Human arm redundancy: a new approach for the inverse kinematics problem.

The inverse kinematics (IK) problem addresses how both humans and robotic systems coordinate movement to resolve redundancy, as in the case of arm reaching where more degrees of freedom are available at the joint versus hand level. This work focuses on which coordinate frames best represent human movements, enabling the motor system to solve the IK problem in the presence of kinematic redundancies. We used a multi-dimensional sparse source separation method to derive sets of basis (or source) functions for both the task and joint spaces, with joint space represented by either absolute or anatomical joint angles. We assessed the similarities between joint and task sources in each of these joint representations, finding that the time-dependent profiles of the absolute reference frame's sources show greater similarity to corresponding sources in the task space. This result was found to be statistically significant. Our analysis suggests that the nervous system represents multi-joint arm movements using a limited number of basis functions, allowing for simple transformations between task and joint spaces. Additionally, joint space seems to be represented in an absolute reference frame to simplify the IK transformations, given redundancies. Further studies will assess this finding's generalizability and implications for neural control of movement.

Toward a unifying framework for the modeling and identification of motor primitives.

A large body of evidence suggests that human and animal movements, despite their apparent complexity and flexibility, are remarkably structured. Quantitative analyses of various classes of motor behaviors consistently identify spatial and temporal features that are invariant across movements. Such invariant features have been observed at different levels of organization in the motor system, including the electromyographic, kinematic, and kinetic levels, and are thought to reflect fixed modules-named motor primitives-that the brain uses to simplify the construction of movement. However, motor primitives across space, time, and organization levels are often described with ad-hoc mathematical models that tend to be domain-specific. This, in turn, generates the need to use model-specific algorithms for the identification of both the motor primitives and additional model parameters. The lack of a comprehensive framework complicates the comparison and interpretation of the results obtained across different domains and studies. In this work, we take the first steps toward addressing these issues, by introducing a unifying framework for the modeling and identification of qualitatively different classes of motor primitives. Specifically, we show that a single model, the anechoic mixture model, subsumes many popular classes of motor primitive models. Moreover, we exploit the flexibility of the anechoic mixture model to develop a new class of identification algorithms based on the Fourier-based Anechoic Demixing Algorithm (FADA). We validate our framework by identifying eight qualitatively different classes of motor primitives from both simulated and experimental data. We show that, compared to established model-specific algorithms for the identification of motor primitives, our flexible framework reaches overall comparable and sometimes superior reconstruction performance. The identification framework is publicly released as a MATLAB toolbox (FADA-T, https://tinyurl.com/compsens) to facilitate the identification and comparison of different motor primitive models.

Rigid soles improve balance in beam walking, but improvements do not persist with bare feet.

Maintaining balance while walking on a narrow beam is a challenging motor task. One important factor is that the foot's ability to exert torque on the support surface is limited by the beam width. Still, the feet serve as a critical interface between the body and the external environment, and it is unclear how the mechanical properties of the feet affect balance. This study examined how constraining the motion of the foot joints with rigid soles influenced balance performance when walking on a beam. We recorded whole-body kinematics of subjects with varying skill levels as they walked on a narrow beam with and without wearing flat, rigid soles on their feet. We computed changes in whole-body motion and angular momentum across the two conditions. Results showed that walking with rigid soles improved balance performance in both expert and novice subjects, but that improvements in balance performance with rigid soles did not affect or transfer to subsequent task performance with bare feet. The absence of any aftereffects suggested that the improved balance performance resulting from constraining the foot joints by a rigid sole was the result of a mechanical effect rather than a change in neural control. Although wearing rigid soles can be used to assist balance, there appears to be limited benefit for training or rehabilitation of balance ability.

Perceptual integration of kinematic components in the recognition of emotional facial expressions.

According to a long-standing hypothesis in motor control, complex body motion is organized in terms of movement primitives, reducing massively the dimensionality of the underlying control problems. For body movements, this low-dimensional organization has been convincingly demonstrated by the learning of low-dimensional representations from kinematic and EMG data. In contrast, the effective dimensionality of dynamic facial expressions is unknown, and dominant analysis approaches have been based on heuristically defined facial "action units," which reflect contributions of individual face muscles. We determined the effective dimensionality of dynamic facial expressions by learning of a low-dimensional model from 11 facial expressions. We found an amazingly low dimensionality with only two movement primitives being sufficient to simulate these dynamic expressions with high accuracy. This low dimensionality is confirmed statistically, by Bayesian model comparison of models with different numbers of primitives, and by a psychophysical experiment that demonstrates that expressions, simulated with only two primitives, are indistinguishable from natural ones. In addition, we find statistically optimal integration of the emotion information specified by these primitives in visual perception. Taken together, our results indicate that facial expressions might be controlled by a very small number of independent control units, permitting very low-dimensional parametrization of the associated facial expression.

Author Correction: Low-dimensional organization of angular momentum during walking on a narrow beam.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

Low-dimensional organization of angular momentum during walking on a narrow beam.

