-Body Muscle Activity During Upright Reaching in Various Directions

The modular control hypothesis suggests that motor commands are built from precoded modules whose specific combined recruitment can allow the performance of virtually any motor task. Despite considerable experimental support, this hypothesis remains tentative as classical findings of reduced dimensionality in muscle activity may also result from other constraints (biomechanical couplings, data averaging or low dimensionality of motor tasks). Here we assessed the effectiveness of modularity in describing muscle activity in a comprehensive experiment comprising 72 distinct point-to-point whole-body movements during which the activity of 30 muscles was recorded. To identify invariant modules of a temporal and spatial nature, we used a space-by-time decomposition of muscle activity that has been shown to encompass classical modularity models. To examine the decompositions, we focused not only on the amount of variance they explained but also on whether the task performed on each trial could be decoded from the single-trial activations of modules. For the sake of comparison, we confronted these scores to the scores obtained from alternative non-modular descriptions of the muscle data. We found that the space-by-time decomposition was effective in terms of data approximation and task discrimination at comparable reduction of dimensionality. These findings show that few spatial and temporal modules give a compact yet approximate representation of muscle patterns carrying nearly all task-relevant information for a variety of whole-body reaching movements.

Adaptive use of interaction torque during arm reaching movement from the optimal control viewpoint

The study aimed at investigating the extent to which the brain adaptively exploits or compensates interaction torque (IT) during movement control in various velocity and load conditions. Participants performed arm pointing movements toward a horizontal plane without a prescribed reach endpoint at slow, neutral and rapid speeds and with/without load attached to the forearm. Experimental results indicated that IT overall contributed to net torque (NT) to assist the movement, and that such contribution increased with limb inertia and instructed speed and led to hand trajectory variations. We interpreted these results within the (inverse) optimal control framework, assuming that the empirical arm trajectories derive from the minimization of a certain, possibly composite, cost function. Results indicated that mixing kinematic, energetic and dynamic costs was necessary to replicate the participants' adaptive behavior at both kinematic and dynamic levels. Furthermore, the larger contribution of IT to NT was associated with an overall decrease of the kinematic cost contribution and an increase of its dynamic/energetic counterparts. Altogether, these results suggest that the adaptive use of IT might be tightly linked to the optimization of a composite cost which implicitly favors more the kinematic or kinetic aspects of movement depending on load and speed.

Direction-dependent arm kinematics reveal optimal integration of gravity cues

The brain has evolved an internal model of gravity to cope with life in the Earth's gravitational environment. How this internal model benefits the implementation of skilled movement has remained unsolved. One prevailing theory has assumed that this internal model is used to compensate for gravity's mechanical effects on the body, such as to maintain invariant motor trajectories. Alternatively, gravity force could be used purposely and efficiently for the planning and execution of voluntary movements, thereby resulting in direction-depending kinematics. Here we experimentally interrogate these two hypotheses by measuring arm kinematics while varying movement direction in normal and zero-G gravity conditions. By comparing experimental results with model predictions, we show that the brain uses the internal model to implement control policies that take advantage of gravity to minimize movement effort.

On the nature of motor planning variables during arm pointing movement: Compositeness and speed dependence

The purpose of this study was to investigate the nature of the variables and rules underlying the planning of unrestrained 3D arm reaching. To identify whether the brain uses kinematic, dynamic and energetic values in an isolated manner or combines them in a flexible way, we examined the effects of speed variations upon the chosen arm trajectories during free arm movements. Within the optimal control framework, we uncovered which (possibly composite) optimality criterion underlays at best the empirical data. Fifteen participants were asked to perform free-endpoint reaching movements from a specific arm configuration at slow, normal and fast speeds. Experimental results revealed that prominent features of observed motor behaviors were significantly speed-dependent, such as the chosen reach endpoint and the final arm posture. Nevertheless, participants exhibited different arm trajectories and various degrees of speed dependence of their reaching behavior. These inter-individual differences were addressed using a numerical inverse optimal control methodology. Simulation results revealed that a weighted combination of kinematic, energetic and dynamic cost functions was required to account for all the critical features of the participants' behavior. Furthermore, no evidence for the existence of a speed-dependent tuning of these weights was found, thereby suggesting subject-specific but speed-invariant weightings of kinematic, energetic and dynamic variables during the motor planning process of free arm movements. This suggested that the inter-individual difference of arm trajectories and speed dependence was not only due to anthropometric singularities but also to critical differences in the composition of the subjective cost function.

