During evolution, living systems, actively interacting with their environment, developed the ability, through sensorimotor contingencies, to construct functional spaces shaping their perception and their movements. These geometries were modularly embedded in specific functional neuro-architectures. In particular, human movements were shown to obey several empirical laws, such as the 2/3 power law, isochrony, or jerk minimization principles, which constrain and adapt motor planning and execution. Outstandingly, such laws can be deduced from a combination of Euclidean, affine, and equi-affine geometries, whose neural correlates have been partly detected in several brain areas including the cerebellum and the basal ganglia. Reviving Pellionisz and Llinas general hypothesis regarding the cerebrum and the cerebellum as geometric machines, we speculate that the cerebellum should be involved in implementing and/or selecting task-specific geometries for motor and cognitive skills. More precisely, the cerebellum is assumed to compute forward internal models to help specific cortical and subcortical regions to select appropriate geometries among, at least, Euclidean and affine geometries. We emphasize that the geometrical role of the cerebellum deserves a renewal of interest, which may provide a better understanding of its specific contributions to motor and associative (cognitive) functions.
In 1954, Penfield and Jasper's findings based on electric stimulation of epileptic patients led them to hypothesize that a sensory representation of the body should be found in the precuneus. They termed this representation the "supplementary sensory" area and emphasized that the exact form of this homunculus could not be specified on the basis of their results. In the decades that followed, their prediction was neglected. The precuneus was found to be involved in numerous motor, cognitive and visual processes, but no work was done on its somatotopic organization. Here, we used a periodic experimental design in which 16 human subjects (eight women) moved 20 body parts to investigate the possible body part topography of the precuneus. We found an anterior-to-posterior, dorsal-to-ventral, toes-to-tongue gradient in a mirror orientation to the SMA. When inspecting body-part-specific functional connectivity, we found differential connectivity patterns for the different body parts to the primary and secondary motor areas and parietal and visual areas, and a shared connectivity to the extrastriate body area, another topographically organized area. We suggest that a whole-body gradient can be found in the precuneus and is connected to multiple brain areas with different connectivity for different body parts. Its exact role and relations to the other known functions of the precuneus such as self-processing, motor imagery, reaching, visuomotor and other body-mind functions should be investigated.
A complex action can be described as the composition of a set of elementary movements. While both kinematic and dynamic elements have been proposed to compose complex actions, the structure of movement decomposition and its neural representation remain unknown. Here, we examined movement decomposition by modeling the temporal dynamics of neural populations in the primary motor cortex of macaque monkeys performing forelimb reaching movements. Using a hidden Markov model, we found that global transitions in the neural population activity are associated with a consistent segmentation of the behavioral output into acceleration and deceleration epochs with directional selectivity. Single cells exhibited modulation of firing rates between the kinematic epochs, with abrupt changes in spiking activity timed with the identified transitions. These results reveal distinct encoding of acceleration and deceleration phases at the level of M1, and point to a specific pattern of movement decomposition that arises from the underlying neural activity. A similar approach can be used to probe the structure of movement decomposition in different brain regions, possibly controlling different temporal scales, to reveal the hierarchical structure of movement composition.
The complex motion abilities of the Octopus vulgaris have been an intriguing research topic for biologists and roboticists alike. Various studies have been conducted on the underlying control architectures employed by these high dimensional biological organisms. Researchers have attempted to replicate these architectures on robotic systems. Contrary to previous approaches, this study focuses on a robotic system, which is only morphologically similar to the Octopus vulgaris, and how it would behave under different control policies. This sheds light on the underlying optimality principles that these biological systems employ. Open loop control policies are obtained through a trajectory optimization method on a learned forward dynamic model. The motion patterns emerging from variations in morphology and environment were then derived to study the role of the body and environment. Results show that for the specific case of dynamic reaching with a soft appendage, the invariance in motion profile is a fundamental constraint imposed by the morphology and environment, independent from the controller. This suggests how morphological design can simplify stable control even for highly dimensional nonlinear dynamical systems and can provide insights into design of new soft robotic mechanisms.
The law of intersegmental coordination (Borghese et al. 1996) may be altered in pathological conditions. Here we investigated the contribution of the basal ganglia (BG) and the cerebellum to lower limb intersegmental coordination by inspecting the plane's orientation and other parameters pertinent to this law in patients with idiopathic Parkinson's disease (PD) or cerebellar ataxia (CA). We also applied a mathematical model that successfully accounts for the intersegmental law of coordination observed in control subjects (Barliya et al. 2009). In the present study. we compared the planarity index (PI), covariation plane (CVP) orientation, and CVP orientation predicted by the model in 11 PD patients, 8 CA patients, and two groups of healthy subjects matched for age, height. weight, and gender to each patient group (Ctrl_PD and Ctrl_CA). Controls were instructed to alter their gait speed to match those of their respective patient group. PD patients were examined after overnight withdrawal of anti-parkinsonian medications (PD-off-med) and then on medication (PD-on-med). PI was above 96% in all gait conditions in all groups suggesting that the law of intersegmental coordination is preserved in both BG and cerebellar pathology. However, the measured and predicted CVP orientations rotated in PD-on-med and PD-off-med compared with Ctrl_PD and in CA vs. Ctrl_CA. These rotations caused by PD and CA were in opposite directions suggesting differences in the roles of the BG and cerebellum in intersegmental coordination during human locomotion.NEW & NOTEWORTHY Kinematic and muscular synergies may have a role in overcoming motor redundancies, which may be reflected in intersegmental covariation. Basal ganglia and cerebellar networks were suggested to be involved in crafting and modulating synergies. We thus compared intersegmental coordination in Parkinson's disease and cerebellar disease patients and found opposite effects in some aspects. Further research integrating muscle activities as well as biomechanical and neural control modeling are needed to account for these findings.
Film theorists and practitioners suggest that motion can be manipulated in movie scenes to elicit emotional responses in viewers. However, our understanding of the role of motion in emotion perception remains limited. On the one hand, movies continuously depict local motion-movements of objects and humans, which are crucial for generating emotional responses. Movie scenes also frequently portray global motion, mainly induced by large camera movements, global motion being yet another source of information used by the brain during natural vision. Here we used functional MRI to elucidate the contributions of local and global motion to emotion perception during movie viewing. Subjects observed long (1 min) movie segments depicting emotional or neutral content. Brain activity in areas that showed preferential responses to emotional content was strongly linked over time with frame-wide variations in global motion, and to a lesser extent with local motion information. Similarly, stronger responses to emotional content were recorded within regions of interest whose activity was attuned to global and local motion over time. Since global motion fields are experienced during self-motion, we suggest that camera movements may induce illusory self-motion cues in viewers that interact with the movie's narrative and with other emotional cues in generating affective responses.
Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685-690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.
When subjects are intentionally preparing a curved trajectory, they are engaged in a time-consuming trajectory planning process that is separate from target selection. To investigate the construction of such a plan, we examined the effect of artificially shortening preparation time on the performance of intentionally curved trajectories using the Timed Response task that enforces initiation of movements prematurely. Fifteen subjects performed obstacle avoidance movements toward one of four targets that were presented 25 or 350 ms before the "go" signal, imposing short and long preparation time conditions with mean values of 170 ms and 493 ms, respectively. While trajectories with short preparation times showed target specificity at their onset, they were significantly more variable and showed larger angular deviations from the lines connecting their initial position and the target, compared to the trajectories with long preparation times. Importantly, the trajectories of the short preparation time movements still reached their end-point targets accurately, with comparable movement durations. We hypothesize that success in the short preparation time condition is a result of an online control mechanism that allows further refinement of the plan during its execution and study this control mechanism with a novel trajectory analysis approach using minimum jerk optimization and geometrical modeling approaches. Results show a later agreement of the short preparation time trajectories with the optimal minimum jerk trajectory, accompanied by a later initiation of a parabolic segment. Both observations are consistent with the existence of an online trajectory planning process. Our results suggest that when preparation time is not sufficiently long, subjects execute a more variable and less optimally prepared initial trajectory and exploit online control mechanisms to refine their actions on the fly.
Here we review recent studies of the cortical circuits subserving the control of posture and movement. This topic is addressed from neurophysiological and evolutionary perspectives describing recent advancements achieved through experimental studies in humans and non-human primates. We also describe current debates and controversies concerning motor mapping within the motor cortex and the different computational approaches aimed at resolving the mystery around motor representations and computations. In recent years there is growing interest in the possibly modular organization of motor representations and dynamical processes and the potential of such studies to provide new clues into motor information processing. Hence this review focuses on motor modularity, highlighting the new research directions inspired by empirical findings and theoretical models developed within the last several years.
In human motor control studies, end-effector (e.g., hand) trajectories have been successfully modeled using optimization principles. Yet, it remains unclear how such trajectories are updated when the end-effector or task goals are perturbed. Here, we present an approach to human and robotic task-level trajectory planning and modification using geometrical invariance and optimization, allowing to adapt learned movements to a priori unknown boundary conditions. The optimization criterion represents a tradeoff between smoothness (minimum jerk) and accuracy (jerk-accuracy model). We show that planning maximally smooth movements allows recovery from perturbations by superimposing specific affine orbits on maximally smooth preplanned trajectories. The generated trajectories are compared with those resulting from other recent approaches used in robotics. Finally, we discuss conditions for affine invariance of maximally smooth task-space trajectories. Possible applications of this study to both human motor control and robotics research studies are discussed.
Introduction: This review on micrographia aims to draw the clinician's attention to non-Parkinsonian etiologies, provide clues to differential diagnosis, and summarize current knowledge on the phenomenology, etiology, and mechanisms underlying micrographia. Methods: A systematic review of the existing literature was performed. Results: Micrographia, namely small sized handwriting has long been attributed to Parkinson's disease. However, it has often been observed as part of the clinical picture of additional neurodegenerative disorders, sometimes antedating the motor signs, or following focal basal ganglia lesions without any accompanying parkinsonism, suggesting that bradykinesia and rigidity are not sine-qua-non for the development of this phenomenon. Therefore, micrographia in a patient with no signs of parkinsonism may prompt the clinician to perform imaging in order to exclude a focal basal ganglia lesion. Dopaminergic etiology in this and other cases is doubtful, since levodopa ameliorates letter stroke size only partially, and only in some patients. Parkinsonian handwriting is often characterized by lack of fluency, slowness, and less frequently by micrographia. Deviations from kinematic laws of motion that govern normal movement, including the lack of movement smoothness and inability to scale movement amplitude to the desired size, may reflect impairments in motion planning, possible loss of automaticity and reduced movement vigor. Conclusions: The etiology, neuroanatomy, mechanisms and models of micrographia are discussed. Dysfunction of the basal ganglia circuitry induced by neurodegeneration or disruption by focal damage give rise to micrographia. (C) 2016 Elsevier Ltd. All rights reserved.
