Journal publications (peer-reviewed)

Optimal control is a prominent approach in robotics and movement neuroscience, among other fields of science. Methods for deriving optimal choices of action have been classically devised either in deterministic or stochastic settings. Here, we consider a setting in-between that retains the stochastic aspect of the controlled system but assumes deterministic open-loop control actions. The rationale stems from observations about the neural control of movement which highlighted that relatively stable behaviors can be achieved without feedback circuitry, via open-loop motor commands adequately tuning the mechanical impedance of the neuromusculoskeletal system. Yet, effective methods for deriving optimal open-loop controls for stochastic systems are lacking overall. This work presents a continuous-time approach based on statistical linearization techniques for the efficient computation of optimal open-loop controls for a broad class of stochastic optimal control problems. We first show that non-trivial departure from the optimal solutions of classical deterministic and stochastic approaches may arise for simple synthetic examples, thereby stressing the originality of the framework. We then exemplify its potential relevance to the planning of biological movement by showing that a well-known phenomenon in motor control, referred to as muscle cocontraction, occurs naturally. More generally, this stochastic optimal control framework may be suited to other fields where the design of optimal open-loop actions is relevant.
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 online 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.
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.
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.
People usually move at a self-selected pace in everyday life. Yet, the principles underlying the formation of human movement vigour remain unclear, particularly in view of intriguing inter-individual variability. It has been hypothesized that how the brain values time may be the cornerstone of such differences, beyond biomechanics. Here, we focused on the vigour of self-paced reaching movement and assessed the stability of vigour via repeated measurements within participants. We used an optimal control methodology to identify a cost of time (CoT) function underlying each participant’s vigour, considering a model of the biomechanical cost of movement. We then tested the extent to which anthropometric or psychological traits, namely boredom proneness and impulsivity, could account for a significant part of interindividual variance in vigour and CoT parameters. Our findings show that the vigour of reaching is largely idiosyncratic and tend to corroborate a relation between the relative steepness of the identified CoT and boredom proneness, a psychological trait relevant to one’s relationship with time in decision-making.
Voluntary movement is hypothesized to rely on a limited number of muscle synergies, the recruitment of which translates task goals into effective muscle activity. In this study, we investigated how to analytically characterize the functional role of different types of muscle synergies in task performance. To this end, we recorded a comprehensive dataset of muscle activity during a variety of whole-body pointing movements. We decomposed the electromyographic (EMG) signals using a space-by-time modularity model which encompasses the main types of synergies. We then used a task decoding and information theoretic analysis to probe the role of each synergy by mapping it to specific task features. We found that the temporal and spatial aspects of the movements were encoded by different temporal and spatial muscle synergies, respectively, consistent with the intuition that there should a correspondence between major attributes of movement and major features of synergies. This approach led to the development of a novel computational method for comparing muscle synergies from different participants according to their functional role. This functional similarity analysis yielded a small set of temporal and spatial synergies that describes the main features of whole-body reaching movements.
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.
The aim of this study is to review the use of muscle synergies (MS) to characterize locomotor organizations in healthy and with brain damage subjects. The various studies have revealed a variety of approaches to extract muscle synergies. In spite of this diversity, the results suggest a redundancy of a small number of MS allow to explain the locomotor organizations. Moreover, MS seem to be able to quantify changes induced by environmental constraints or therapeutic management (age, walking speed, etc.). However, some methodological choices such as filtering or temporal normalizations could induce interpretation bias. In spite of the heterogeneity of the studies focus on the brain injury patient, all findings move towards a reduced number of SM explaining locomotor activities. These MS are dependent on a set of factors as the severity of the lesion or the type of rehabilitation. After the analysis of the selected articles, we believe that MS can be a relevant approach in the characterization of locomotor activities in the spinal cord injury with appropriated methodological and algorithmic choices.
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.
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.
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.
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.