Evidence for subjective values guiding posture and movement coordination in a free-endpoint whole-body reaching task

When moving, humans must overcome intrinsic (body centered) and extrinsic (target-related) redundancy, requiring decisions when selecting one motor solution among several potential ones. During classical reaching studies the position of a salient target determines where the participant should reach, constraining the associated motor decisions. We aimed at investigating implicit variables guiding action selection when faced with the complexity of human-environment interaction. Subjects had to perform whole body reaching movements towards a uniform surface. We observed little variation in the self-chosen motor strategy across repeated trials while movements were variable across subjects being on a continuum from a pure 'knee flexion' associated with a downward center of mass (CoM) displacement to an 'ankle dorsi-flexion' associated with an upward CoM displacement. Two optimality criteria replicated these two strategies: a mix between mechanical energy expenditure and joint smoothness and a minimization of the amount of torques. Our results illustrate the presence of idiosyncratic values guiding posture and movement coordination that can be combined in a flexible manner as a function of context and subject. A first value accounts for the reach efficiency of the movement at the price of selecting possibly unstable postures. The other predicts stable dynamic equilibrium but requires larger energy expenditure and jerk.

Task-discriminative space-by-time factorization of muscle activity

Movement generation has been hypothesized to rely on a modular organization of muscle activity. Crucial to this hypothesis is the ability to perform reliably a variety of motor tasks by recruiting a limited set of modules and combining them in a task-dependent manner. Thus far, existing algorithms that extract putative modules of muscle activations, such as Non-negative Matrix Factorization (NMF), identify modular decompositions that maximize the reconstruction of the recorded EMG data. Typically, the functional role of the decompositions, i.e., task accomplishment, is only assessed a posteriori. However, as motor actions are defined in task space, we suggest that motor modules should be computed in task space too. In this study, we propose a new module extraction algorithm, named DsNM3F, that uses task information during the module identification process. DsNM3F extends our previous space-by-time decomposition method (the so-called sNM3F algorithm, which could assess task performance only after having computed modules) to identify modules gauging between two complementary objectives: reconstruction of the original data and reliable discrimination of the performed tasks. We show that DsNM3F recovers the task dependence of module activations more accurately than sNM3F. We also apply it to electromyographic signals recorded during performance of a variety of arm pointing tasks and identify spatial and temporal modules of muscle activity that are highly consistent with previous studies. DsNM3F achieves perfect task categorization without significant loss in data approximation when task information is available and generalizes as well as sNM3F when applied to new data. These findings suggest that the space-by-time decomposition of muscle activity finds robust task-discriminating modular representations of muscle activity and that the insertion of task discrimination objectives is useful for describing the task modulation of module recruitment.

Reach endpoint formation during the visuomotor planning of free arm pointing

Volitional motor control generally involves deciding 'where to go' and 'how to go there'. Understanding how these two constituent pieces of motor decision coordinate is an important issue in neuroscience. Although the two processes could be intertwined, they are generally thought to occur in series, whereby visuomotor planning begins with the knowledge of a final hand position to attain. However, daily activities are often compatible with an infinity of final hand positions. The purpose of the present study was to test whether the reach endpoint ('where') is an input of arm motor planning ('how') in such ecological settings. To this end, we considered a free pointing task, namely arm pointing to a long horizontal line, and investigated the formation of the reach endpoint through eye-hand coordination. Although eye movement always preceded hand movement, our results showed that the saccade initiation was delayed by ~ 120 ms on average when the line was being pointed to as compared with a single target dot; the hand reaction time was identical in the two conditions. When the latency of saccade initiation was relatively brief, subjects often performed double, or even triple, saccades before hand movement onset. The number of saccades triggered was found to significantly increase as a function of the primary saccade latency and accuracy. These results suggest that knowledge about the reach endpoint built up gradually along with the arm motor planning process, and that the oculomotor system delayed the primary reach-related saccade in order to gain more information about the final hand position.