The default mode network (DMN) has been implicated in an array of social-cognitive functions, including self-referential processing, theory of mind, and mentalizing. Yet, the properties of the external stimuli that elicit DMN activity in relation to these domains remain unknown. Previous studies suggested that motion kinematics is utilized by the brain for social-cognitive processing. Here, we used functional MRI to examine whether the DMN is sensitive to parametric manipulations of observed motion kinematics. Preferential responses within core DMN structures differentiating non-biological from biological kinematics were observed for the motion of a realistically looking, human-like avatar, but not for an abstract object devoid of human form. Differences in connectivity patterns during the observation of biological versus non-biological kinematics were additionally observed. Finally, the results additionally suggest that the DMN is coupled more strongly with key nodes in the action observation network, namely the STS and the SMA, when the observed motion depicts human rather than abstract form. These findings are the first to implicate the DMN in the perception of biological motion. They may reflect the type of information used by the DMN in social-cognitive processing.
The bend propagation involved in the stereotypical reaching movement of the octopus arm has been extensively studied. While these studies have analyzed the kinematics of bend propagation along the arm during its extension, possible length changes have been ignored. Here, the elongation profiles of the reaching movements of Octopus vulgaris were assessed using three-dimensional reconstructions. The analysis revealed that, in addition to bend propagation, arm extension movements involve elongation of the proximal part of the arm, i.e., the section from the base of the arm to the propagating bend. The elongations are quite substantial and highly variable, ranging from an average strain along the arm of -0.12 (i.e. shortening) up to 1.8 at the end of the movement (0.57 +/- 0.41, n = 64 movements, four animals). Less variability was discovered in an additional set of experiments on reaching movements (0.64 +/- 0.28, n = 30 movements, two animals), where target and octopus positions were kept more stationary. Visual observation and subsequent kinematic analysis suggest that the reaching movements can be broadly segregated into two groups. The first group involves bend propagation beginning at the base of the arm and propagating towards the arm tip. In the second, the bend is formed or present more distally and reaching is achieved mainly by elongation and straightening of the segment proximal to the bend. Only in the second type of movements is elongation significantly positively correlated with the distance of the bend from the target. Wesuggest that reaching towards a target is generated by a combination of both propagation of a bend along the arm and arm elongation. These two motor primitives may be combined to create a broad spectrum of reaching movements. The dynamical model, which recapitulates the biomechanics of the octopus muscular hydrostatic arm, suggests that achieving the observed elongation requires an extremely low ratio of longitudinal to transverse mus
To cope with the exceptional computational complexity that is involved in the control of its hyper-redundant arms , the octopus has adopted unique motor control strategies in which the central brain activates rather autonomous motor programs in the elaborated peripheral nervous system of the arms [2, 3]. How octopuses coordinate their eight long and flexible arms in locomotion is still unknown. Here, we present the first detailed kinematic analysis of octopus arm coordination in crawling. The results are surprising in several respects: (1) despite its bilaterally symmetrical body, the octopus can crawl in any direction relative to its body orientation; (2) body and crawling orientation are monotonically and independently controlled; and (3) contrasting known animal locomotion, octopus crawling lacks any apparent rhythmical patterns in limb coordination, suggesting a unique non-rhythmical output of the octopus central controller. We show that this uncommon maneuverability is derived from the radial symmetry of the arms around the body and the simple pushing-by-elongation mechanism by which the arms create the crawling thrust. These two together enable a mechanism whereby the central controller chooses in a moment-to-moment fashion which arms to recruit for pushing the body in an instantaneous direction. Our findings suggest that the soft molluscan body has affected in an embodied way [4, 5] the emergence of the adaptive motor behavior of the octopus.
The two-thirds power law, nu = gamma kappa(-1/3), expresses a robust local relationship between the geometrical and temporal aspects of human movement, represented by curvature kappa and speed nu, with a piecewise constant gamma. This law is equivalent to moving at a constant equi-affine speed and thus constitutes an important example of motor invariance. Whether this kinematic regularity reflects central planning or peripheral biomechanical effects has been strongly debated. Motor imagery, i.e., forming mental images of a motor action, allows unique access to the temporal structure of motor planning. Earlier studies have shown that imagined discrete movements obey Fitts's law and their durations are well correlated with those of actual movements. Hence, it is natural to examine whether the temporal properties of continuous imagined movements comply with the two-thirds power law. A novel experimental paradigm for recording sparse imagery data from a continuous cyclic tracing task was developed. Using the likelihood ratio test, we concluded that for most subjects the distributions of the marked positions describing the imagined trajectory were significantly better explained by the two-thirds power law than by a constant Euclidean speed or by two other power law models. With nonlinear regression, the beta parameter values in a generalized power law, nu = gamma kappa(-beta), were inferred from the marked position records. This resulted in highly variable yet mostly positive beta values. Our results imply that imagined trajectories do follow the two-thirds power law. Our findings therefore support the conclusion that the coupling between velocity and curvature originates in centrally represented motion planning.
Topographic organization is one of the main principles of organization in the human brain. Specifically, whole-brain topographic mapping using spectral analysis is responsible for one of the greatest advances in vision research. Thus, it is intriguing that although topography is a key feature also in the motor system, whole-body somatosensory-motor mapping using spectral analysis has not been conducted in humans outside M1/SMA. Here, using this method, we were able to map a homunculus in the globus pallidus, a key target area for deep brain stimulation, which has not been mapped noninvasively or in healthy subjects. The analysis clarifies contradictory and partial results regarding somatotopy in the caudal-cingulate zone and rostral-cingulate zone in the medial wall and in the putamen. Most of the results were confirmed at the single-subject level and were found to be compatible with results from animal studies. Using multivoxel pattern analysis, we could predict movements of individual body parts in these homunculi, thus confirming that they contain somatotopic information. Using functional connectivity, we demonstrate interhemispheric functional somatotopic connectivity of these homunculi, such that the somatotopy in one hemisphere could have been found given the connectivity pattern of the corresponding regions of interest in the other hemisphere. When inspecting the somatotopic and nonsomatotopic connectivity patterns, a similarity index indicated that the pattern of connected and nonconnected regions of interest across different homunculi is similar for different body parts and hemispheres. The results show that topographical gradients are even more widespread than previously assumed in the somatosensory-motor system. Spectral analysis can thus potentially serve as a gold standard for defining somatosensory-motor system areas for basic research and clinical applications.
The short-lasting attenuation of brain oscillations is termed event-related desynchronization (ERD). It is frequently found in the alpha and beta bands in humans during generation, observation, and imagery of movement and is considered to reflect cortical motor activity and action-perception coupling. The shared information driving ERD in all these motor-related behaviors is unknown. We investigated whether particular laws governing production and perception of curved movement may account for the attenuation of alpha and beta rhythms. Human movement appears to be governed by relatively few kinematic laws of motion. One dominant law in biological motion kinematics is the 2/3 power law (PL), which imposes a strong dependency of movement speed on curvature and is prominent in action-perception coupling. Here we directly examined whether the 2/3 PL elicits ERD during motion observation by characterizing the spatiotemporal signature of ERD. ERDs were measured while human subjects observed a cloud of dots moving along elliptical trajectories either complying with or violating the 2/3 PL. We found that ERD within both frequency bands was consistently stronger, arose faster, and was more widespread while observing motion obeying the 2/3 PL. An activity pattern showing clear 2/3 PL preference and lying within the alpha band was observed exclusively above central motor areas, whereas 2/3 PL preference in the beta band was observed in additional prefrontal-central cortical sites. Our findings reveal that compliance with the 2/3 PL is sufficient to elicit a selective ERD response in the human brain.
There is growing experimental evidence that the engagement of different brain areas in a given motor task may change with practice, although the specific brain activity patterns underlying different stages of learning, as defined by kinematic or dynamic performance indices, are not well understood. Here we studied the change in activation in motor areas during practice on sequences of handwriting-like trajectories, connecting four target points on a digitizing table "as rapidly and as accurately as possible" while lying inside an fMRI scanner. Analysis of the subjects' pooled kinematic and imaging data, acquired at the beginning, middle, and end of the training period, revealed no correlation between the amount of activation in the contralateral M1, PM (dorsal and ventral), supplementary motor area (SMA), preSMA, and Posterior Parietal Cortex (PPC) and the amount of practice per-se. Single trial analysis has revealed that the correlation between the amount of activation in the contralateral M1 and trial mean velocity was partially modulated by performance gains related effects, such as increased hand motion smoothness. Furthermore, it was found that the amount of activation in the contralateral preSMA increased when subjects shifted from generating straight point-to-point trajectories to their spatiotemporal concatenation into a smooth, curved trajectory. Altogether, our results indicate that the amount of activation in the contralateral M1, PMd, and preSMA during the learning of movement sequences is correlated with performance gains and that high level motion features (e.g., motion smoothness) may modulate, or even mask correlations between activity changes and low-level motion attributes (e.g., trial mean velocity).
How does the human motor system encode our incredibly diverse motor repertoire in an efficient manner? One possible way of encoding movements efficiently is to represent them according to their shape/trajectory without regard to their size, by using neural populations that are invariant across scale. To examine this hypothesis, we recorded movement kinematics and functional magnetic resonance imaging (fMRI) while subjects wrote three letters in two different scales. A classification algorithm was trained to identify each letter according to its associated voxel-by-voxel response pattern in each of several motor areas. Accurate decoding of letter identity was possible in primary motor cortex (M1) and anterior intraparietal sulcus (alPS) regardless of the letter's scale. These results reveal that large, distributed neural populations in human M1 and alPS encode complex handwriting movements regardless of their particular dynamics and kinematics, in a scaler-invariant manner.
Two empathy-related processes were recently distinguished neuroscientifically: automatic embodied-simulation (ES) based on visceromotor representation of another's affective state via cingulo-insulary circuit, and emotional sharing relying on cognitive 'theory of mind' (ToM) via prefrontal-temporoparietal circuit. Evidence that these regions are not only activated but also function as networks during empathic experience has yet to been shown. Employing a novel approach by analyzing fMRI fluctuations of network cohesion while viewing films portraying personal loss, this study demonstrates increased connectivity during empathic engagement (probed by behavioral and parasympathetic indices) both within these circuits, and between them and a set of limbic regions. Notably, this effect was context-dependent: when witnessing as a determined-loss presented as a future event, the ToM and ToM-limbic cohesion positively correlated with state-and empathy indices. During the dramatic peak of this condition, the ToM cohesion was positively correlated with the trait-empathy index of personal distress. However, when the loss was presented as a probabilistic real-time occurrence, ToM cohesion negatively correlated with state-empathy index, which positively correlated with ES-limbic cohesion. In this case, it was the ES-limbic cohesion during the emotional peak which was correlated with personal distress scores. The findings indicate a dichotomy between regulated empathy toward determined-loss and vicarious empathy toward a real-time occurrence.