To want something now rather than later is a common attitude that reflects the brain's tendency to value the passage of time. Because the time taken to accomplish an action inevitably delays task achievement and reward acquisition, this idea was ported to neural movement control within the “cost of time” theory. This theory provides a normative framework to account for the underpinnings of movement time formation within the brain and the origin of a self-selected pace in human and animal motion. Then, how does the brain exactly value time in the control of action? To tackle this issue, we used an inverse optimal control approach and developed a general methodology allowing to squarely sample infinitesimal values of the time cost from experimental motion data. The cost of time underlying saccades was found to have a concave growth, thereby confirming previous results on hyperbolic reward discounting, yet without making any prior assumption about this hypothetical nature. For self-paced reaching, however, movement time was primarily valued according to a striking sigmoidal shape; its rate of change consistently presented a steep rise before a maximum was reached and a slower decay was observed. Theoretical properties of uniqueness and robustness of the inferred time cost were established for the class of problems under investigation, thus reinforcing the significance of the present findings. These results may offer a unique opportunity to uncover how the brain values the passage of time in healthy and pathological motor control and shed new light on the processes underlying action invigoration.
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 Nonnegative 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.
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 where 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 is to test whether the reach endpoint (“where”) is an input of arm motor planning (“how”) in such ecological settings. To this aim, 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. While eye movement always preceded hand movement, our results showed that the saccade initiation was delayed by ~120 msec on average when pointing to the line as compared to 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, 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 procrastinated the primary reach-related saccade in order to gain more information about the final hand position.
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 in order 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 further understand how the CNS plans and control 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 analysed and compared to various theoretical optimal models predictions (minimum absolute work-jerk; jerk; torque change; variance). We found both direction-dependent and joint-dependent variations in several kinematic parameters. Notably, directional asymmetries decreased according to a proximo-distal 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 dynamical context of the action.
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 var- ious 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 en- compasses all influential models of muscle activation modularity. We introduce a new model (named space-by-time decomposition) that factorizes muscle activations into concurrent spa- tial and temporal modules. To infer these modules, we develop an algorithm, referred to as sample-based non-negative matrix tri-factorization (sNM3F). We test the space-by-time de- composition 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 tempo- ral 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.
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, 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.
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.
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.
In the last years of research in cognitive control, neuroscience and humanoid robotics have converged to different frameworks which aim, on one side, at modeling and analyzing human motion, and, on the other side, at enhancing motor abilities of humanoids. In this paper we try to cover the gap between the two areas, giving an overview of the literature in the two fields which concerns the production of movements. First, we survey computational motor control models based on optimality principles; then, we review available implementations and techniques to transfer these principles to humanoid robots, with a focus on the limitations and possible improvements of the current implementations. Moreover, we propose Stochastic Optimal Control as a framework to take into account delays and noise, thus catching the unpredictability aspects typical of both humans and humanoids systems. Optimal Control in general can also easily be integrated with Machine Learning frameworks, thus resulting in a computational implementation of human motor learning. This survey is mainly addressed to roboticists attempting to implement human-inspired controllers on robots, but can also be of interest for researchers in other fields, such as computational motor control.
When submitted to a visuo-motor 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 visuo-motor rotation paradigms are performed on the horizontal plane, where the reaching motor plan requires always 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 visuo-motor 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 visuo-motor 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 non-optimal 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.
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.
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 inter-subject and inter-trial 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 inter-trial 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.
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.
Following exposure to weightlessness, the CNS 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 space-flight of ten days. Five cosmonauts performed forward point-to-point arm movements in the sagittal plane 40 days before, 24h and 72h after the space-flight. We found that, while the shape of hand velocity profiles remained unaffected after the space-flight, hand path curvature significantly increased one day after landing and returned to pre-flight level the third day. Control experiments, carried-out by ten subjects in normal-gravity conditions, showed that loading the arm with varying loads (from 0.3 Kg to 1.350 Kg) did not affect path curvature. Therefore, changes in path curvature after space-flight 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 following exposure to microgravity corresponded to a planning process that overestimated gravity level and optimized movements in a hypergravity environment (approximately 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, the gravity level, and the sensory consequences of the motor commands (72h). These observations provide novel insights into how the CNS evaluates body (inertia) and environmental (gravity) states during sensorimotor adaptation of point-to-point arm movements following exposure to weightlessness.