Energy-related optimal control accounts for gravitational load: comparing shoulder, elbow, and wrist rotations

We permanently deal with gravity force. Experimental evidences revealed that moving against gravity strongly differs from moving along the gravity vector. This directional asymmetry has been attributed to an optimal planning process that optimizes gravity force effects to minimize energy. Yet, only few studies have considered the case of vertical movements in the context of optimal control. What kind of cost is better suited to explain kinematic patterns in the vertical plane? Here, we aimed to understand further how the central nervous system (CNS) plans and controls vertical arm movements. Our reasoning was the following: if the CNS optimizes gravity mechanical effects on the moving limbs, kinematic patterns should change according to the direction and the magnitude of the gravity torque being encountered in the motion. Ten subjects carried out single-joint movements, i.e., rotation around the shoulder (whole arm), elbow (forearm), and wrist (hand) joints, in the vertical plane. Joint kinematics were analyzed and compared with various theoretical optimal model predictions (minimum absolute work-jerk, jerk, torque change, and variance). We found both direction-dependent and joint-dependent variations in several kinematic parameters. Notably, directional asymmetries decreased according to a proximodistal gradient. Numerical simulations revealed that our experimental findings could be attributed to an optimal motor planning (minimum absolute work-jerk) that integrates the direction and the magnitude of gravity torque and minimizes the absolute work of forces (energy-related cost) around each joint. Present results support the general idea that the CNS implements optimal solutions according to the dynamic context of the action.

A unifying model of concurrent spatial and temporal modularity in muscle activity

Modularity in the central nervous system (CNS), i.e., the brain capability to generate a wide repertoire of movements by combining a small number of building blocks ("modules"), is thought to underlie the control of movement. Numerous studies reported evidence for such a modular organization by identifying invariant muscle activation patterns across various tasks. However, previous studies relied on decompositions differing in both the nature and dimensionality of the identified modules. Here, we derive a single framework that encompasses all influential models of muscle activation modularity. We introduce a new model (named space-by-time decomposition) that factorizes muscle activations into concurrent spatial and temporal modules. To infer these modules, we develop an algorithm, referred to as sample-based nonnegative matrix trifactorization (sNM3F). We test the space-by-time decomposition on a comprehensive electromyographic dataset recorded during execution of arm pointing movements and show that it provides a low-dimensional yet accurate, highly flexible and task-relevant representation of muscle patterns. The extracted modules have a well characterized functional meaning and implement an efficient trade-off between replication of the original muscle patterns and task discriminability. Furthermore, they are compatible with the modules extracted from existing models, such as synchronous synergies and temporal primitives, and generalize time-varying synergies. Our results indicate the effectiveness of a simultaneous but separate condensation of spatial and temporal dimensions of muscle patterns. The space-by-time decomposition accommodates a unified view of the hierarchical mapping from task parameters to coordinated muscle activations, which could be employed as a reference framework for studying compositional motor control.

A methodology for assessing the effect of correlations among muscle synergy activations on task-discriminating information

Muscle synergies have been hypothesized to be the building blocks used by the central nervous system to generate movement. According to this hypothesis, the accomplishment of various motor tasks relies on the ability of the motor system to recruit a small set of synergies on a single-trial basis and combine them in a task-dependent manner. It is conceivable that this requires a fine tuning of the trial-to-trial relationships between the synergy activations. Here we develop an analytical methodology to address the nature and functional role of trial-to-trial correlations between synergy activations, which is designed to help to better understand how these correlations may contribute to generating appropriate motor behavior. The algorithm we propose first divides correlations between muscle synergies into types (noise correlations, quantifying the trial-to-trial covariations of synergy activations at fixed task, and signal correlations, quantifying the similarity of task tuning of the trial-averaged activation coefficients of different synergies), and then uses single-trial methods (task-decoding and information theory) to quantify their overall effect on the task-discriminating information carried by muscle synergy activations. We apply the method to both synchronous and time-varying synergies and exemplify it on electromyographic data recorded during performance of reaching movements in different directions. Our method reveals the robust presence of information-enhancing patterns of signal and noise correlations among pairs of synchronous synergies, and shows that they enhance by 9–15% (depending on the set of tasks) the task-discriminating information provided by the synergy decompositions. We suggest that the proposed methodology could be useful for assessing whether single-trial activations of one synergy depend on activations of other synergies and quantifying the effect of such dependences on the task-to-task differences in muscle activation patterns.