The two-thirds power law, postulating an inverse local relation between the velocity and cubed root of curvature of planar trajectories, is a long-established simplifying principle of human hand movements. In perception, the motion of a dot along a planar elliptical path appears most uniform for speed profiles closer to those predicted by the power law than to constant Euclidean speed, a kinetic-visual illusion. Mathematically, complying with this law is equivalent to moving at constant planar equi-affine speed, while unconstrained three-dimensional drawing movements generally follow constant spatial equi-affine speed. Here we test the generalization of this illusion to visual perception of spatial motion for a dot moving along five differently shaped paths, using stereoscopic projection. The movements appeared most uniform for speed profiles closer to constant spatial equi-affine speed than to constant Euclidean speed, with path torsion (i.e., local deviation from planarity) directly affecting the speed profiles perceived as most uniform, as predicted for constant spatial equi-affine speed. This demonstrates the dominance of equi-affine geometry in spatial motion perception. However, constant equi-affine speed did not fully account for the variability among the speed profiles selected as most uniform for different shapes. Moreover, in a followup experiment, we found that viewing distance affected the speed profile reported as most uniform for the extensively studied planar elliptical motion paths. These findings provide evidence for the critical role of equi-affine geometry in spatial motion perception and contribute to the mounting evidence for the role of non-Euclidean geometries in motion perception and production.
This article discusses the compositional structure of hand movements by analyzing and modeling neural and behavioral data obtained from experiments where a monkey (Macaca fascicularis) performed scribbling movements induced by a search task. Using geometrically based approaches to movement segmentation, it is shown that the hand trajectories are composed of elementary segments that are primarily parabolic in shape. The segments could be categorized into a small number of classes on the basis of decreasing intra-class variance over the course of training. A separate classification of the neural data employing a hidden Markov model showed a coincidence of the neural states with the behavioral categories. An additional analysis of both types of data by a data mining method provided evidence that the neural activity patterns underlying the behavioral primitives were formed by sets of specific and precise spike patterns. A geometric description of the movement trajectories, together with precise neural timing data indicates a compositional variant of a realistic synfire chain model. This model reproduces the typical shapes and temporal properties of the trajectories; hence the structure and composition of the primitives may reflect meaningful behavior.
The endpoint trajectories of human movements fulfill characteristic power laws linking velocity and curvature. The parameters of these power laws typically vary between different segments of longer action sequences. These parameters might thus be exploited for the unsupervised segmentation of actions into movement primitives. For the example of sign language we investigate whether such segments can be identified by Bayesian binning (BB), using a Gaussian observation model whose mean has a polynomial time dependence. We show that this method yields good segmentation and correctly models ground truth kinematics composed of consecutive segments derived from wrist trajectories recorded from users of Israeli Sign Language (ISL). Importantly, polynomial orders between 3 and 5 yield an optimal trade-off between complexity and accuracy of the trajectory approximation, in accordance with the minimum acceleration and minimum jerk models. Comparing the orders of the polynomials best approximating natural kinematics against those needed to fit the power law ground truth data suggests that kinematic properties not compatible with power laws are also not adequately represented by low order polynomials and require higher order polynomials for a good approximation.
The octopus arm is a muscular hydrostat and due to its deformable and highly flexible structure it is capable of a rich repertoire of motor behaviors. Its motor control system uses planning principles and control strategies unique to muscular hydrostats. We previously reconstructed a data set of octopus arm movements from records of natural movements using a sequence of 3D curves describing the virtual backbone of arm configurations. Here we describe a novel representation of octopus arm movements in which a movement is characterized by a pair of surfaces that represent the curvature and torsion values of points along the arm as a function of time. This representation allowed us to explore whether the movements are built up of elementary kinematic units by decomposing each surface into a weighted combination of 2D Gaussian functions. The resulting Gaussian functions can be considered as motion primitives at the kinematic level of octopus arm movements. These can be used to examine underlying principles of movement generation. Here we used combination of such kinematic primitives to decompose different octopus arm movements and characterize several movement prototypes according to their composition. The representation and methodology can be applied to the movement of any organ which can be modeled by means of a continuous 3D curve.
The seemingly simple everyday actions of moving limb and body to accomplish a motor task or interact with the environment are incredibly complex. To reach for a target we first need to sense the target's position with respect to an external coordinate system; we then need to plan a limb trajectory which is executed by issuing an appropriate series of neural commands to the muscles. These, in turn, exert appropriate forces and torques on the joints leading to the desired movement of the arm. Here we review some of the earlier work as well as more recent studies on the control of human movement, focusing on behavioral and modeling studies dealing with task space and joint-space movement planning. At the task level, we describe studies investigating trajectory planning and inverse kinematics problems during point-to-point reaching movements as well as two-dimensional (2D) and three-dimensional (3D) drawing movements. We discuss models dealing with the two-thirds power law, particularly differential geometrical approaches dealing with the relation between path geometry and movement velocity. We also discuss optimization principles such as the minimum-jerk model and the isochrony principle for point-to-point and curved movements. We next deal with joint-space movement planning and generation, discussing the inverse kinematics problem and common solutions to the problems of kinematic redundancy. We address the question of which reference frames are used by the nervous system and review studies examining the employment of kinematic constraints such as Donders' and Listing's laws. We also discuss optimization approaches based on Riemannian geometry. One principle of motor coordination during human locomotion emerging from this body of work is the intersegmental law of coordination. However, the nature of the coordinate systems underlying motion planning remains of interest as they are related to the principles governing the control of human arm movements. (C) 2012 Elsevi
Here, we examine how different emotions-happiness, fear, sadness and anger-affect the kinematics of locomotion. We focus on a compact representation of locomotion properties using the intersegmental law of coordination (Borghese et al. in J Physiol 494(3):863-879, 1996), which states that, during the gait cycle of human locomotion, the elevation angles of the thigh, shank and foot do not evolve independently of each other but form a planar pattern of co-variation. This phenomenon is highly robust and has been extensively studied. The orientation of the plane has been correlated with changes in the speed of locomotion and with reduction in energy expenditure as speed increases. An analytical model explaining the conditions underlying the emergence of this plane and predicting its orientation reveals that it suffices to examine the amplitudes of the elevation angles of the different segments along with the phase shifts between them (Barliya et al. in Exp Brain Res 193:371-385, 2009). We thus investigated the influence of different emotions on the parameters directly determining the orientation of the intersegmental plane and on the angular rotation profiles of the leg segments, examining both the effect of changes in walking speed and effects independent of speed. Subjects were professional actors and na <ve subjects with no training in acting. As expected, emotions were found to strongly affect the kinematics of locomotion, particularly walking speed. The intersegmental coordination patterns revealed that emotional expression caused additional modifications to the locomotion patterns that could not be explained solely by a change in speed. For all emotions except sadness, the amplitude of thigh elevation angles changed from those in neutral locomotion. The intersegmental plane was also differently oriented, especially during anger. We suggest that, while speed is the dominant variable allowing discrimination between different emotional gaits, emotion can be relia
A crucial attribute in movement encoding is an adequate balance between suppression of unwanted muscles and activation of required ones. We studied movement encoding across the primary motor cortex (M1) and supplementary motor area (SMA) by inspecting the positive and negative blood oxygenation level-dependent (BOLD) signals in these regions. Using periodic and event-related experiments incorporating the bilateral/axial movements of 20 body parts, we report detailed mototopic imaging maps in M1 and SMA. These maps were obtained using phase-locked analysis. In addition to the positive BOLD, significant negative BOLD was detected in M1 but not in the SMA. The negative BOLD spatial pattern was neither located at the ipsilateral somatotopic location nor randomly distributed. Rather, it was organized somatotopically across the entire homunculus and inversely to the positive BOLD, creating a negative BOLD homunculus. The neuronal source of negative BOLD is unclear. M1 provides a unique system to test whether the origin of negative BOLD is neuronal, because different arteries supply blood to different regions in the homunculus, ruling out blood-stealing explanations. Finally, multivoxel pattern analysis showed that positive BOLD in M1 and SMA and negative BOLD in M1 contain somatotopic information, enabling prediction of the moving body part from inside and outside its somatotopic location. We suggest that the neuronal processes underlying negative BOLD participate in somatotopic encoding in M1 but not in the SMA. This dissociation may emerge because of differences in the activity of these motor areas associated with movement suppression.
Ample evidence exists for coupling between action and perception in neurologically healthy individuals, yet the precise nature of the internal representations shared between these domains remains unclear. One experimentally derived view is that the invariant properties and constraints characterizing movement generation are also manifested during motion perception. One prominent motor invariant is the "two-third power law," describing the strong relation between the kinematics of motion and the geometrical features of the path followed by the hand during planar drawing movements. The two-thirds power law not only characterizes various movement generation tasks but also seems to constrain visual perception of motion. The present study aimed to assess whether motor invariants, such as the two thirds power law also constrain motion perception in patients with Parkinson's disease (PD). Patients with PD and age-matched controls were asked to observe the movement of a light spot rotating on an elliptical path and to modify its velocity until it appeared to move most uniformly. As in previous reports controls tended to choose those movements close to obeying the two-thirds power law as most uniform. Patients with PD displayed a more variable behavior, choosing on average, movements closer but not equal to a constant velocity. Our results thus demonstrate impairments in how the two-thirds power law constrains motion perception in patients with PD, where this relationship between velocity and curvature appears to be preserved but scaled down. Recent hypotheses on the role of the basal ganglia in motor timing may explain these irregularities. Alternatively, these impairments in perception of movement may reflect similar deficits in motor production.
We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparametrized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm's configuration space may provide insights into the emerging properties of the movements generated by the motor system.
Human movements, besides entailing the presence of a body shape, comply with characteristic kinematic laws of motion. Psychophysical studies show that low-level motion perception is biased toward stimuli complying with these laws. However, the neuronal structures that are sensitive to the kinematic laws of observed bodily movements are still largely unknown. We investigated this issue by dissociating, by means of computer-generated characters, form and motion information during the observation of human movements. In a functional imaging experiment, we compared the levels of blood oxygen level-dependent activity elicited by human actions complying with or violating the kinematic laws of human movements. Actions complying with normal kinematic laws of motion differentially activated the left dorsal premotor and dorsolateral prefrontal cortex as well as the medial frontal cortex. These findings suggest that the kinematic laws of human movements specifically modulate the responses of neuronal circuits also involved in action recognition and that are predominantly located in the left frontal lobe.
Hyperredundant limbs with a virtually unlimited number of degrees of freedom (DOFs) pose a challenge for both biological and computational systems of motor control. In the flexible arms of the octopus, simplification strategies have evolved to reduce the number of controlled DOFs [1-3]. Motor control in the octopus nervous system is hierarchically organized [4, 5]. A relatively small central brain integrates a huge amount of visual and tactile information from the large optic lobes and the peripheral nervous system of the arms [6-9] and issues commands to lower motor centers controlling the elaborated neuromuscular system of the arms. This unique organization raises new questions on the organization of the octopus brain and whether and how it represents the rich movement repertoire. We developed a method of brain microstimulation in freely behaving animals and stimulated the higher motor centers-the basal lobes-thus inducing discrete and complex sets of movements. As stimulation strength increased, complex movements were recruited from basic components shared by different types of movement. We found no stimulation site where movements of a single arm or body part could be elicited. Discrete and complex components have no central topographical organization but are distributed over wide regions.