Previous kinematic and kinetic studies revealed that, when accomplishing a whole-body pointing task beyond arm's length, a modular and flexible organization could represent a robust solution to control simultaneously target pointing and equilibrium maintenance. Here, we investigated the underlying mechanisms that produce such a coordinative kinematic structure. We monitored the activity of a large number of muscles spread throughout subjects' bodies while they performed pointing movements beyond arm's length, either with or without imposition of postural or pointing constraints. Analyses revealed that muscle signals lied on a tri-dimensional hyper-plane and were temporally organized according to a triphasic pattern (three components, each one exhibiting one single peak of activation and the peaks being consecutive in time). Such a functional muscle synergy was found to be robust across conditions. Also the activities of the separate groups of muscles acting at each body joint resulted tri-dimensional. In particular, those associated with the muscles of the lower-body joints (ankle, knee and hip) always presented the three sequences in all conditions. However, a slightly different organization was found for the muscle activities of the upper-limb, suggesting a moderate level of flexibility of the activity of such muscles to movement constraints. The present findings link together, in a hierarchical view of motor control, the joint coordination characterizing whole-body pointing movements with a basic muscle synergistic organization, namely a triphasic pattern.
How fast can we correct a planned movement following an unexpected target jump? Subjects, starting in an upright standing position, were required to point to a target that randomly and unexpectedly jumps forward to a constant spatial location. Rapid motor corrections in the upper and lower limbs, with latency responses of less than 100 ms, were revealed by contrasting electromyographic activities in perturbed and unperturbed trials. The earliest responses were observed primarily in the anterior section of the deltoïdus anterior (shoulder) and the tibialis anterior (leg) muscles. Our findings indicate that visual on-going movement corrections may be accomplished via fast loops at the level of the upper and lower limbs and may not require cortical involvement.
The control of movement is highly complex because of the biomechanical redundancy of the musculoskeletal system (Bernstein, 1967). To cope with the large number of degrees of freedom, humans and animals likely rely on a modular control architecture. In other words, the CNS may activate flexible combinations of motor primitives instead of controlling each muscle independently, a motor primitive being a premotor drive generated by some neuronal population (for example, in the spinal cord) that recruits a covarying group of muscles that remain in a fixed relationship during recruitment (Hart and Giszter, 2010). Hence, motor primitives may represent the building blocks of movement organization. An important direction for research is to investigate the neural basis of this organization in the spinal cord, i.e., the neural mechanisms that select the muscle activation patterns required to achieve a behavioral goal. [...]
This paper develops the mathematical side of a theory of inactivations in human biomechanics. This theory has been validated by practical experiments, including zero-gravity experiments. The theory mostly relies on Pontryagin’s maximum principle on the one side and on transversality theory on the other side. It turns out that the periods of silence in the activation of muscles that are observed in practice during the motions of the arm can appear only if “something like the energy expenditure” is minimized. Conversely, minimization of a criterion taking into account the “energy expenditure” guaranties the presence of these periods of silence, for sufficiently short movements.
The aim of this study was to determine whether the timing of the muscular synergies was influenced by the reduction of the base of support when we initiate a whole body reaching movement. To answer this question, we performed a principal component analysis on electromyographic activities of 24 muscles recorded on the leg, the trunk, and the arm. Our results demonstrated that during the initiation of the whole body pointing movement, only three principal components accounted for at least 95% of the variance for the overall muscular data, both when the equilibrium constraints were normal and when the base of support was reduced. These principal components were strongly correlated despite the fact that the center of mass forward displacement and the center of pressure backward displacements significantly decreased when the base of support was reduced. It suggests that the central nervous system did not change the overall timing of the muscular synergies when new equilibrium constraints were introduced in the task but was rather able to tune their amplitude as evidenced by the modification of the center of mass and center of pressure displacements.
Hand reaching and bipedal equilibrium are two important functions of the human motor behavior. However, how the brain plans goal-oriented actions combining target reaching with equilibrium regulation is not yet clearly understood. An important question is whether postural control and reaching are integrated in one single module or controlled separately. Here, we show that postural control and reaching motor commands are processed by means of a modular and flexible organization. Principal component and correlation analyses between pairs of angles were used to extract global and local coupling during a whole-body pointing beyond arm's length. A low-dimensional organization of the redundant kinematic chain allowing simultaneous target reaching and regulation of the center of mass (CoM) displacement in extrinsic space emerged from the first analysis. In follow-up experiments, both the CoM and finger trajectories were constrained by asking participants to reach from a reduced base of support with or without knee flexion, or by moving the endpoint along a predefined trajectory (straight or semicircular trajectories). Whereas joint covaried during free conditions and under equilibrium restrictions, it was decomposed in two task-dependent and task-independent modules, corresponding to a dissociation of arm versus legs, trunk, and head coordination, respectively, under imposed finger path conditions. A numerical simulation supported the idea that both postural and focal subtasks are basically integrated into the same motor command and that the CNS is able to combine or to separate the movement into autonomous functional synergies according to the task requirements.
