Publications

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.

Human movements are characterized by their invariant spatiotemporal features. The kinematic features and internal movement timing were accounted for by the mixture of geometries model using a combination of Euclidean, affine and equi-affine geometries. Each geometry defines a unique parametrization along a given curve and the net tangential velocity arises from a weighted summation of the logarithms of the geometric velocities. The model was also extended to deal with geometrical singularities forcing unique constraints on the allowed geometric mixture. Human movements were shown to optimize different costs. Specifically, hand trajectories were found to maximize motion smoothness by minimizing jerk. The minimum jerk model successfully accounted for a range of human end-effector motions including unconstrained and path-constrained trajectories. The two modeling approaches involving motion optimality and the geometries mixture model are here further combined to form a joint model whereby specific compositions of geometries can be selected to generate an optimal behavior. The optimization serves to define the timing along a path. Additionally, new notions regarding the nature of movement primitives used for the construction of complex movements naturally arise from the consideration of the two modelling approaches. In particular, we suggest that motion primitives may consist of affine orbits; trajectories arising from the group of full-affine transformations. Affine orbits define the movements shape. Particular mixtures of geometries achieve the smoothest possible motions, defining timing along each orbit. Finally, affine orbits can be extracted from measured human paths, enabling movement segmentation and an affine-invariant representation of hand trajectories.

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.

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.

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.

[No abstract available]

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. We suggest 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 muscle force (

The two-thirds power law, (Formula presented), expresses a robust local relationship between the geometrical and temporal aspects of human movement, represented by curvature k and speed v, with a piecewise constant γ. 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 Fittss 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 twothirds power law than by a constant Euclidean speed or by two other power law models. With nonlinear regression, the β parameter values in a generalized power law, (Formula presented), were inferred from the marked position records. This resulted in highly variable yet mostly positive β 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 ahomunculus 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.

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 determinedloss and vicarious empathy toward a real-time occurrence.

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, 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. 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 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

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.

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 cingulate gyrus, and orbitofrontal cortex. Conclusions. The findings suggest that the SMA proper takes part in the control of kinematic parameters of endeffector motion, and thus lend support to the idea of connecting neuroprosthetic devices to the human SMA.

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.

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.

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 1 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.

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 stipulated by the two-thirds power law and similar models.

Motor Sequence learning has a central role in humans' daily motor activities. Here we describe the mechanisms underlying the acquisition, representation, and retention of implicit and explicit learning of motor sequences and the currently available knowledge concerning the neural substrates mediating these processes. We present an anatomically supported model that describes the brain areas mediating motor sequence learning and discuss the explanation it provides for the findings that a newly trained motor task is represented in terms of several different coordinate systems (extrinsic spatial coordinates vs. intrinsic motor coordinates) throughout the training period as is evident from the evolution of different task features (e.g., speed and accuracy). We then discuss several possible mechanisms (superposition, coarticulation) allowing for the concatenation of basic motion elements (primitives) into smoothly performed movements or motor sequences and discuss the importance of sleep in motot consolidation, retention, and performance.

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.

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 explanations for the role that the equi-affine metric may play in internal representations of motion perception and production.

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 °/s) 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 (500 Hz) 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.

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. Furthermore, the movement is judged to be more uniform when there are minimal differences in angular, tangential and perhaps also in affine velocities, along the trajectory. Our results suggest the existence of similar underlying constraints that affect both the motion perception and production systems when the movements are associated with very large velocities or large changes in velocity along more curved portions of the trajectory. Our observations therefore provide further insight into the possibility that these constraints are either imposed by the underlying neuronal dynamics, the internal architecture of the cortical neural populations or the variables used in the coding of both sensory and motor information regarding movement.

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.

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.