Muscle synergies in neuroscience and robotics: from input-space to task-space perspectives

In this paper we review the works related to muscle synergies that have been carried-out in neuroscience and control engineering. In particular, we refer to the hypothesis that the central nervous system (CNS) generates desired muscle contractions by combining a small number of predefined modules, called muscle synergies. We provide an overview of the methods that have been employed to test the validity of this scheme, and we show how the concept of muscle synergy has been generalized for the control of artificial agents. The comparison between these two lines of research, in particular their different goals and approaches, is instrumental to explain the computational implications of the hypothesized modular organization. Moreover, it clarifies the importance of assessing the functional role of muscle synergies: although these basic modules are defined at the level of muscle activations (input-space), they should result in the effective accomplishment of the desired task. This requirement is not always explicitly considered in experimental neuroscience, as muscle synergies are often estimated solely by analyzing recorded muscle activities. We suggest that synergy extraction methods should explicitly take into account task execution variables, thus moving from a perspective purely based on input-space to one grounded on task-space as well.

Investigating reduction of dimensionality during single-joint elbow movements: a case study on muscle synergies

A long standing hypothesis in the neuroscience community is that the central nervous system (CNS) generates the muscle activities to accomplish movements by combining a relatively small number of stereotyped patterns of muscle activations, often referred to as “muscle synergies.” Different definitions of synergies have been given in the literature. The most well-known are those of synchronous, time-varying and temporal muscle synergies. Each one of them is based on a different mathematical model used to factor some EMG array recordings collected during the execution of variety of motor tasks into a well-determined spatial, temporal or spatio-temporal organization. This plurality of definitions and their separate application to complex tasks have so far complicated the comparison and interpretation of the results obtained across studies, and it has always remained unclear why and when one synergistic decomposition should be preferred to another one. By using well-understood motor tasks such as elbow flexions and extensions, we aimed in this study to clarify better what are the motor features characterized by each kind of decomposition and to assess whether, when and why one of them should be preferred to the others. We found that three temporal synergies, each one of them accounting for specific temporal phases of the movements could account for the majority of the data variation. Similar performances could be achieved by two synchronous synergies, encoding the agonist-antagonist nature of the two muscles considered, and by two time-varying muscle synergies, encoding each one a task-related feature of the elbow movements, specifically their direction. Our findings support the notion that each EMG decomposition provides a set of well-interpretable muscle synergies, identifying reduction of dimensionality in different aspects of the movements. Taken together, our findings suggest that all decompositions are not equivalent and may imply different neurophysiological substrates to be implemented.

Quantitative evaluation of muscle synergy models: a single-trial task decoding approach

Muscle synergies, i.e., invariant coordinated activations of groups of muscles, have been proposed as building blocks that the central nervous system (CNS) uses to construct the patterns of muscle activity utilized for executing movements. Several efficient dimensionality reduction algorithms that extract putative synergies from electromyographic (EMG) signals have been developed. Typically, the quality of synergy decompositions is assessed by computing the Variance Accounted For (VAF). Yet, little is known about the extent to which the combination of those synergies encodes task-discriminating variations of muscle activity in individual trials. To address this question, here we conceive and develop a novel computational framework to evaluate muscle synergy decompositions in task space. Unlike previous methods considering the total variance of muscle patterns (VAF based metrics), our approach focuses on variance discriminating execution of different tasks. The procedure is based on single-trial task decoding from muscle synergy activation features. The task decoding based metric evaluates quantitatively the mapping between synergy recruitment and task identification and automatically determines the minimal number of synergies that captures all the task-discriminating variability in the synergy activations. In this paper, we first validate the method on plausibly simulated EMG datasets. We then show that it can be applied to different types of muscle synergy decomposition and illustrate its applicability to real data by using it for the analysis of EMG recordings during an arm pointing task. We find that time-varying and synchronous synergies with similar number of parameters are equally efficient in task decoding, suggesting that in this experimental paradigm they are equally valid representations of muscle synergies. Overall, these findings stress the effectiveness of the decoding metric in systematically assessing muscle synergy decompositions in task space.