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.
This paper is devoted to the behavior of human arms during pointing movements. Several assumptions have already been made about the planning of such motions. None of these assumptions is able, up to now, to explain certain nonintuitive dynamic phenomena, in particular certain asymmetries in the motion and certain time intervals of inactivity of the muscles. In this paper, we propose an assumption explaining all these phenomena. Two strong points in this work are the following. First, our assumption is that human beings minimize a certain criterion that physically makes sense, namely, a compromise between the absolute work of external forces and a comfort term. Second, our conclusions do not rely on any numerical experiment and are completely justified mathematically (i.e., without any argument from simulation or “experimental mathematics,” such arguments being usually considered as acceptable in neurobiology). Also, the conclusion that total inactivity holds during some time subintervals of the movement is shown to be a stable property (in our model).
The authors investigated the influence of normal aging upon equilibrium and kinematics features during a whole-body task. Eight young (23±1.51 years) and eight elderly (74.5±4.5 years) adults reached from a standing position an object placed in front of them on the ground. The authors found smaller Center of Masse (CoM) and Center of Pressure (CoP) antero-posterior displacements in elderly than in young adults. Wrist paths were curved in young but straight in elderly adults. Wrist peak velocity and duration were respectively lower and greater in elderly compared to young adults. However, Principal-Component-Analysis did not reveal differences in angle coordination between the two groups, suggesting so that modifications in equilibrium and wrist kinematics reflect an adaptation process that compensates age-related physiological changes. The authors hypothesized that equilibrium preservation in elderly contributes to wrist kinematics modifications. The authors verified this premise by placing young adults under equilibrium restrictions (reduced base of support) and observing that they reproduced the behavior of elderly adults. The authors propose that wrist kinematics is equilibrium dependent and that such a strategy is included in the motor plan of elderly adults.

  Chapters (peer-reviewed)

In this chapter, we present a mathematical theory of human movement vigor. At the core of the theory is the concept of the cost of time. According to it, natural movement cannot be too slow because the passage of time entails a cost which makes slow moves undesirable. Within this framework, an inverse methodology is available to reliably and robustly characterize how the brain penalizes time from experimental motion data. Yet, a general theory of human movement pace should not only account for the self-selected speed but should also include situations where slow or fast speed instructions are given by an experimenter or required by a task. In particular, the limit case of a “maximal speed” instruction is linked to Fitts’s law, i.e. the speed/accuracy trade-off. This chapter first summarizes the cost of time theory and the procedure used for its accurate identification. Then, the case of slow/fast movements is investigated but changing the duration of goal-directed movements can be done in various ways in this framework. Here we show that only one strategy seems plausible to account for both slow/fast and self-paced reaching movements. By relying upon a free-time optimal control formulation of the motor planning problem, this chapter provides a comprehensive treatment of the linear-quadratic case for single degree of freedom arm movements but the principles are easily extendable to multijoint and/or artificial systems.

  Conference proceedings and abstracts (peer-reviewed)

Establishing a symbiotic relationship between a human and a exoskeleton is the end goal in many applications in order to provide benefits to the user. However, the literature focusing on the human side of human-exoskeleton interaction has remained less exhaustive than the literature focusing on the design (hardware/software) of the exoskeleton device itself. It is, though, essential to understand how a human adapts his motor control when interacting with an exoskeleton. Motor adaptation is an implicit process carried out by the central nervous system when the body encounters a perturbation, a paradigm that has been extensively studied in the field of human motor control research. When wearing an exoskeleton, even “as-transparentas- possible”, contact/interaction forces may impact well-known motor control laws in a way that may be detrimental to the user, and even compromise usability in real applications. The present paper investigates how interaction with a backdrivable upper-limb exoskeleton (ABLE) set in “transparent” mode of control affects the kinematics/dynamics of human movement in a simple task.We find that important motor control features are preserved when moving with ABLE but an overall movement slowness occurs, likely as a response to increased inertia according to optimal control simulations. Such a human motor control approach illustrates one possible way to assess the degree of symbiosis between human and exoskeleton, i.e. by grounding on well-known findings in motor control research.