Tracking animal movements in 3D space is an essential part of many biomechanical studies. The most popular technique for human motion capture uses markers placed on the skin which are tracked by a dedicated system. However, this technique may be inadequate for tracking animal movements, especially when it is impossible to attach markers to the animal's body either because of its size or shape or because of the environment in which the animal performs its movements. Attaching markers to an animal's body may also alter its behavior. Here we present a nearly automatic markerless motion capture system that overcomes these problems and successfully tracks octopus arm movements in 3D space. The system is based on three successive tracking and processing stages. The first stage uses a recently presented segmentation algorithm to detect the movement in a pair of video sequences recorded by two calibrated cameras. In the second stage, the results of the first stage are processed to produce 2D skeletal representations of the moving arm. Finally, the 2D skeletons are used to reconstruct the octopus arm movement as a sequence of 3D curves varying in time. Motion tracking, segmentation and reconstruction are especially difficult problems in the case of octopus arm movements because of the deformable, non-rigid structure of the octopus arm and the underwater environment in which it moves. Our successful results suggest that the motion-tracking system presented here may be used for tracking other elongated objects. (C) 2009 Elsevier B.V. All rights reserved.
Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk) motion is satisfied for parabolic trajectories having constant equi-affine speed, which thus comply with the geometric constraint known as the two-thirds power law. Here we empirically test the hypothesis that parabolic segments provide a compact representation of spontaneous drawing movements. Monkey scribblings performed during a period of practice were recorded. Practiced hand paths could be approximated well by relatively long parabolic segments. Following practice, the orientations and spatial locations of the fitted parabolic segments could be drawn from only 2-4 clusters, and there was less discrepancy between the fitted parabolic segments and the executed paths. This enabled us to show that well-practiced spontaneous scribbling movements can be represented as sequences ("words'') of a small number of elementary parabolic primitives ("letters''). A movement primitive can be defined as a movement entity that cannot be intentionally stopped before its completion. We found that in a well-trained monkey a movement was usually decelerated after receiving a reward, but it stopped only after the completion of a sequence composed of several parabolic segments. Piece-wise parabolic segments can be generated by applying affine geometric transformations to a single parabolic template. Thus, complex movements might be constructed by applying sequences of suitable geometric transformations to a few templates. Our findings therefore suggest that the motor system aims at achieving more parsimonious internal representations through practice, that parabolas serve as geometric primitives and that non-Euclidean variables
Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limac, ons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the bra
The trajectory of the index finger during grasping movements was compared to the trajectories predicted by three optimization-based models. The three models consisted of minimizing the integral of the weighted squared joint derivatives along the path (inertia-like cost), minimizing torque change, and minimizing angular jerk. Of the three models, it was observed that the path of the fingertip and the joint trajectories, were best described by the minimum angular jerk model. This model, which does not take into account the dynamics of the finger, performed equally well when the inertia of the finger was altered by adding a 20 g weight to the medial phalange. Thus, for the finger, it appears that trajectories are planned based primarily on kinematic considerations at a joint level.
Object. The supplementary motor area (SMA) plays an important role in planning, initiation, and execution of motor acts. Patients with SMA lesions are impaired in various kinematic parameters, such as velocity and duration of movement. However, the relationships between neuronal activity and these parameters in the human brain have not been fully characterized. This is a Study of single-neuron activity during a continuous volitional motor task, with the goal of clarifying these relationships for SMA neurons and other frontal lobe regions in humans. Methods. The participants were 7 patients undergoing evaluation for epilepsy surgery requiring implantation of intracranial depth electrodes. Single-unit recordings were conducted while the patients played a computer game involving movement of a cursor in a simple maze. Results. In the SMA proper, most of the recorded units exhibited a monotonic relationship between the unit firing rate and hand motion speed. The vast majority of SMA proper units with this property showed an inverse relation, that is, firing rate decrease with speed increase. In addition, most of the SMA proper units were selective to the direction of hand motion. These relationships were far less frequent in the pre-SMA, anterior cingullate gyrus, and orbitofrontal cortex. Conclusions. The findings Suggest that the SMA proper takes part in the control of kinematic parameters of end-effector motion, and thus lend support to the idea of connecting neuroprosthetic devices to the human SMA. (DOI: 10.3171/2008.10.JNS08466)
It has long been acknowledged that planar hand drawing movements conform to a relationship between movement speed and shape, such that movement speed is inversely proportional to the curvature to the power of one-third. Previous literature has detailed potential explanations for the power law's existence as well as systematic deviations from it. However, the case of speed-shape relations for three-dimensional (3D) drawing movements has remained largely unstudied. In this paper we first derive a generalization of the planar power law to 3D movements, which is based on the principle that this power law implies motion at constant equi-affine speed. This generalization results in a 3D power law where speed is inversely related to the one-third power of the curvature multiplied by the one-sixth power of the torsion. Next, we present data from human 3D scribbling movements, and compare the obtained speed-shape relation to that predicted by the 3D power law. Our results indicate that the introduction of the torsion term into the 3D power law accounts for significantly more of the variance in speed-shape relations of the movement data and that the obtained exponents are very close to the predicted values. (c) 2008 Elsevier Srl. All rights reserved.
The recording of movement kinematics during functional magnetic resonance imaging (fMRI) experiments is complicated due to technical constraints of the imaging environment. Nevertheless, to study the functions of brain areas related to motor control, reliable and accurate records of movement trajectories and speed profiles are needed. We present a method designed to record and characterize the kinematic properties of drawing- and handwriting-like forearm movements during fMRI studies by recording pen stroke trajectories. The recording system consists of a translucent plastic board, a plastic pen containing fiber optics and a halogen light power source, a CCD camera, a video monitor and a PC with a video grabber card. Control experiments using a commercially available digitizer tablet have demonstrated the reliability of the data recorded during fMRI. Since the movement tracking signal is purely optical, there is no interaction with the MR (echoplanar) images. Thus, the method allows to obtain movement records with high spatial and temporal resolution which are suitable for the kinematic analysis of hand movements in fMRI studies. (c) 2008 Elsevier Srl. All rights reserved.
The law of intersegmental coordination is a kinematic law that describes the coordination patterns among the elevation angles of the lower limb segments during locomotion (Borghese et al. in J Physiol 494:863-879, 1996). This coordination pattern reduces the number of degrees of freedom of the lower limb to two, i.e. the elevation angles covary along a plane in angular space. The properties of the plane that constrains the time course of the elevation angles have been extensively studied, and its orientation was found to be correlated with gait velocity and energy expenditure (Bianchi et al. in J Neurophysiol 79:2155-2170, 1998). Here, we present a mathematical model that represents the rotations of the elevation angles in terms of simple oscillators with appropriate phase shifts between them. The model explains what requirements the time courses of the elevation angles must fulfill in order for the angular covariation relationship to be planar. Moreover, an analytical formulation is proposed for both the orientation of the plane and for the eccentricity of the nearly elliptical shape that is generated within this plane, in terms of the amplitudes and relative phases of the first harmonics of the segments elevation angles. The model presented here sheds some new light on the possible interactions among the Central Pattern Generators possibly underlying the control of biped locomotion. The model precisely specifies how any two segments in the limb interact, and how a change in gait velocity affects the orientation of the intersegmental coordination plane mainly through a change in phase shifts between the segments. Implications of this study with respect to neural control of locomotion and other motor activities are discussed.
The aim of this study was to pinpoint the nature of the visual features used in the automatic mapping of perceived movements into similar executed movements, following the direct matching hypothesis. In Experiment I subjects imitated the lifting of one of two fingers, presented with different orientations. As predicted, stimuli which were further rotated away from the posture of the executing hand elicited slower reaction times. In Experiment 2, we verified that this orientation effect was not a purely perceptual effect by presenting the same stimuli but asking subjects to respond Verbally. No orientation effect was found using a verbal response. In Experiment 3, we replaced the moving fingers by two arbitrary objects moving with the trajectories of the finger tips of Experiment 1. The same orientation effect as in Experiment 1 was observed. We conclude that in this experiment participants are using purely kinematic features to map perceived into executed movements. (C) 2008 Elsevier Inc. All rights reserved.
Maoz U, Berthoz A, Flash T. Complex unconstrained three-dimensional hand movement and constant equi-affine speed. J Neurophysiol 101: 1002-1015, 2009. First published December 10, 2008; doi: 10.1152/jn.90702.2008. One long-established simplifying principle behind the large repertoire and high versatility of human hand movements is the two-thirds power law-an empirical law stating a relationship between local geometry and kinematics of human hand trajectories during planar curved movements. It was further generalized not only to various types of human movements, but also to motion perception and prediction, although it was unsuccessful in explaining unconstrained three-dimensional (3D) movements. Recently, movement obeying the power law was proved to be equivalent to moving with constant planar equi-affine speed. Generalizing such motion to 3D space-i.e., to movement at constant spatial equi-affine speed-predicts the emergence of a new power law, whose utility for describing spatial scribbling movements we have previously demonstrated. In this empirical investigation of the new power law, subjects repetitively traced six different 3D geometrical shapes with their hand. We show that the 3D power law explains the data consistently better than both the two-thirds power law and an additional power law that was previously suggested for spatial hand movements. We also found small yet systematic modifications of the power-law's exponents across the various shapes, which further scrutiny suggested to be correlated with global geometric factors of the traced shape. Nevertheless, averaging over all subjects and shapes, the power-law exponents are generally in accordance with constant spatial equi-affine speed. Taken together, our findings provide evidence for the potential role of non-Euclidean geometry in motion planning and control. Moreover, these results seem to imply a relationship between geometry and kinematics that is more complex than the simple local one stipulate
Previous studies have suggested that several types of rules govern the generation of complex arm movements. One class of rules consists of optimizing an objective function (e.g., maximizing motion smoothness). Another class consists of geometric and kinematic constraints, for instance the coupling between speed and curvature during drawing movements as expressed by the two-thirds power law. It has also been suggested that complex movements are composed of simpler elements or primitives. However, the ability to unify the different rules has remained an open problem. We address this issue by identifying movement paths whose generation according to the two-thirds power law yields maximally smooth trajectories. Using equi-affine differential geometry we derive a mathematical condition which these paths must obey. Among all possible solutions only parabolic paths minimize hand jerk, obey the two-thirds power law and are invariant under equi-affine transformations (which preserve the fit to the two-thirds power law). Affine transformations can be used to generate any parabolic stroke from an arbitrary parabolic template, and a few parabolic strokes may be concatenated to compactly form a complex path. To test the possibility that parabolic elements are used to generate planar movements, we analyze monkeys' scribbling trajectories. Practiced scribbles are well approximated by long parabolic strokes. Of the motor cortical neurons recorded during scribbling more were related to equi-affine than to Euclidean speed. Unsupervised segmentation of simulta- neously recorded multiple neuron activity yields states related to distinct parabolic elements. We thus suggest that the cortical representation of movements is state-dependent and that parabolic elements are building blocks used by the motor system to generate complex movements.