In this paper, we describe our recent results in the development of a new class of soft, continuous backbone ("continuum") robot manipulators. Our work is strongly motivated by the dexterous appendages found in cephalopods, particularly the arms and suckers of octopus, and the arms and tentacles of squid. Our ongoing investigation of these animals reveals interesting and unexpected functional aspects of their structure and behavior. The arrangement and dynamic operation of muscles and connective tissue observed in the arms of a variety of octopus species motivate the underlying design approach for our soft manipulators. These artificial manipulators feature biomimetic actuators, including artificial muscles based on both electro-active polymers (EAP) and pneumatic (McKibben) muscles. They feature a "clean" continuous backbone design, redundant degrees of freedom, and exhibit significant compliance that provides novel operational capacities during environmental interaction and object manipulation. The unusual compliance and redundant degrees of freedom provide strong potential for application to delicate tasks in cluttered and/or unstructured environments. Our aim is to endow these compliant robotic mechanisms with the diverse and dexterous grasping behavior observed in octopuses. To this end, we are conducting fundamental research into the manipulation tactics, sensory biology, and neural control of octopuses. This work in turn leads to novel approaches to motion planning and operator interfaces for the robots. The paper describes the above efforts, along with the results of our development of a series of continuum tentacle-like robots, demonstrating the unique abilities of biologically-inspired design.

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.

The two-thirds power law, an empirical law stating an inverse non-linear relationship between the tangential hand speed and the curvature of its trajectory during curved motion, is widely acknowledged to be an invariant of upper-limb movement. It has also been shown to exist in eyemotion, locomotion and was even demonstrated in motion perception and prediction. This ubiquity has fostered various attempts to uncover the origins of this empirical relationship. In these it was generally attributed either to smoothness in hand- or joint-space or to the result of mechanisms that damp noise inherent in the motor system to produce the smooth trajectories evident in healthy human motion. We show here that white Gaussian noise also obeys this power-law. Analysis of signal and noise combinations shows that trajectories that were synthetically created not to comply with the power-law are transformed to power-law compliant ones after combination with low levels of noise. Furthermore, there exist colored noise types that drive non-power-law trajectories to power-law compliance and are not affected by smoothing. These results suggest caution when running experiments aimed at verifying the power-law or assuming its underlying existence without proper analysis of the noise. Our results could also suggest that the power-law might be derived not from smoothness or smoothness-inducing mechanisms operating on the noise inherent in our motor system but rather from the correlated noise which is inherent in this motor system.

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.

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.

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.

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.

Describes a prototype robot for selective harvesting of melons. The robot consists of a Cartesian manipulator mounted on a mobile platform which is driven by a tractor. Melons are detected with a real-time machine vision system which consists of two black and white cameras. Melon ripeness is measured by an electronic sniffer. Intelligent control was implemented using the blackboard architecture. The robot was tested on two different melon cultivars in two different seasons. In real field conditions 85-88 per cent of the fruit is detected and over 85 per cent of the fruit is successfully picked.

Keywords: BASAL GANGLIA; MOVEMENTS

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 locations along a path that curved toward the initial hand position. These inferred locations show a strong resemblance to the intermediate locations of saccades generated in a similar double-step paradigm. These similarities in the specification of target locations used in the generation of eye and hand movements may serve to simplify visuomotor integration.

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.

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.

When the hand is displaced from an equilibrium position, the muscles generate elastic forces to restore the original posture. In a previous study, Mussa-Ivaldi et al. (1985) have measured and characterized the field of elastic forces associated with hand posture in the horizontal plane. Hand stiffness which describes the relation between force and displacement vectors in the vicinity of equilibrium position was measured and graphically represented by an ellipse, characterized by its size, shape and orientation. The results indicated that the shape and orientation of the stiffness ellipse are strongly dependent on arm configuration. At any given hand position, however, the values of these parameters were found to remain invariant among subjects and over time. In this study we investigate the underlying causes for the observed spatial pattern of variation of the hand stiffness ellipse. Mathematically analyzing the relation between hand and joint stiffness matrices, we found that in order to produce the observed spatial variations of the stiffness ellipse, the shoulder stiffness must covary in the workspace with the stiffness component provided by the two-joint muscles. This condition was found to be satisfied by the measured joint stiffness components. Using anatomical data and considering the effects that muscle cross-sections and changes in muscle moment arms have on the joint stiffness matrix, we found that these anatomical factors are not sufficient to account for the observed pattern of variation of joint stiffness in the workspace. To examine whether the coupling between shoulder and two-joint stiffnesses results from the coactivation of muscles contributing to these stiffnesses, EMG signals were recorded from shoulder, elbow and two-joint muscles. Our results indicated that, while some muscle coactivation may indeed exist, it can be found for only some of the muscles and in only part of the workspace.

The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.