Extraction of muscle synergies from electromyography (EMG) recordings relies on the analysis of multi-trial muscle activation data. To identify the underlying modular structure, dimensionality reduction algorithms are usually applied to the EMG signals. This process requires a rigid alignment of muscle activity across trials that is typically achieved by the normalization of the length of each trial. However, this time-normalization ignores important temporal variability that is present on single trials as result of neuromechanical processes or task demands. To overcome this limitation, we propose a novel method that simultaneously aligns muscle activity data and extracts spatial and temporal muscle synergies. This approach relies on an unsupervised learning algorithm that extends our previously developed space-by-time decomposition to incorporate the identification of linear time warps for individual trials. We apply the proposed method to high-dimensional spatiotemporal EMG data recorded during performance of whole-body reaching movements and show that it identifies meaningful spatial and temporal structure in muscle activity despite differences in trial lengths. We suggest that this algorithm is a useful tool to identify muscle synergies in a variety of natural self-paced motor behaviors.
Human movement may be affected by different motor deficits such as musculoskeletal disorders (MSDs) in an occupational context or hemiplegia/hemiparesis following a stroke. On the one hand, MSDs are mainly situated in the upper limbs and they represent the first occupational disease in Europe at the present time (INRS, 2015). They are partly due to awkward postures and muscle efforts in response to high force requirements during a professional task. To decrease MSDs, upper-limb exoskeletons may be employed [...]
In this paper we propose a methodology to control a novel class of actuators that we called passive noise rejection variable stiffness actuators (pnrVSA). Differently from nowadays classical VSA designs, this novel class of actuators mimics the human musculoskeletal ability to increase noise rejection without relying on feedback. To fully highlight the potentialities behind these actuators we consider movement planning under two constraints: (1) absence of feedback, i.e. purely open-loop planning; (2) uncertain dynamic model. Under these constraints, movement planning can be formalized as an open-loop stochastic optimal control. Due to the lack of classical methods forcing the open-loop nature of the computed solution, we used here a slight modification of available methodologies based on importance sampling of trajectories using forward diffusion processes. Simulations show that the proposed algorithm can be effectively used to plan open-loop movements with pnrVSA. In particular, two different scenarios are considered: the control of a single joint pnrVSA and the control of a two degrees of freedom planar arm equipped with antagonist pnrVSAs at each joint. In both cases, movement has to be planned in presence of uncertain dynamics for unstable tasks. It is shown that open-loop stochastic optimal control can modulate the intrinsic stiffness of the system to cope with both instability and noise.
In this paper we suggest basic principles to design a novel type of passive variable impedance actuator aimed at replicating a specific property of human co-contraction, related to the ability to cope with uncertainties affecting any physical/biological system. In particular the dynamical model of the proposed actuator is such that the variance of the state vector in response to noisy disturbances can be reduced by tuning the passive stiffness of the system. By means of a linearization analysis we characterize the mathematical properties that a non-linear dynamical system should have in order to possess this noise rejection property. We provide a practical example of such a system based on non-linear springs whose critical feature is to attach some elastic elements to a fixed reference (e.g. “ground”). We then show that this antagonist actuator structure is actually analog to Hill’s model of the human muscle/tendon system, emphasizing its biological relevance. We finally illustrate how time-varying stiffness can be efficiently planned feedforwardly to reject disturbances that may affect task achievement. To this aim, we use the formalism of stochastic optimal control to derive open-loop controls anticipating the consequences of unpredictability and instability linked to the task. We conclude that the suggested actuators are well-suited to mimic the main features of human co-contraction and plan to implement this type of actuator on the robot platform iCub in a near future.
One of the most important features for a system capable of working in uncertain and unstructured environments is reliability. Nowadays robots are excellent machines, but are still not able to interact with their surrounding environment as humans or animals do. Recent studies highlight the role played by impedance changes in the human arm during manipulation tasks. In particular the possibility to vary the stiffness of shoulder, elbow and wrist allows humans to interact easily with fast changing environments while rejecting unpredictable noise disturbances [1]. Several studies also showed how the capability of “co-contracting” antagonistic muscles is required to interact with noisy/unpredictable environments. Starting from these premises we recently proposed novel design principles to build actuators with the ability to actively regulate the passive noise rejection (i.e. the ability to cancel the effect of disturbances without explicitly relying on feedback) [2]. In the present paper we implement these principles in the mechanical design of a novel actuator. The actuator is composed of two electric motors in agonist-antagonist configuration. The final design includes also four non-linear springs whose force-displacement characteristic has been customized on the specific application requirements. Validation of the proposed non-linear spring design has been conducted on a prototype and results are reported in this paper. Future works foreseen the integration of the proposed actuators on a two limbed robot with six artificial muscle, (three agonist-antagonist pairs) in a simple and biarticular configuration.