Walking on a beam is a challenging motor skill that requires the regulation of upright balance and stability. The difficulty in beam walking results from the reduced base of support compared to that afforded by flat ground. One strategy to maintain stability and hence avoid falling off the beam is to rotate the limb segments to control the body's angular momentum. The aim of this study was to examine the coordination of the angular momentum variations during beam walking. We recorded movement kinematics of participants walking on a narrow beam and computed the angular momentum contributions of the body segments with respect to three different axes. Results showed that, despite considerable variability in the movement kinematics, the angular momentum was characterized by a low-dimensional organization based on a small number of segmental coordination patterns. When the angular momentum was computed with respect to the beam axis, the largest fraction of its variation was accounted for by the trunk segment. This simple organization was robust and invariant across all participants. These findings support the hypothesis that control strategies for complex balancing tasks might be easier to understand by investigating angular momentum instead of the segmental kinematics.

Kinematics of the coordination of pointing during locomotion.

In natural motor behaviour arm movements, such as pointing or reaching, often need to be coordinated with locomotion. The underlying coordination patterns are largely unexplored, and require the integration of both rhythmic and discrete movement primitives. For the systematic and controlled study of such coordination patterns we have developed a paradigm that combines locomotion on a treadmill with time-controlled pointing to targets in the three-dimensional space, exploiting a virtual reality setup. Participants had to walk at a constant velocity on a treadmill. Synchronized with specific foot events, visual target stimuli were presented that appeared at different spatial locations in front of them. Participants were asked to reach these stimuli within a short time interval after a "go" signal. We analysed the variability patterns of the most relevant joint angles, as well as the time coupling between the time of pointing and different critical timing events in the foot movements. In addition, we applied a new technique for the extraction of movement primitives from kinematic data based on anechoic demixing. We found a modification of the walking pattern as consequence of the arm movement, as well as a modulation of the duration of the reaching movement in dependence of specific foot events. The extraction of kinematic movement primitives from the joint angle trajectories exploiting the new algorithm revealed the existence of two distinct main components accounting, respectively, for the rhythmic and discrete components of the coordinated movement pattern. Summarizing, our study shows a reciprocal pattern of influences between the coordination patterns of reaching and walking. This pattern might be explained by the dynamic interactions between central pattern generators that initiate rhythmic and discrete movements of the lower and upper limbs, and biomechanical factors such as the dynamic gait stability.

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

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

Model selection for the extraction of movement primitives.

A wide range of blind source separation methods have been used in motor control research for the extraction of movement primitives from EMG and kinematic data. Popular examples are principal component analysis (PCA), independent component analysis (ICA), anechoic demixing, and the time-varying synergy model (d'Avella and Tresch, 2002). However, choosing the parameters of these models, or indeed choosing the type of model, is often done in a heuristic fashion, driven by result expectations as much as by the data. We propose an objective criterion which allows to select the model type, number of primitives and the temporal smoothness prior. Our approach is based on a Laplace approximation to the posterior distribution of the parameters of a given blind source separation model, re-formulated as a Bayesian generative model. We first validate our criterion on ground truth data, showing that it performs at least as good as traditional model selection criteria [Bayesian information criterion, BIC (Schwarz, 1978) and the Akaike Information Criterion (AIC) (Akaike, 1974)]. Then, we analyze human gait data, finding that an anechoic mixture model with a temporal smoothness constraint on the sources can best account for the data.

Variant and invariant features characterizing natural and reverse whole-body pointing movements.

Previous investigations showed that kinematics and muscle activity associated with natural whole-body movements along the gravity direction present modular organizations encoding specific aspects relative to both the motor plans and the motor programmes underlying movement execution. It is, however, still unknown whether such modular structures characterize also the reverse movements, when the displacement of a large number of joints is required to take the whole body back to a standing initial posture. To study what motor patterns are conserved across the reversal of movement direction, principal component analysis and non-negative matrix factorization were therefore applied, respectively, to the time series describing the temporal evolution of the elevation angles associated with all the body links and to the electromyographic signals of both natural and reverse whole-body movements. Results revealed that elevation angles were highly co-varying in time and that despite some differences in the global parameters characterizing the different movements (indicating differences in high-level variable associated with the selected motor plans), the level of joint co-variation did not change across movement direction. In contrast, muscle organization of the forward whole-body pointing tasks was found to be different with respect to that characterizing the reverse movements. Such results agree with previous findings, according to which the central nervous system exploits, dependently on the direction of motion, different motor plans for the execution of whole-body movements. However, in addition, this study shows how such motor plans are translated into different muscle strategies that equivalently assure a high level of co-variation in the joint 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.

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

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

Manifold reaching paradigm: how do we handle target redundancy?

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

The motor system plays the violin: a musical metaphor inferred from the oscillatory activity of the α-motoneuron pools during locomotion.

Despite substantial advances in the field, particularly resulting from physiological studies in animals, the neural mechanisms underlying the generation of many motor behaviors in humans remain unclear. A recent study (Cappellini G et al. J Neurophysiol 104: 3064-3073, 2010) sheds more light on this topic. Like the string of a violin, the α-motoneuron pools in the spinal cord during locomotion show continuous and oscillatory patterns of activation. In this report, the implications and relevance of this finding are discussed in a general framework that includes neurophysiology, optimal control theory, and robotics.

Equilibrium constraints do not affect the timing of muscular synergies during the initiation of a whole body reaching movement.

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.