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

Although premovement beta-band event-related desynchronization (ß-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 ß-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 ß-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 ß-ERD. Indeed, linear mixed models showed that estimated action cost predicted variations of ß-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 ß-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 support the existence of an idiosyncratic, cognitive cost of time that underlies the invigoration of basic isometric reaching movements.NEW & NOTEWORTHY Movement vigor is generally thought to result from a trade-off between time and motor costs. However, it remains unclear whether the time cost only modulates vigor around some nominal value explained by a minimal motor cost or whether it determines movement invigoration more broadly. Here, we present an original paradigm allowing us to neutralize the cost of movement and provide new evidence that a cost of time must underlie the invigoration of isometric reaching movements.

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.

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.

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.

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.

Why Don't We Move Slower? The Value of Time in the Neural Control of Action.

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. SIGNIFICANCE STATEMENT: Movement time is a fundamental characteristic of neural motor control, but the principles underlying its formation remain little known. This work addresses that question within the inverse optimal control framework where the challenge is to uncover what optimality criterion underlies a system's behavior. Here we rely on the "cost of time" theory that finds its roots into the brain's tendency to discount the actual value of future reward. It asserts that the time elapsed until action completion entails a cost, thereby making slow moves nonoptimal. By means of a thorough theoretical analysis, the present article shows how to sample the infinitesimal values of the time cost without prior assumption about its hypothetical nature and emphasizes its sigmoidal shape for reaching.

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.

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.

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.

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.

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).

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.

Human babies start to walk on their own when they are about one year old, but before that, they can move their legs to produce movements called 'stepping', where they take steps when held over a surface; and kicking, where they kick in the air when lying on their backs. These two behaviors are known as 'locomotor precursors' and can be observed from birth. Previous studies suggest that infants produce these movements by activating a small number of motor primitives, different modules in the nervous system ­ each activating a combination of muscles to produce a movement. However, babies and toddlers exhibit a lot of variability when they move, which is a hallmark of typical development that furthers exploring and learning. So far, it has been unclear whether such differences arise as soon as babies are born and if so, how a small number of motor primitives could result in this variability. Hinnekens et al. hypothesized that the great variety of movements in infants can be generated from a small set of motor primitives, when several cycles of flexing and extending the legs are considered. To test their hypothesis, the researchers first needed to establish how and when infants generate this variability of movement. To do so, they used electromyography to record the leg muscle activity of 18 babies during either movement resulting in a body displacement (locomotor movement) or rhythmic movement. These measurements were taken at either two or three timepoints between birth and the onset of walking. Next, the scientists used a state-of-the-art machine learning approach to model the neural basis underlying these recordings, which showed that newborns generate a lot of movement variability, but they do so by activating a small number of motor primitives, which they can combine in different ways. Hinnekens et al. also show that as babies get older, the number of motor primitives increases while the variety of movements decreases due to a more steady activation of each motor primitive. Cerebral plasticity is maximal during the first year of life, and infants can regularly learn new motor skills, each leading to the ability to perform more movements. Motor variability is believed to play an important role in this learning process and is known to be decreased in atypical development. As such, examining motor variability may be a promising tool to identify neurodevelopmental delays at younger ages.

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.

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.

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.

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.

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.