The time needed to adapt to a perturbation depends critically on the amount of the available a-priori information: the more we know about the perturbation, the less experience we need to learn how to compensate for it. The drawback of such a model-based approach is the loss of generality, because rigid assumptions do not allow to rapidly adapt to new perturbations. A possible intermediate solution is represented by a modular strategy, in which the generality is gained through new combinations of pre-learned models. Starting from the assumption that modules might represent a way to store a-priori information in the central nervous system, the present paper explores the consequences of such a modular forward model in human motor learning, in the context of reaching movements. In particular, we tested the prediction that in presence of a modular control, perturbations not compatible with the existing modules should be learned with more difficulty than compatible perturbations. To this aim, we confronted human subjects with two different kinematic perturbations of comparable difficulty: one compatible with the natural kinematic modules (or intra-modular) and one incompatible with them (extra-modular). We observed that human subjects adapt faster to intra-modular perturbations, thus providing evidence in favor of the adoption of a modular strategy by the central nervous system. The obtained results have some interesting consequence within the context of modular learning, hereafter discussed.
Recently, a number of variable impedance actuator designs have been proposed under di erent motivations (safe human-robot interaction, mechanical robustness and energy storing to cite a few). In a recent paper (Berret et al. (2011)) we observed that none of the available designs seem to reproduce an important characteristic of human muscles, i.e. the ability to open-loop reject disturbances by means of muscle co-activation. Starting form this observation, we recently designed a novel single-joint actuator (nr-VIA) based on the use of non-linear springs in agonistantagonist con guration. In this paper we discuss some control related characteristics of the proposed design. The theoretical analysis is conducted without specifying the potential energy of the springs. We first design a control law capable of monotonically increasing the joint-sti ness (i.e. disturbance rejection) without changing the joint equilibrium configuration; this result is obtained with minimal requirements on the potential energy of the springs. The same control law is then proven (under more restrictive conditions) to monotonically decrease the sensitivity of the joint equilibrium with respect to the actuation variables, a desirable property when trying to achieve a finer control over joint positioning.
Muscle co-contraction can be modeled as an active modulation of the passive musculo-skeletal compliance. Within this context, recent findings in human motor control have shown that active compliance modulation is fundamental when planning movements in presence of unpredictability and uncertainties. Along this line of research, this paper investigates the link between active impedance control and unpredictability, with special focus on robotic applications. Different types of actuators are considered and confronted to extreme situations such as moving in an unstable force field and controlling a system with significant delays in the feedback loop. We use tools from stochastic optimal control to illustrate the possibility of optimally planning the intrinsic system stiffness when performing movements in such situations. In the extreme case of total feedback absence, different actuators model are considered and their performance in dealing with unpredictability compared. Finally, an application of the proposed theories on planning reaching movements with the iCub humanoid platform is proposed.
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 analysing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion (Todorov 2004). 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 behavioural data. The cost proposed in this study includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements which used smooth cost functions [i.e. that have continuous derivatives up to some desired order, like the minimum jerk (Flash and Hogan 1985) or minimum torque change (Uno et al. 1989) models], the present model has the particularity of using a cost function that is not smooth. We have demonstrated in Berret et al. (2008) that under these assumptions agonistic and antagonistic muscles are inactivated during overlapping periods of time, for quick enough movements. Moreover, it has been 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 have checked the existence of simultaneous inactivation of opposing muscles during fast vertical arm movements.
In this paper, we present several constructive results about nonholonomic interpolation, in the perspective of motion planning in robotics. We specially treat the case of a set of nonholonomic constraints of corank p<=3. In fact, we are able to treat almost all generic cases for p<=3. But also, we show what may happen for larger corank. We give complete details in the Engel’s case, which, from the point of view of robotics, corresponds to the kinematic constraints of a car with a trailer.