Motor algebra, a 4D degenerate geometric algebra, offers a rigorous yet simple representation of the 3D velocity of a rigid body. Using this representation, we Study 3D extended arm pointing and reaching movements. We analyze the choice of arm orientation about the vector connecting the shoulder and the wrist, in cases for which this orientation is not prescribed by the task. Our findings show that the changes in this orientation throughout the movement were very small, possibly indicating all underlying motion planning strategy. We additionally examine the decomposition of movements into submovements and reconstruct the motion by assuming Superposition of the velocity profiles of the underlying submovements by analyzing both the translational and rotational components of the 3D spatial velocity. This movement decomposition method reveals a larger number of submovement than is found using previously applied submovement extraction methods that are based only on the analysis of the hand tangential velocity. The reconstructed velocity profiles and final orientations are relatively close to the actual values, indicating that single-axis submovements may be the basic building blocks underlying 3D movement construction.
Behavioral and modeling studies have established that curved and drawing human hand movements obey the 2/3 power law, which dictates a strong coupling between movement curvature and velocity. Human motion perception seems to reflect this constraint. The functional MRI study reported here demonstrates that the brain's response to this law of motion is much stronger and more widespread than to other types of motion. Compliance with this law is reflected in the activation of a large network of brain areas subserving motor production, visual motion processing, and action observation functions. Hence, these results strongly support the notion of similar neural coding for motion perception and production. These findings suggest that cortical motion representations are optimally tuned to the kinematic and geometrical invariants characterizing biological actions.
Few computational models have addressed the spatiotemporal features of unconstrained three-dimensional (3D) arm motion. Empirical observations made on hand paths, speed profiles, and arm postures during point-to-point movements led to the assumption that hand path and arm posture are independent of movement speed, suggesting that the geometric and temporal properties of movements are decoupled. In this study, we present a computational model of 3D movements for an arm with four degrees of freedom based on the assumption that optimization principles are separately applied at the geometric and temporal levels of control. Geometric properties ( path and posture) are defined in terms of geodesic paths with respect to the kinetic energy metric in the Riemannian configuration space. Accordingly, a geodesic path can be generated with less muscular effort than on any other, nongeodesic path, because the sum of all configuration-speed- dependent torques vanishes. The temporal properties of the movement ( speed) are determined in task space by minimizing the squared jerk along the selected end- effector path. The integration of both planning levels into a single spatiotemporal representation simplifies the control of arm dynamics along geodesic paths and results in movements with near minimal torque change and minimal peak value of kinetic energy. Thus, the application of Riemannian geometry allows for a reconciliation of computational models previously proposed for the description of arm movements. We suggest that geodesics are an emergent property of the motor system through the exploration of dynamical space. Our data validated the predictions for joint trajectories, hand paths, final postures, speed profiles, and driving torques.
Octopus arms, as well as other muscular hydrostats, are characterized by a very large number of degrees of freedom and a rich motion repertoire. Over the years, several attempts have been made to elucidate the interplay between the biomechanics of these organs and their control systems. Recent developments in electrophysiological recordings from both the arms and brains of behaving octopuses mark significant progress in this direction. The next stage is relating these recordings to the octopus arm movements, which requires an accurate and reliable method of movement description and analysis. Here we describe a semiautomatic computerized system for 3D reconstruction of an octopus arm during motion. It consists of two digital video cameras and a PC computer running custom- made software. The system overcomes the difficulty of extracting the motion of smooth, nonrigid objects in poor viewing conditions. Some of the trouble is explained by the problem of light refraction in recording underwater motion. Here we use both experiments and simulations to analyze the refraction problem and show that accurate reconstruction is possible. We have used this system successfully to reconstruct different types of octopus arm movements, such as reaching and bend initiation movements. Our system is noninvasive and does not require attaching any artificial markers to the octopus arm. It may therefore be of more general use in reconstructing other nonrigid, elongated objects in motion.
Humans interact with their environment through sensory information and motor actions. These interactions may be understood via the underlying geometry of both perception and action. While the motor space is typically considered by default to be Euclidean, persistent behavioral observations point to a different underlying geometric structure. These observed regularities include the "two-thirds power law", which connects path curvature with velocity, and "local isochrony", which prescribes the relation between movement time and its extent. Starting with these empirical observations, we have developed a mathematical framework based on differential geometry, Lie group theory and Cartan's moving frame method for the analysis of human hand trajectories. We also use this method to identify possible motion primitives, i.e., elementary building blocks from which more complicated movements are constructed. We show that a natural geometric description of continuous repetitive hand trajectories is not Euclidean but equi-affine. Specifically, equi-affine velocity is piecewise constant along movement segments, and movement execution time for a given segment is proportional to its equi-affine arc-length. Using this mathematical framework, we then analyze experimentally recorded drawing movements. To examine movement segmentation and classification, the two fundamental equi-affine differential invariants-equi-affine arc-length and curvature are calculated for the recorded movements. We also discuss the possible role of conic sections, i.e., curves with constant equi-affine curvature, as motor primitives and focus in more detail on parabolas, the equi-affine geodesics. Finally, we explore possible schemes for the internal neural coding of motor commands by showing that the equi-affine framework is compatible with the common model of population coding of the hand velocity vector when combined with a simple assumption on its dynamics. We then discuss several alternative explanation
Object manipulation with the hand is a complex task. The task has redundancies at many levels, allowing many possibilities for the selection of grasp points, the orientation and posture of the hand, the forces to be applied at each fingertip and the impedance properties of the hand. Despite this inherent complexity, humans perform object manipulation nearly effortlessly. This article presents experimental findings of how humans grasp and manipulate objects, and examines the compatibility of grasps selected for specific tasks. This is accomplished by looking at the velocity transmission and force transmission ellipsoids, which represent the transmission ratios of the corresponding quantity from the joints to the object, as well as the stiffness ellipsoid which represents the directional stiffness of the grasp. These ellipsoids allow visualization of the grasp Jacobian and grasp stiffness matrices. The results show that the orientation of the ellipsoids can be related to salient task requirements.
We recently showed that extensive training on a sequence of planar hand trajectories passing through several targets resulted in the co-articulation of movement components and in the formation of new movement elements (primitives) (Sosnik et al. in Exp Brain Res 156(4):422-438, 2004). Reduction in movement duration was accompanied by the gradual replacing of a piecewise combination of rectilinear trajectories with a single, longer curved one, the latter affording the maximization of movement smoothness ("global motion planning"). The results from transfer experiments, conducted by the end of the last training session, have suggested that the participants have acquired movement elements whose attributes were solely dictated by the figural (i.e., geometrical) form of the path, rather than by both path geometry and its time derivatives. Here we show that the acquired movement generation strategy ("global motion planning") was not specific to the trained configuration or total movement duration. Performance gain (i.e., movement smoothness, defined by the fit of the data to the behavior, predicted by the "global planning" model) transferred to non-trained configurations in which the targets were spatially co-aligned or when participants were instructed to perform the task in a definite amount of time. Surprisingly, stringent accuracy demands, in transfer conditions, resulted not only in an increased movement duration but also in reverting to the straight trajectories (loss of co-articulation), implying that the performance gain was dependent on accuracy constraints. Only 28.5% of the participants (two out of seven) who were trained in the absence of visual feedback from the hand (dark condition) co-articulated by the end of the last training session compared to 75% (six out of eight) who were trained in the light, and none of them has acquired a geometrical motion primitive. Furthermore, six naive participants who trained in dark condition on large size targets have a
The extremely flexible octopus arm provides a unique opportunity for studying movement control in a highly redundant motor system. We describe a novel preparation that allows analysis of the peripheral nervous system of the octopus arm and its interaction with the muscular and mechanosensory elements of the arm's intrinsic muscular system. First we examined the synaptic responses in muscle fibers to identify the motor pathways from the axial nerve cord of the arm to the surrounding musculature. We show that the motor axons project to the muscles via nerve roots originating laterally from the arm nerve cord. The motor field of each nerve is limited to the region where the nerve enters the arm musculature. The same roots also carry afferent mechanosensory information from the intrinsic muscle to the axial nerve cord. Next, we characterized the pattern of activity generated in the dorsal roots by electrically stimulating), the axial nerve cord. The evoked activity, although far reaching and long lasting, cannot alone account for the arm extension movements generated by similar electrical stimulation. The mismatch between patterns of activity in the isolated cord and in an intact arm may stem from the involvement of mechanosensory feedback in natural arm extension.
An optimization approach applied to mechanical linkage models is used to simulate human arm movements. Predicted arm trajectories are the result of minimizing a nonlinear performance index that depends on kinematic or dynamic variables of the movement. A robust optimization algorithm is presented that computes trajectories which satisfy the necessary conditions with high accuracy. It is especially adapted to the analysis of discrete and rhythmic movements. The optimization problem is solved by parameterizing each generalized coordinate (e.g., joint angular displacement) in terms of Jacobi polynomials and Fourier series, depending on whether discrete or rhythmic movements are considered, combined with a multiple shooting algorithm. The parameterization of coordinates has two advantages. First, it provides an initial guess for the multiple shooting algorithm which solves the optimization problem with high accuracy. Second, it leads to a low dimensional representation of discrete and rhythmic movements in terms of expansion coefficients. The selection of a suitable feature space is an important prerequisite for comparison, recognition and classification of movements. In addition, the separate computational analysis of discrete and rhythmic movements is motivated by their distinct neurophysiological realizations in the cortex. By investigating different performance indices subject to different boundary conditions, the approach can be used to examine possible strategies that humans adopt in selecting specific arm motions for the performance of different tasks in a plane and in three-dimensional space.
The vestibular system detects the velocity of the head even in complete darkness, and thus contributes to spatial orientation. However, during vestibular estimation of linear passive self-motion distance in darkness, healthy human subjects mainly rely on time, and they replicate also stimulus duration when required to reproduce previous self-rotation. We then made the hypothesis that the perception of vestibular-sensed motion duration is embedded within encoding of motion kinetics. The ability to estimate time during passive self-motion in darkness was examined with a self-rotation reproduction paradigm. Subjects were required to replicate through self-driven transport the plateau velocity (30, 60 and 90 Vs) and duration (2, 3 and 4 s) of the previously imposed whole-body rotation (trapezoid velocity profile) in complete darkness; the rotating chair position was recorded (500Hz) during the whole trials. The results showed that the peak velocity, but not duration, of the plateau phase of the imposed rotation was accurately reproduced. Suspecting that the velocity instruction had impaired the duration reproduction, we added a control experiment requiring subjects to reproduce two successive identical rotations separated by a momentary motion interruption (MMI). The MMI was of identical duration to the previous plateau phase. MMI duration was fidelitously reproduced whereas that of the plateau phase was hypometric (i.e. lesser reproduced duration than plateau) suggesting that subjective time is shorter during vestibular stimulation. Furthermore, the accurate reproduction of the whole motion duration, that was not required, indicates an automatic process and confirms that vestibular duration perception is embedded within motion kinetics. (c) 2006 Elsevier Ireland Ltd. All rights reserved.
