Enrico Chiovetto

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.

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.

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.

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.

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.

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.

Joint torque analysis of push recovery motions during human walking

Most of their lifetime humans can recover from disturbances during walking motions very well. Our assumption is that to recover from disturbances during walking requires higher internal torques in the joints than motions without disturbances. To measure the internal joint torques in experiments is complicated and expensive. In this work we propose an optimality based simulation environment that allows to determine the internal torques in the joints of a human during disturbed walking motions. The human is represented by a two dimensional (2D) rigid multi-body model consisting of 14 segments controlled by torques in 13 rotational joints resulting in 16 degrees of freedom (DoF). The disturbance is modeled as external force acting on the model. A least-squares optimal control problem that minimizes the distance between the joint angles of the model and joint angles gained from motion capture experiments, while satisfying the dynamics and constraints of the human model, is set up. The analysis of perturbed and unperturbed walking motions shows that the torques in the joints vary according to the strength and duration of the disturbance. The calculation of the internal joint torques is important for the development of new control strategies or set up of humanoid robots and prostheses. It can also be used in the context of sport sciences to improve training or therapies.

On the Origins of Modularity in Motor Control

The control of movement is highly complex because of the biomechanical redundancy of the musculoskeletal system ([Bernstein, 1967][1]). 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

MODULATION OF ANTICIPATORY POSTURAL ACTIVITY FOR MULTIPLE CONDITIONS OF A WHOLE-BODY POINTING TASK

This is a study on associated postural activities during the anticipatory segments of a multijoint movement. Several previous studies have shown that they are task dependant. The previous studies, however, have mostly been limited in demonstrating the presence of modulation for one task condition, that is, one aspect such as the distance of the target or the direction of reaching. Real-life activities like whole-body pointing, however, can vary in several ways. How specific is the adaptation of the postural activities for the diverse possibilities of a whole-body pointing task? We used a classification paradigm to answer this question. We examined the anticipatory postural electromyograms for four different types of whole-body pointing tasks. The presence of task-dependent modulations in these signals was probed by performing four-way classification tests using a support vector machine (SVM). The SVM was able to achieve significantly higher than chance performance in correctly predicting the movements at hand (Chance performance 25%). Using only anticipatory postural muscle activity, the correct movement at hand was predicted with a mean rate of 62%. Because this is 37% above chance performance, it suggests the presence of postural modulation for diverse conditions. The anticipatory activities consisted of both activations and deactivations. Movement prediction with the use of the activating muscles was significantly better than that obtained with the deactivating muscles. This suggests that more specific modulations for the movement at hand take place through activation, whereas the deactivation is more general. The study introduces a new method for investigating adaptations in motor control. It also sheds new light on the quantity and quality of information available in the feedforward segments of a voluntary multijoint motor activity.

Bayesian Approaches for Learning of Primitive-Based Compact Representations of Complex Human Activities

Human full-body activities, such as choreographed dances, are comprised of sequences of individual actions. Research in motor control shows that such individual actions can be approximated by superpositions of simplified elements, called movement primitives. Such primitives can be employed to model complex coordinated movements, as occurring in martial arts or dance. In this chapter, we will briefly outline several biologically-inspired definitions of movement primitives and will discuss a new algorithm that unifies many existing models and which identifies such primitives with higher accuracy than alternative unsupervised learning techniques. We combine this algorithm with methods from Bayesian inference to optimize the complexity of the learned models and to identify automatically the best generative model underlying the identification of such primitives. We also discuss efficient probabilistic methods for the automatic segmentation of action sequences. The developed unsupervised segmentation method is based on Bayesian binning, an algorithm that models a longer data stream by the concatenation of an optimal number of segments, at the same time estimating the optimal temporal boundaries between those segments. Applying this algorithm to motion capture data from a TaeKwonDo form, and comparing the automatically generated segmentation results with human psychophysical data, we found a good agreement between automatically generated segmentations and human performance. Furthermore, the segments agree with the minimum jerk hypothesis about human movement [32]. These results suggest that a similar approach might be useful for the decomposition of dances into primitive-like movement components, providing a new approach for the derivation of compressed descriptions of dances that is based on principles from biological motor control.