  Miscellaneous

In this manuscript, I present a synthesis of my past works related to the optimal and modular control hypotheses for human movement. Optimal control theory is often thought to imply that the brain computes global optima continuously for each motor task it faces. Modular control theory typically assumes that the brain explicitly stores genuine synergies in specific neural circuits whose combined recruitment yields task-effective motor commands. Said like that, these two influential motor control theories are pushed to extreme positions. A more nuanced view is discussed in this manuscript, which is framed within Marr’s tri-level computational theory applied to movement neuroscience. It is argued that optimal control is best viewed as helping to understand “why” certain movements are preferred over others but does not say much about how the brain would practically trigger optimal strategies. We also argue that dimensionality reduction found in muscle activities may be a by-product of optimality and cannot be attributed to neurally hardwired synergies stricto sensu, in particular when the synergies are extracted from factorization algorithms applied to electromyographic data such that their nature is strongly dictated by the methodology itself. Hence, more modeling work is required in order to critically test the modularity hypothesis and assess its potential neural origins. An adequate mathematical formulation of hierarchical motor control could help to bridge the gap between optimality and modularity, and advance our knowledge about the organization of motor control in general. For what concerns my research project, I propose to investigate the principles underlying self-paced movement formation. This is a critical issue in neuroscience because many neural disorders like Parkinson’s disease lead to a loss of motion vigor as well as in human-machine interfaces for reasons of usability/acceptability (e.g. interaction with an exoskeleton). Time is notably a key variable influencing the speed of our daily movements. Recently, a theory according to which the duration of movement might entail a cost for our central nervous system has been proposed: the cost of time (CoT) hypothesis. A methodology allowing to reliably identify this CoT, presumably playing a role in motor planning and decision-making, has been successfully developed within the optimal control framework. Yet, several questions regarding the very existence of a CoT, its assumptions, origin, nature or consistency remain unresolved. The goal of this project is to test these questions from both experimental and theoretical viewpoints. Dans ce mémoire, je présente une synthèse de mes travaux antérieurs portants sur les hypothèses du contrôle optimal et du contrôle modulaire pour le mouvement humain. La théorie du contrôle optimal est souvent vue comme impliquant que le cerveau calcule continuellement des optima globaux pour chaque tâche motrice à laquelle il est confronté. La théorie du contrôle modulaire suppose, quant à elle, que le cerveau stockerait d'authentiques synergies dans ses circuits neuronaux et dont l'activation combinée donnerait lieu à des commandes motrices adéquates vis-à-vis de la tâche à réaliser. Stipulées ainsi, ces deux théories influentes du contrôle moteur sont positionnées de manière extrême. Une vue plus nuancée est discutée dans ce manuscrit, dans le cadre de la théorie computationnelle à 3 niveaux de Marr, appliquée aux neurosciences du mouvement. Il est argumenté que la réduction de dimensionnalité trouvée dans les activités musculaires pourrait être le sous-produit d'une contrainte d'optimalité de plus haut niveau et qu'elle ne peut pas être attribuée stricto sensu à de réelles synergies codées au niveau neural. Ceci est en particulier vrai quand les synergies sont extraites à partir d'algorithmes de factorisation appliqués à des données électromyographiques si bien que leur nature est profondément dictée par la méthodologie employée. Plus de travaux de modélisation sont donc requis pour tester de manière critique l'hypothèse de modularité et ses potentielles origines neurales. Une formulation mathématique adéquate d'un contrôle moteur hiérarchique pourrait notamment aider à combler l'écart entre optimalité et modularité, et faire avancer nos connaissances sur l'organisation du contrôle moteur en général. Résumé En ce qui concerne mon projet de recherche, il vise à mieux comprendre d'où vient la vitesse du mouvement humain. Ceci est un enjeu crucial en neurosciences en raison des troubles neuromoteurs qui affectent la vigueur des gestes (ex : maladie de Parkinson) ainsi que pour l'acceptabilité/utilisabilité des interfaces homme-machine (ex : interaction avec un exosquelette). Le temps est de fait une variable clé influençant la vitesse de nos mouvements au quotidien. La théorie du coût du temps (CdT) selon laquelle la durée du mouvement entraînerait un coût pour le cerveau a été proposée. Ce CdT a pu être identifié dans le cadre du contrôle optimal. Cependant de nombreuses questions liées à l'existence même du CdT, ses hypothèses, sa nature ou consistance restent en suspens. Elles seront traitées dans ce projet tant d'un point de vue expérimental que théorique.