In an earlier study, Viviani and Stucchi (J Exp Psychol Hum Percept Perform 18:603-623, 1992) have introduced a visual illusion, whereby it was shown that when subjects are asked to determine what movement of a light spot, when tracing an elliptical trajectory, appears to be most uniform, they tend to choose movements that are close to obeying the 2/3 power law (Lacquaniti et al. Acta Psychol 54:115-130, 1983) rather than constant speed movements, even though the actual changes in velocity could exceed 200%. Here we have extended the study of this illusion by directly testing the effect of the shape (eccentricity) and size (perimeter) of the elliptical trajectory, the duration of the tracing of the ellipse and the effect of fixation on the subjects' decision regarding movement uniformity. We found that the ellipse's eccentricity and tracing out speed of the elliptical trajectory significantly affect the subjects' decisions, although the effect of eccentricity seems to be stronger than that of speed. Our findings also indicated that fixation significantly affects the subject's decision for ellipses that are more eccentric. Surprisingly, the ellipse's perimeter had a much smaller effect on the subjects' decisions, although changes in the ellipse's perimeter should have the same effect on the average velocity as changes in the time it takes to trace out the ellipse. This suggested the possibility that the subjects based their decision regarding movement uniformity on other velocity variables in addition to tangential velocity. Computer simulations we have performed have led us to conclude that the subjects' perception of movement uniformity may also be based on assessing the variations in angular velocity and possibly also in affine velocity. Our behavioral and simulation studies thus suggest that the motion perception system is quite responsive to variations in the velocity along an elliptical trajectory but in a way that depends on the path's curvature. Furthermor
This study tested the validity of the assumption that intrinsic kinematic constraints, such as Listing's law, can account for the geometric features of three-dimensional arm movements. In principle, if the arm joints follow a Listing's constraint, the hand paths may be predicted. Four individuals performed 'extended arm', 'radial', 'Cyfrontal plane', and 'random mixed' movements to visual targets to test Listing's law assumption. Three-dimensional rotation vectors of the upper arm and forearm were calculated from three-dimensional marker data. Data fitting techniques were used to test Donders' and Listing's laws. The coefficient values obtained from fitting rotation vectors to the surfaces described by a second-order equation were analyzed. The results showed that the coefficients that represent curvature and twist of the surfaces were often not significantly different from zero, particularly not during randomly mixed and extended arm movements. These coefficients for forearm rotations were larger compared to those for the upper arm segment rotations. The mean thickness of the rotation surfaces ranged between 1.7 degrees and 4.7 degrees for the rotation vectors of the upper arm segment and 2.6 degrees and 7.5 degrees for those of the forearm. During frontal plane movements, forearm rotations showed large twist scores while upper arm segment rotations showed large curvatures, although the thickness of the surfaces remained low. The curvatures, but not the thicknesses of the surfaces, were larger for large versus small amplitude radial movements. In conclusion, when examining the surfaces obtained for the different movement types, the rotation vectors may lie within manifolds that are anywhere between curved or twisted manifolds. However, a two-dimensional thick surface may roughly represent a global arm constraint. Our findings suggest that Listing's law is implemented for some types of arm movement, such as pointing to targets with the extended arm and during rad
This study was aimed at examining the assumption that three-dimensional (3D) hand movements follow specific paths that are dictated by the operation of a Listing's law constraint at the intrinsic joint level of the arm. A kinematic model was used to simulate hand paths during 3D point-to-point movements. The model was based on the assumption that the shoulder obeys a 2D Listing's constraint and that rotations are about fixed single-axes. The elbow rotations were assumed to relate linearly to those of the shoulder. Both joints were assumed to rotate without reversals, and to start and end rotating simultaneously with zero initial and final velocities. Model predictions were compared to experimental observations made on four right-handed individuals that moved toward virtual objects in "extended arm", "radial", and "frontal plane" movement types. The results showed that the model was partially successful in accounting for the observed behavior. Best hand-path predictions were obtained for extended arm movements followed by radial ones. Frontal plane movements resulted in the largest discrepancies between the predicted and the observed paths. During such movements, the upper arm rotation vectors did not obey Listing's law and this may explain the observed discrepancies. For other movement types, small deviations from the predicted paths were observed which could be explained by the fact that single-axis rotations were not followed even though the rotation vectors remained within Listing's plane. Dynamic factors associated with movement execution, which were not taken into account in our purely kinematic approach, could also explain some of these small discrepancies. In conclusion, a kinematic model based on Listing's law can describe an intrinsic joint strategy for the control of arm orientation during pointing and reaching movements, but only in conditions in which the movements closely obey the Listing's plane assumption.
One of the key problems in motor control is mastering or reducing the number of degrees of freedom (DOFs) through coordination . This problem is especially prominent with hyper-redundant limbs such as the extremely flexible arm of the octopus . Several strategies for simplifying these control problems have been suggested for human point-to-point arm movements [3-6]. Despite the evolutionary gap and morphological differences, humans and octopuses evolved similar strategies when fetching food to the mouth. To achieve this precise point-to-point-task, octopus arms generate a quasi-articulated structure based on three dynamic joints. A rotational movement around these joints brings the object to the mouth . Here, we describe a peripheral neural mechanism-two waves of muscle activation propagate toward each other, and their collision point sets the medial-joint location. This is a remarkably simple mechanism for adjusting the length of the segments according to where the object is grasped. Furthermore, similar to certain human arm movements, kinematic invariants were observed at the joint level rather than at the end-effector level, suggesting intrinsic control coordination. The evolutionary convergence to similar geometrical and kinematic features suggests that a kinematically constrained articulated limb controlled at the level of joint space is the optimal solution for precise point-to-point movements.
In recent years different lines of evidence have led to the idea that motor actions and movements in both vertebrates and invertebrates are composed of elementary building blocks. The entire motor repertoire can be spanned by applying a well-defined set of operations and transformations to these primitives and by combining them in many different ways according to well-defined syntactic rules. Motor and movement primitives and modules might exist at the neural, dynamic and kinematic levels with complicated mapping among the elementary building blocks subserving these different levels of representation. Hence, while considerable progress has been made in recent years in unravelling the nature of these primitives, new experimental, computational and conceptual approaches are needed to further advance our understanding of motor compositionality.
The dynamic model of the octopus arm described in the first paper of this 2-part series was used here to investigate the neural strategies used for controlling the reaching movements of the octopus arm. These are stereotypical extension movements used to reach toward an object. In the dynamic model, sending a simple propagating neural activation signal to contract all muscles along the arm produced an arm extension with kinematic properties similar to those of natural movements. Control of only 2 parameters fully specified the extension movement: the amplitude of the activation signal (leading to the generation of muscle force) and the activation traveling time (the time the activation wave takes to travel along the arm). We found that the same kinematics could be achieved by applying activation signals with different activation amplitudes all exceeding some minimal level. This suggests that the octopus arm could use minimal amplitudes of activation to generate the minimal muscle forces required for the production of the desired kinematics. Larger-amplitude signals would generate larger forces that increase the arm's stability against perturbations without changing the kinematic characteristics. The robustness of this phenomenon was demonstrated by examining activation signals with either a constant or a bell-shaped velocity profile. Our modeling suggests that the octopus arm biomechanics may allow independent control of kinematics and resistance to perturbation during arm extension movements.
The octopus arm requires special motor control schemes because it consists almost entirely of muscles and lacks a rigid skeletal support. Here we present a 2D dynamic model of the octopus arm to explore possible strategies of movement control in this muscular hydrostat. The arm is modeled as a multisegment structure, each segment containing longitudinal and transverse muscles and maintaining a constant volume, a prominent feature of muscular hydrostats. The input to the model is the degree of activation of each of its muscles. The model includes the external forces of gravity, buoyancy, and water drag forces (experimentally estimated here). It also includes the internal forces generated by the arm muscles and the forces responsible for maintaining a constant volume. Using this dynamic model to investigate the octopus reaching movement and to explore the mechanisms of bend propagation that characterize this movement, we found the following. 1) A simple command producing a wave of muscle activation moving at a constant velocity is sufficient to replicate the natural reaching movements with similar kinematic features. 2) The biomechanical mechanism that produces the reaching movement is a stiffening wave of muscle contraction that pushes a bend forward along the arm. 3) The perpendicular drag coefficient for an octopus arm is nearly 50 times larger than the tangential drag coefficient. During a reaching movement, only a small portion of the arm is oriented perpendicular to the direction of movement, thus minimizing the drag force.
There is extensive experimental evidence linking instantaneous velocity to curvature in drawing and hand-writing movements. The empirical relationship between these characteristics of motion and path is well described by a power law in which the velocity varies in proportion to the one-third power of the radius of curvature. It was recently shown that a similar relationship can be observed during locomotion along curved elliptical paths raising the possibility that these very different motor activities might, at some level, share the same planning strategies. It has, however, been noted that the ellipse is a special case with respect to the one-third power law and therefore these previous results might not provide strong evidence that the one-third power law is a general feature of locomotion around curved paths. For this reason the experimental study of locomotion and its comparison with hand writing is extended here to non-elliptical paths. Subjects walked along predefined curved paths consisting of two complex shapes drawn on the ground: the cloverleaf and the limacon. It was found that the data always supported a close relationship between instantaneous velocity and curvature. For these more complex paths, however, the relationship is shape-dependent-although velocity and curvature can still be linked by a power law, the exponent depends on the geometrical form of the path. The results demonstrate the existence of a close relationship between instantaneous velocity and curvature in locomotion that is more general than the one-third power law. The origins of this relationship and its possible explanation in the mechanical balance of forces and in central planning are discussed.
The progressive multistage stabilization of memory (consolidation) relies on post-acquisition neural reorganization. We hypothesize that two processes subserve procedural memory consolidation and are reflected in delayed post-acquisition performance gains: (1) synaptic consolidation, which is classical Hebbian, and (2) in some tasks, concurrently or consequently, "system consolidation," which might in some skills be sleep-dependent. Behavioral interference may affect either type of consolidation.
In telerobotic systems human actions are mapped to robot actions. In an illustrative object manipulation experiment various human grasps were translated to configurationally similar robotic grasps. The experiment's results highlight the problems and suboptimal performance incurred when such a resemblance is maintained. A new approach to telerobotics based on the construction of object-action pairs is presented. Actions are identified in the context of the object they are being performed on according to features extracted from the human grasp and transport motion. A priori knowledge is introduced to the robot controller using object centered programming and a relational database.