Visual gravity influences arm movement planning

When submitted to a visuomotor rotation, subjects show rapid adaptation of visually guided arm reaching movements, indicated by a progressive reduction in reaching errors. In this study, we wanted to make a step forward by investigating to what extent this adaptation also implies changes into the motor plan. Up to now, classical visuomotor rotation paradigms have been performed on the horizontal plane, where the reaching motor plan in general requires the same kinematics (i.e., straight path and symmetric velocity profile). To overcome this limitation, we considered vertical and horizontal movement directions requiring specific velocity profiles. This way, a change in the motor plan due to the visuomotor conflict would be measurable in terms of a modification in the velocity profile of the reaching movement. Ten subjects performed horizontal and vertical reaching movements while observing a rotated visual feedback of their motion. We found that adaptation to a visuomotor rotation produces a significant change in the motor plan, i.e., changes to the symmetry of velocity profiles. This suggests that the central nervous system takes into account the visual information to plan a future motion, even if this causes the adoption of nonoptimal motor plans in terms of energy consumption. However, the influence of vision on arm movement planning is not fixed, but rather changes as a function of the visual orientation of the movement. Indeed, a clear influence on motion planning can be observed only when the movement is visually presented as oriented along the vertical direction. Thus vision contributes differently to the planning of arm pointing movements depending on motion orientation in space.

Evidence for composite cost functions in arm movement planning: an inverse optimal control approach

An important issue in motor control is understanding the basic principles underlying the accomplishment of natural movements. According to optimal control theory, the problem can be stated in these terms: what cost function do we optimize to coordinate the many more degrees of freedom than necessary to fulfill a specific motor goal? This question has not received a final answer yet, since what is optimized partly depends on the requirements of the task. Many cost functions were proposed in the past, and most of them were found to be in agreement with experimental data. Therefore, the actual principles on which the brain relies to achieve a certain motor behavior are still unclear. Existing results might suggest that movements are not the results of the minimization of single but rather of composite cost functions. In order to better clarify this last point, we consider an innovative experimental paradigm characterized by arm reaching with target redundancy. Within this framework, we make use of an inverse optimal control technique to automatically infer the (combination of) optimality criteria that best fit the experimental data. Results show that the subjects exhibited a consistent behavior during each experimental condition, even though the target point was not prescribed in advance. Inverse and direct optimal control together reveal that the average arm trajectories were best replicated when optimizing the combination of two cost functions, nominally a mix between the absolute work of torques and the integrated squared joint acceleration. Our results thus support the cost combination hypothesis and demonstrate that the recorded movements were closely linked to the combination of two complementary functions related to mechanical energy expenditure and joint-level smoothness.

To reach an object, the brain has to select among a set of possible arm trajectories that displace the hand from an initial to a final desired position. Because of the intrinsic redundancy characterizing the human arm, the number of admissible joint trajectories toward the goal is generally infinite. However, many studies have demonstrated that the range of actual trajectories can be limited to those that result from the fulfillment of some optimal rules. Various cost functions were shown to be relevant in the literature. A peculiar aspect of most of these costs is that each one of them aims at optimizing one specific feature of the movement. The necessary motor flexibility of everyday life, however, might rely on the combination of such cost functions rather than on a single one. Testing this cost combination hypothesis has never been attempted. To this aim we propose a reaching task involving target redundancy to facilitate the comparisons of different candidate costs and to identify the best-fitting one (possibly composite). Using a numerical inverse optimal control method, we show that most participants produced movements corresponding to a strict combination of two subjective costs linked to the mechanical energy consumption and the joint-level smoothness.

An ensemble analysis of electromyographic activity during whole body pointing with the use of support vector machines

We explored the use of support vector machines (SVM) in order to analyze the ensemble activities of 24 postural and focal muscles recorded during a whole body pointing task. Because of the large number of variables involved in motor control studies, such multivariate methods have much to offer over the standard univariate techniques that are currently employed in the field to detect modifications. The SVM was used to uncover the principle differences underlying several variations of the task. Five variants of the task were used. An unconstrained reaching, two constrained at the focal level and two at the postural level. Using the electromyographic (EMG) data, the SVM proved capable of distinguishing all the unconstrained from the constrained conditions with a success of approximately 80% or above. In all cases, including those with focal constraints, the collective postural muscle EMGs were as good as or better than those from focal muscles for discriminating between conditions. This was unexpected especially in the case with focal constraints. In trying to rank the importance of particular features of the postural EMGs we found the maximum amplitude rather than the moment at which it occurred to be more discriminative. A classification using the muscles one at a time permitted us to identify some of the postural muscles that are significantly altered between conditions. In this case, the use of a multivariate method also permitted the use of the entire muscle EMG waveform rather than the difficult process of defining and extracting any particular variable. The best accuracy was obtained from muscles of the leg rather than from the trunk. By identifying the features that are important in discrimination, the use of the SVM permitted us to identify some of the features that are adapted when constraints are placed on a complex motor task.