This thesis is aimed at better understanding how the Central Nervous System (CNS) plans and controls movements and, in particular, how the gravity field is integrated within these processes. To perform rapid movements, the CNS must anticipate the effects of gravity on the moving limb. To tackle this, experiments in humans and modeling works have been undertaken. The experimental paradigms used here are pointing movements toward a target involving only the arm or the whole body. Concerning the arm movements, our work was grounded on a singular observation showing that upward and downward movements exhibit significant differences, suspected to be due to gravity. In order to test this hypothesis, a theory based upon the minimization of the absolute work of forces produced by muscles has been developed. It postulates that human movements are optimal and minimize in particular an energetic quantity. The main theoretical result is the demonstration of an equivalence between the minimization of a criterion including the absolute work of forces and the presence of simultaneous inactivation periods of agonistic and antagonistic muscles acting at a joint. Experiments have confirmed the existence of such periods of silence in muscular activities at the times predicted by the model. Therefore, we have concluded that the optimality criterion used by the brain to plan movements includes a term similar to the absolute work. A by-product of this result is that both gravitational and inertial forces are integrated into the same motor plan, within the minimization of energy expenditure. However, in most daily-life motor tasks, minimizing energy can not be the only goal of the action; preserving balance or be precise must also be taken into account. An experimental protocol has been elaborated in order to clarify how the CNS coordinates the control of posture and movement for whole-body pointing tasks. Our results confirm the idea of a modular organization of movements for such multi-goal tasks, i.e. performed from the combination of pre-programmed sequences. In conclusion, this work suggests that the CNS integrates the biomechanical properties of the body and the environmental constraints within a single motor plan. Depending on the task, the CNS could optimize a compromise between energy consumption, safety, or movement precision. Moreover, these results reinforce the idea that an internal model of gravity exists and is strongly implied in human motricity.

Ces travaux de thèse ont pour objectif de mieux comprendre comment le système nerveux central (SNC) planifie et contrôle les mouvements et, plus particulièrement, comment il intègre la gravité dans ces processus. Pour réaliser des mouvements, le SNC doit prédire les effets de la gravitation sur les segments corporels. Dans cette optique, des expériences sur l’Homme et des travaux de modélisation ont été entrepris. Les paradigmes expérimentaux considérés ici sont des mouvements de pointage vers une cible impliquant uniquement les segments du bras ou bien tout le corps. Concernant les mouvements du bras, nos travaux ont eu pour objectif initial d’expliquer un phénomène expérimental montrant que des mouvements dirigés vers le haut et vers le bas présentent des différences significatives, suspectées être dues à la gravité. Pour tenter de justifier cette hypothèse, une théorie basée sur la minimisation du travail absolu des forces produites par les muscles a été développée. Elle postule que les mouvements humains sont optimaux et minimisent notamment une quantité énergétique. Le principal résultat théorique est la démonstration d’une équivalence entre la minimisation d’un coût contenant le travail absolu des forces et la présence d’inactivations simultanées des muscles agonistes et antagonistes agissant à une articulation. Des expérimentations ont confirmé l’existence de périodes de silence dans l’activité des muscles aux instants prédits par le modèle. Nous avons ainsi pu en déduire que le critère d’optimalité utilisé par le cerveau pour planifier les mouvements inclut un terme du type minimum de travail absolu. Un résultat corollaire est que les forces gravitaires et inertielles sont intégrées au même plan moteur, dans un processus minimisant l’énergie dépensée. Cependant, pour la plupart des mouvements de la vie courante, minimiser l’énergie ne peut être le seul objectif ; maintenir l’équilibre ou optimiser la précision doivent aussi être pris en compte. Un protocole expérimental a été élaboré dans le but de mieux comprendre comment le SNC coordonne le contrôle de la posture et du mouvement pour des tâches plus complexes, impliquant le corps entier. Nos résultats confirment l’idée d’une organisation modulaire du mouvement, c’est-à-dire réalisée par la combinaison de séquences pré-programmées. En conclusion, ces travaux suggèrent que le SNC intègre les propriétés mécaniques du corps et les contraintes de l’environnement dans un même plan moteur. En fonction de la tâche, le SNC pourrait choisir d’optimiser un compromis entre l’énergie consommée, la sûreté ou la précision du mouvement. En outre, ces résultats renforcent l’idée qu’un modèle interne de la gravité existe et est fortement impliqué dans la motricité humaine.