The skilled generation of motor sequences involves the appropriate choice, ordering and timing of a sequence of simple, stereotyped movement elements. Nevertheless, a given movement element within a well-rehearsed sequence can be modified through interaction with its neighboring elements (co-articulation). We show that extensive training on a sequence of planar hand trajectories passing through several targets resulted in the co-articulation of movement components, and in the formation of new movement elements (primitives). Reduction in movement duration was accompanied by the gradual replacement of straight trajectories by longer curved ones, the latter affording the maximization of movement smoothness. Surprisingly, the curved trajectories were generated even when new target configurations were introduced, i.e., when target distances were scaled, movement direction reversed or when different start and end positions were used, indicating the acquisition of geometrically defined movement elements. However, the new trajectories were not shared by the untrained hand. Altogether, our results suggest that novel movement elements can be acquired through extensive training in adults.
When do learning-related changes in performance occur? Here we show that the knowledge of a sequence of movements evolves through several distinctive phases that depend on two critical factors: the amount of practice as well as the passage of time. Our results show the following. (i) Within a given session, large performance gains constituted a signature for motor novelty. Such gains occurred only for newly introduced conditions irrespective of the absolute level of performance. (ii) A single training session resulted in both immediate but also time-dependent, latent learning hours after the termination of practice. Time in sleep determined the time of expression of these delayed gains. Moreover, the delayed gains were sequence-specific, indicating a qualitative change in the representation of the task within 24 h posttraining. (iii) Prolonged training resulted in additional between-session gains that, unlike the effects of a single training session, were confined to the trained hand. Thus, the effects of multisession training were qualitatively different than the immediate and time-dependent effects of a single session. Altogether, our results indicate multiple time-dependent shifts in the representation of motor experience during the acquisition of skilled performance.
In this chapter we briefly review combined modeling and behavioral studies aimed at inquiring into the principles that underlie the generation of human goal-directed motor behavior. In particular, we study motion planning, the construction of complex and sequential motor tasks from motor primitives and the issue of coordinate systems. We also demonstrate our efforts in characterizing motor deficits in neurological patients and particularly in neglect patients by comparing their motor performance to that of neurologically healthy subjects.
The movements of the human arm have been extensively studied for a variety of goal-directed experimental tasks. Analyses of the trajectory and velocity of the arm have led to many hypotheses for the planning strategies that the CNS might use. One family of control hypotheses, including minimum jerk, snap and their generalizations to higher orders, comprises those that favor smooth movements through the optimization of an integral cost function. The predictions of each order of this family are examined for two standard experimental tasks: point-to-point movements and the periodic tracing of figural forms, and compared both with experiment and the two-thirds power law. The aim of the analyses is to generalize previous numerical observations as well as to examine movement segmentation. It is first shown that contrary to recent statements in the literature, the only members of this family of control theories that match reaching movement experiments well are minimum jerk and snap. Then, for the case of periodic drawing, both the ellipse and cloverleaf are examined and the experimentally observed power law is derived from a first-principles approach. The results for the ellipse are particularly general, representing a unification of the two-thirds power law and smoothness hypotheses for ellipses of all reasonable eccentricities. For complex shapes it is shown that velocity profiles derived from the cost-function approach exhibit the same experimental features that were interpreted as segmented control by the CNS. Because the cost function contains no explicit segmented control, this result casts doubt on such an interpretation of the experimental data.
There are infinitely many different combinations of arm postures which will place the hand at the same point in space . Given this abundance, how is one configuration chosen over another? Two main hypotheses have been proposed to solve this problem . Postural models suggest that the posture adopted is purely determined by the desired hand position (known as Donders' law) [3, 4]. Transport models suggest that the adopted posture depends on where the hand has moved from. A specific transport model, the minimum work model, has been proposed in which the adopted posture is the one that minimizes the amount of work required to move the hand to the new location . The postural model predicts that the posture will be independent of where the hand has moved from, whereas the transport models predict that the posture will depend on the previous posture. We have devised a simple redundant task-touching a target bar using a hand-held virtual stick-to examine these models. The results show that neither model alone can account for the data. We propose a control planning strategy in which there is a combined cost function that has both a postural term as well as a transport term.
Switching difficulties in Parkinson's disease (PD) are expressed in both mental and motor tasks. The authors of the present study investigated whether those deficits coexist in the same patient and are positively correlated. They tested 8 nondemented PD patients and 6 age-matched control participants by using the modified Wisconsin Card Sorting Test and a motor switching paradigm that is based on the task of reaching toward visual targets, the location of which could unexpectedly be altered within the reaction time. In both mental and motor tasks, patients performed significantly worse than controls. There were no significant correlations between the two types of pathology in individual patients. Mental and motor switching deteriorate in PD patients, but the deficits are not necessarily of parallel severity.
New concepts and computational models that integrate behavioral and neurophysiological observations have addressed several of the most fundamental long-standing problems in motor control. These problems include the selection of particular trajectories among the large number of possibilities, the solution of inverse kinematics and dynamics problems, motor adaptation and the learning of sequential behaviors.
For goal-directed arm movements, the nervous system generates a sequence of motor commands that bring the arm toward the target. Control of the octopus arm is especially complex because the arm can be moved in any direction, with a virtually infinite number of degrees of freedom. Here we show that arm extensions can be evoked mechanically or electrically in arms whose connection with the brain has been severed. These extensions show kinematic features that are almost identical to normal behavior, suggesting that the basic motor program for voluntary movement is embedded within the neural circuitry of the arm itself. Such peripheral motor programs represent considerable simplification in the motor control of this highly redundant appendage.
This paper presents a real-time algorithm for modifying the trajectory of a manipulator approaching a moving target. The algorithm is based on the superposition scheme; a model developed based on human motion behavior. The algorithm generates a smooth trajectory toward the new target by calculating the vectorial sum between the first trajectory (initial position and first target) and second trajectory (between first and second target location). The algorithm searches for the switch hme that will result in a minimum time trajectory. The idea of the algorithm is to define some domain where the optimal switching time can be found, reduce this domain as much as possible to decrease the number of the points that must be checked and try every remaining candidate in this domain to find numerically the best (optimal) switch time. The algorithm was implemented on an Adept-one robotic system taking into account velocity constraints. The actual velocity profile was found to be less smooth than specified by the mathematical model. When the switch occurs at the middle of the trajectory when the speed is close to its maximum, the change in the movement direction is performed more gently.
Edge completion is the interpolation of gaps between edge segments which are extracted from an image. We provide a new analytic solution to this problem within equi-affine plane geometry, which is the natural framework for the interpolation of pairs of line segments. The desired curves are the geodesics of equi-affine plane geometry, namely parabolic arcs, which generalize the connection of points by straight lines in Euclidean geometry. Whereas most common methods of edge completion are invariant only under the group of Euclidean motions, SE(2), this solution has the advantage of being invariant under the larger group of equi-affine transformations, SA(2), that is more relevant to computer vision. In addition to these geometric qualities, the parabola is a simple algebraic curve which renders it computationally attractive, especially in comparison to the popular elastica curves.
Intelligent sensing, planning, and control of a prototype robotic melon harvester is described. The robot consists of a Cartesian manipulator mounted on a mobile platform pulled by a tractor. Black and white image processing is used to detect and locate the melons. Incorporation of knowledge-based rules adapted to the specific melon variety reduces false detections. Task, motion and trajectory planning algorithms and their integration are described. The intelligent control system consists of a distributed blackboard system with autonomous modules for sensing, planning and control, Procedures for evaluating performance of the robot performing in an unstructured and changing environment are described. The robot was tested in the field on two different melon cultivars during two different seasons. Over 85% of the fruit were successfully detected and picked.
This work deals with the problem of end-effector trajectory modification for a robot manipulator when it must respond to unexpected changes in target location. Trajectory modification and corrections are particularly important in dealing with dynamic tasks. In this paper, we present and discuss the superposition strategy derived from the study of arm trajectory modification in human subjects, According to this strategy, the motion toward the initial target location continues unmodified as planned from its beginning to its end even after the target location has unexpectedly changed. However, a trajectory leading from the first target to the final one is added vectorially to the initial one to yield the combined modified motion. A method for choosing the temporal parameters of this trajectory modification scheme is suggested so as to minimize the total travelling time under existing kinematic constraints (including both joint and hand space constraints), Then, a variant of this strategy is presented, dealing with trajectory modification in the case that the targets (both the initial and final ones) specify the desired end-point orientation rather than position.
Objectives - To investigate capabilities of arm trajectory modification in patients with Parkinson's disease and elderly subjects using a double step target displacement paradigm. Methods - Nine patients with Parkinson's disease and seven age matched control subjects were instructed to move a stylus towards visual targets presented on a digitising table. Within each session, in some trials the target location was changed before initiation of movement and the subjects were to modify their movements towards the new target (switching trials). In other trials the target location was not changed (control trials). This procedure was repeated for four different target configurations, using interstimulus time intervals of six different durations. The subjects' hand trajectories were recorded and their kinematic characteristics were analysed. Results - In switching trials, about 40% of the movements were aimed directly toward the final target location in both groups. When the trajectories were initially directed toward the first target and then modified toward the second, the reaction time (RT) to the second stimulus (RT2) was longer than to the first stimulus (RT1). The RT,IRT, ratio was significantly larger in patients with Parkinson's disease than in healthy elderly subjects. Conclusions - Patients with Parkinson's disease and elderly subjects are substantially slower in responding to a required modification of their movement than in responding to the required movement initiation. Patients with Parkinson's disease have impaired capabilities in processing simultaneously the motor responses to two visual stimuli presented in rapid succession.
The extreme flexibility of the octopus arm allows it to perform many different movements, yet octopuses reach toward a target in a stereotyped manner using a basic invariant motor structure: a bend traveling from the base of the arm toward the tip (Gutfreund et al., 1996a). To study the neuronal control of these movements, arm muscle activation [electromyogram (EMG)] was measured together with the kinematics of reaching movements. The traveling bend is associated with a propagating wave of muscle activation, with maximal muscle activation slightly preceding the traveling bend. Tonic activation was occasionally maintained afterward. Correlation of the EMG signals with the kinematic variables (velocities and accelerations) reveals that a significant part of the kinematic variability can be explained by the level of muscle activation. Furthermore, the EMG level measured during the initial stages of movement predicts the peak velocity attained toward the end of the reaching movement. These results suggest that feed-forward motor commands play an important role in the control of movement velocity and that simple adjustment of the excitation levels at the initial stages of the movement can set the velocity profile of the whole movement. A simple model of octopus arm extension is proposed in which the driving force is set initially and is then decreased in proportion to arm diameter at the bend. The model qualitatively reproduces the typical velocity profiles of octopus reaching movements, suggesting a simple control mechanism for bend propagation in the octopus arm.