Manifold reaching paradigm: how do we handle target redundancy?

How the central nervous system coordinates the many intrinsic degrees of freedom of the musculoskeletal system is a recurrent question in motor control. Numerous studies addressed it by considering redundant reaching tasks such as point-to-point arm movements, for which many joint trajectories and muscle activations are usually compatible with a single goal. There exists, however, a different, extrinsic kind of redundancy that is target redundancy. Many times, indeed, the final point to reach is neither specified nor unique. In this study, we aim to understand how the central nervous system tackles such an extrinsic redundancy by considering a reaching-to-a-manifold paradigm, more specifically an arm pointing to a long vertical bar. In this case, the endpoint is not defined a priori and, therefore, subjects are free to choose any point on the bar to successfully achieve the task. We investigated the strategies used by subjects to handle this presented choice. Our results indicate both intersubject and intertrial consistency with respect to the freedom provided by the task. However, the subjects' behavior is found to be more variable than during classical point-to-point reaches. Interestingly, the average arm trajectories to the bar and the structure of intertrial endpoint variations could be explained via stochastic optimal control with an energy/smoothness expected cost and signal-dependent motor noise. We conclude that target redundancy is first overcome during movement planning and then exploited during movement execution, in agreement with stochastic optimal feedback control principles, which illustrates how the complementary problems of goal and movement selection may be resolved at once.

Sensorimotor adaptation of point-to-point arm movements after spaceflight: the role of internal representation of gravity force in trajectory planning

After an exposure to weightlessness, the central nervous system operates under new dynamic and sensory contexts. To find optimal solutions for rapid adaptation, cosmonauts have to decide whether parameters from the world or their body have changed and to estimate their properties. Here, we investigated sensorimotor adaptation after a spaceflight of 10 days. Five cosmonauts performed forward point-to-point arm movements in the sagittal plane 40 days before and 24 and 72 h after the spaceflight. We found that, whereas the shape of hand velocity profiles remained unaffected after the spaceflight, hand path curvature significantly increased 1 day after landing and returned to the preflight level on the third day. Control experiments, carried out by 10 subjects under normal gravity conditions, showed that loading the arm with varying loads (from 0.3 to 1.350 kg) did not affect path curvature. Therefore, changes in path curvature after spaceflight cannot be the outcome of a control process based on the subjective feeling that arm inertia was increased. By performing optimal control simulations, we found that arm kinematics after exposure to microgravity corresponded to a planning process that overestimated the gravity level and optimized movements in a hypergravity environment (∼1.4 g). With time and practice, the sensorimotor system was recalibrated to Earth's gravity conditions, and cosmonauts progressively generated accurate estimations of the body state, gravity level, and sensory consequences of the motor commands (72 h). These observations provide novel insights into how the central nervous system evaluates body (inertia) and environmental (gravity) states during sensorimotor adaptation of point-to-point arm movements after an exposure to weightlessness.

The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements.

When performing reaching and grasping movements, the brain has to choose one trajectory among an infinite set of possibilities. Nevertheless, because human and animal movements provide highly stereotyped features, motor strategies used by the brain were assumed to be optimal according to certain optimality criteria. In this study, we propose a theoretical model for motor planning of arm movements that minimizes a compromise between the absolute work exerted by the muscles and the integral of the squared acceleration. We demonstrate that under these assumptions agonistic and antagonistic muscles are inactivated during overlapping periods of time for quick enough movements. Moreover, it is shown that only this type of criterion can predict these inactivation periods. Finally, experimental evidence is in agreement with the predictions of the model. Indeed, we report the existence of simultaneous inactivation of opposing muscles during fast vertical arm movements. Therefore, this study suggests that biological movements partly optimize the energy expenditure, integrating both inertial and gravitational forces during the motor planning process.