We present a general scheme for learning sensorimotor tasks which allows rapid on-line learning and generalization of the learned knowledge to unfamiliar objects. The scheme consists of two modules, the first generating candidate actions and the second estimating their quality. Both modules work in an alternating fashion until apr action which is expected to provide satisfactory performance is generated, at which point the system executes the action. This design decomposes the learning problem rind thus simplifies it and allows direct generalization among objects for the quality estimation. Since the proposed scheme requires some initial knowledge about the task, we developed a method for off-line selection of heuristic strategies and quality predicting features, based on statistical analysis. The usefulness of the scheme was demonstrated in the context of learning visually guided grasping, We consider a system that coordinates a parallel-jaw gripper and a fixed camera. The system learns successful grasp configurations using a special coding, which allows it to apply stored examples to unfamiliar target objects. The system learns to estimate grasp quality by learning a function from relevant visual features to the quality. An experimental setup easing an AdeptOne manipulator was developed to test the scheme. The system demonstrated an ability to grasp a relatively wide variety of objects, and its performance had significantly improved with practice following a small number of trials.
Arm movements in 3-D space were studied to investigate the reduction in the number of rotational degrees of freedom in the shoulder and elbow during pointing movements with the fully extended arm and during pointing movements to targets in various directions and at various distances relative to the shoulder, requiring flexion/extension in the elbow. The postures of both the upper arm and forearm can be described by rotation vectors, which represent these postures as a rotation from a reference position to the current position. The rotation vectors describing the posture of the upper arm and forearm were found to lie in a 2-D (curved) surface both for pointing with the fully extended arm and for pointing with elbow flexion. This result generalizes on previous results on the reduction of the number of degrees of freedom from three to two in the shoulder for the fully extended arm to a similar reduction in the number of degrees of freedom for the upper arm and forearm for normal arm movements involving also elbow flexion and extension. The orientation of the 2-D surface fitted to the rotation vectors describing the position of the upper arm and forearm was the same for pointing with the extended arm and for movements with flexion/extension of the elbow. The scatter in torsion of the rotation vectors describing the position of the upper arm and forearm relative to the 2-D surface was typically 3-4 degrees, which is small considering the range of similar to 180 and 360 degrees for torsional rotations of the upper arm and the forearm, respectively. Donders' law states that arm posture for pointing to a target does not depend on previous positions of the arm. The results of our experiments demonstrate that the upper arm violates Donders' law. However, the variations in torsion of the upper arm are small, typically a few degrees. These deviations from Donders' law have been overlooked in previous studies, presumably because the variations are relatively small. These vari
Octopus arm movements provide an extreme example of controlled movements of a flexible arm with virtually unlimited degrees of freedom. This study aims to identify general principles in the organization of these movements. Video records of the movements of Octopus vulgaris performing the task of reaching toward a target were studied. The octopus extends its arm toward the target by a wave-like propagation of a bend that travels from the base of the arm toward the tip. Similar bend propagation is seen in other octopus arm movements, such as locomotion and searching. The kinematics (position and velocity) of the midpoint of the bend in three-dimensional space were extracted using the direct linear transformation algorithm. This showed that the bend tends to move within a single linear plane in a simple, slightly curved path connecting the center of the animal's body with the target location. Approximately 70% of the reaching movements demonstrated a stereotyped tangential velocity profile, An invariant profile was observed when movements were normalized for velocity and distance. Two arms, extended together in the same behavioral context, demonstrated identical velocity profiles. The stereotyped features of the movements were also observed in spontaneous arm extensions (not toward an external target). The simple and stereotypic appearance of the bend trajectory suggests that the position of the bend in space and time is the controlled variable. We propose that this strategy reduces the immense redundancy of the octopus arm movements and hence simplifies motor control.
Keywords: Engineering, Biomedical
Keywords: Computer Science, Information Systems; Neurosciences
In this work we have studied what mechanisms might possibly underlie arm trajectory modification when reaching toward visual targets. The double-step target displacement paradigm was used with inter-stimulus intervals (ISIs) in the range of 10-300 ms. For short ISIs, a high percentage of the movements were found to be initially directed in between the first and second target locations (averaged trajectories). The initial direction of motion was found to depend on the target configuration, and on D: the time difference between the presentation of the second stimulus and movement onset. To account for the kinematic features of the averaged trajectories two modification schemes were compared: the superposition scheme and the abort-replan scheme. According to the superposition scheme, the modified trajectories result from the vectorial addition of two elemental motions: one for moving between the initial hand position and an intermediate location, and a second one for moving between that intermediate location and the final target. According to the abort-replan scheme, the initial plan for moving toward the intermediate location is aborted and smoothly replaced by a new plan for moving from the hand position at the time the trajectory is modified to the final target location. In both tested schemes we hypothesized that due to the quick displacement of the stimulus, the internally specified intermediate goal might be influenced by both stimuli and may be different from the location of the first stimulus. It was found that the statistically most successful model in accounting for the measured data is based on the superposition scheme. It is suggested that superposition of simple independent elemental motions might be a general principle for the generation of modified motions, which allows for efficient, parallel planning. For increasing values of D the inferred locations of the intermediate targets were found to gradually shift from the first toward the second target lo
The kinematic properties of upper limb trajectories of simple reaching movements have been analysed in patients with idiopathic torsion dystonia (ITD). The velocity profiles differed from those of neurologically healthy subjects by being less symmetric. In several patients movement execution was slow due to a longer deceleration time. This phenomenon was even more conspicuous in the absence of visual feedback from the limb and was accompanied by a significant decrease in the final accuracy. These findings show that patients with ITD have deficits in central motor mechanisms beyond abnormal muscle activation patterns. Similarities between kinematic properties of patients with ITD and patients with Parkinson's disease including the deterioration of motor performance in ITD in the absence of visual feedback from the limb, suggest the existence of abnormalities in sensorimotor integration in both diseases.
Two approaches to the study of movement planning were contrasted. Data on the drawing of complex two-dimensional trajectories were used to test whether the covariations of the kinematic and geometrical parameters of the movement formalized by the two-thirds power law and by the isochrony principle (P. Viviani & R. Schneider, 1991) can be derived from the minimum-jerk model hypothesis (T. Flash & N. Hogan, 1985). The convergence of the 2 approaches was satisfactory insofar as the relation between tangential velocity and curvature is concerned (two-thirds power law). Global isochrony could not be deduced from the optimal control hypothesis. Scaling of velocity within movement subunits can instead be derived from the minimum-jerk hypothesis. The implications vis-a-vis the issue of movement planning are discussed with an emphasis on the representation used by the motor control system for coding the intended trajectories.
Keywords: motor control; robotics; robot manipulators; trajectory planning; adaptation; neural network models
Keywords: Computer Science, Artificial Intelligence; Engineering, Biomedical; Engineering, Chemical
Unconstrained point-re-point reaching movements performed in the horizontal plane tend to follow roughly straight hand paths with smooth, bell-shaped velocity profiles. The objective of the research reported here was to explore the hypothesis that these data reflect an underlying learning process that prefers simple paths in space. Under this hypothesis, movements are learned based only on spatial errors between the actual hand path and a desired hand path; temporally varying targets are not allowed. We designed a neural network architecture that learned to produce neural commands to a set of muscle-like actuators based only on information about spatial errors. Following repetitive executions of the reaching task, the network was able to generate point-to-point horizontal arm movements and the resulting muscle activation patterns and hand trajectories were found to be similar to those observed experimentally for human subjects. The implications of our results with respect to current theories of multijoint limb movement generation are discussed.
Using the dynamic optimization approach to the description of arm trajectories, the present paper examines trajectory planning principles underlying the generation of sequential arm movements in neurologically normal and Parkinsonian subjects. The paper discusses a possible scheme for sequence generation involving the super-position of temporally overlapping trajectory units. Evidence for the feasibility of this scheme is drawn from a recent study of arm tracking responses to double-step stimuli. The paper also discusses a possible criterion according to which basic strokes can be identified, and it examines to what extent the difficulties that Parkinson's disease patients have in generating motor sequences emerge from their inability to preplan a simple stroke or movement chunk as a single unit.
This work presents an evaluation of the associative search network (ASN) learning scheme when used for learning control parameters for robot motion. The control method used is impedance control in which the controlled variables are the dynamic relations between the motion variables of the robot manipulator's tip and the forces exerted by the tip. The main task used is that of wiping a surface whose geometry is not precisely known. The learning scheme does not use a model of the robot and its environment. It is a stochastic scheme that uses a single scalar value as a measure of the system performance. The scheme is found to perform quite well. A few variants of the main scheme are discussed. Modifying the virtual trajectory, externally to the ASN scheme, improved performance remarkably.
A near-minimum-time task-planning algorithm for fruit-harvesting robots having to pick fruits at N given locations is presented. For the given kinematic and inertial parameters of the manipulator, the algorithm determines the near-optimal sequence of fruit locations through which the arm should pass and finds the near-minimum-time path between these points. The sequence of motions was obtained by solving the Traveling Salesman Problem (TSP) using the distance along the geodesics in the manipulator's inertia space, between every two fruit locations, as the cost to be minimized. The algorithm presented here was applied to define the motions of a citrus-picking robot and was tested for a cylindrical robot on fruit position data collected from 20 trees. Significant reduction in the required computing time was achieved by dividing the volume containing the fruits into subvolumes and estimating the geodesic distance rather than calculating it. Nevertheless, in most cases the solution of the TSP, based on the estimated geodesic distance, produced nearly the same fruit sequence as the one resulting from the use of the exact geodesic distance between the fruit locations. Results of simulation tests enabled us to assess the influence of the robot's kinematic and dynamic parameters and of the spatial distribution of fruits on the motion sequence being selected. The proposed algorithm can help in selecting the most efficient robot design for any robot having to perform a sequence of tasks at N known locations.
In this paper we study the question of how an aimed arm movement is modified in response to a sudden change in target location occurring during the reaction or movement time. Earlier monkey and human studies demonstrated that aimed arm movements can be elicited in quick succession, without appreciable delays in responding to the target displacement, beyond the normal reaction time. Nevertheless, it is not yet clear how this motor task is performed. A first guess is that when a new visual stimulus appears the old plan is aborted and a new one conceived. Upon analyzing human arm movements, however, we find that the observations can be well accounted for by a different movement modification scheme. It appears that a new plan is vectorially added to the original plan. Among the implications of this result is the possibility of parallel planning of elemental movements and further support for the idea that arm movements are internally represented in terms of hand motion through external space.
We describe a new approach to the visual recognition of cursive handwriting. An effort is made to attain human-like performance by using a method based on pictorial alignment and on a model of the process of handwriting. The alignment approach permits recognition of character instances that appear embedded in connected strings. A system embodying this approach has been implemented and tested on five different word sets. The performance was stable both across words and across writers. The system exhibited a substantial ability to interpret cursive connected strings without recourse to lexical knowledge.