Movement curvature planning through force field internal models

Human motion studies have focused primarily on modeling straight point-to-point reaching movements. However, many goal-directed reaching movements, such as movements directed towards oneself, are not straight but rather follow highly curved trajectories. These movements are particularly interesting to study since they are essential in our everyday life, appear early in development and are routinely used to assess movement deficits following brain lesions. We argue that curved and straight-line reaching movements are generated by a unique neural controller and that the observed curvature of the movement is the result of an active control strategy that follows the geometry of one’s body, for instance to avoid trajectories that would hit the body or yield postures close to the joint limits. We present a mathematical model that accounts for such an active control strategy and show that the model reproduces with high accuracy the kinematic features of human data during unconstrained reaching movements directed toward the head. The model consists of a nonlinear dynamical system with a single stable attractor at the target. Embodiment-related task constraints are expressed as a force field that acts on the dynamical system. Finally, we discuss the biological plausibility and neural correlates of the model’s parameters and suggest that embodiment should be considered as a main cause for movement trajectory curvature.     

Reaching a Better Understanding of the Control of Bimanual Movements in Older Adults

The ability to interact skilfully with the environment is essential for independent living and therefore a critical factor for the aging population. Here we investigate the differences between young and older adults in a bimanual reaching task where the goal is to bring two objects together to the same location with a synchronous placement. Older (mean age 74) and young (mean age 20) adults were asked to pick up two spatially disparate objects, one in each hand, and bring them together to place them in one of three trays laid out in front of them from left to right. The results showed that the older adults were no more detrimentally affected than the young by asymmetric bimanual movements compared to symmetric ones, and both groups completed their movements in the same time. Nevertheless, compared to the young, the older adult group produced reaches characterised by higher peak velocities (although this effect was marginal), shorter hover times, and where the movement distance varied for each hand the scaling of the kinematic profile across the two limbs diverged from that found with younger participants. They then spent longer than the young in the final adjustment phase and during this phase they made more adjustments than the young, and as a result were more synchronous in terms of the final placement of the objects. It seems that the older adults produced reach movements that were designed to reach the vicinity of the tray quite rapidly, after which time they made discreet adjustments to their initial trajectories in order to exercise the precision necessary to place the objects in the tray. These findings are consistent with the idea that older adults have problems using online control (as they wait until they can fixate both objects before making adjustments).     

A possible correlation between the basal ganglia motor function and the inverse kinematics calculation

The main hypothesis of this study, based on experimental data showing the relations between the BG activities and kinematic variables, is that BG are involved in computing inverse kinematics (IK) as a part of planning and decision-making. Indeed, it is assumed that based on the desired kinematic variables (such as velocity) of a limb in the workspace, angular kinematic variables in the joint configuration space are calculated. Therefore, in this paper, a system-level computational model of BG is proposed based on geometrical rules, which is able to compute IK. Next, the functionality of each part in the presented model is interpreted as a function of a nucleus or a pathway of BG. Moreover, to overcome existing redundancy in possible trajectories, an optimization problem minimizing energy consumption is defined and solved to select an optimal movement trajectory among an infinite number of possible ones. The validity of the model is checked by simulating it to control a three-segment manipulator with rotational joints in a plane. The performance of the model is studied for different types of movement including different reaching movements, a continuous circular movement and a sequence of tracking movements. Furthermore, to demonstrate the physiological similarity of the presented model to the BG structure, the neuronal activity of each part of the model considered as a BG nucleus is verified. Some changes in model parameters, inspired by the dopamine deficiency, also allow simulating some symptoms of Parkinson’s disease such as bradykinesia and akinesia.     

Decoding hand movement velocity from electroencephalogram signals during a drawing task

Background  

Decoding neural activities associated with limb movements is the key of motor prosthesis control. So far, most of these studies have been based on invasive approaches. Nevertheless, a few researchers have decoded kinematic parameters of single hand in non-invasive ways such as magnetoencephalogram (MEG) and electroencephalogram (EEG). Regarding these EEG studies, center-out reaching tasks have been employed. Yet whether hand velocity can be decoded using EEG recorded during a self-routed drawing task is unclear.     

Adjustment of the human arm viscoelastic properties to the direction of reaching

The viscoelastic properties of the human arm were measured by means of short force perturbations during fast reaching movements in two orthogonal directions. A linear spring model with time delay described the neuromuscular system of the human arm. The obtained viscoelastic parameters ensured movement stability in spite of the time delay of 50 ms. The stiffness and viscosity ellipses appeared to be predominantly orthogonal to the movement direction, which reduced the effect of force perturbation in the direction orthogonal to the reaching movement. Thus, it can be argued that the viscoelastic properties of the neuromuscular system of the human arm are adjusted to the direction of movement according to a “path preserving” strategy, which minimizes the deviation of the movement path from a straight line, when exposed to an unexpected external force.     

Kinematic invariants during cyclical arm movements

It has been observed that the motion of the arm end-point (the hand, fingertip or the tip of a pen) is characterized by a number of regularities (kinematic invariants). Trajectory is usually straight, and the velocity profile has a bell shape during point-to-point movements. During drawing movements, a two-thirds power law predicts the dependence of the end-point velocity on the trajectory curvature. Although various principles of movement organization have been discussed as possible origins of these kinematic invariants, the nature of these movement trajectory characteristics remains an open question. A kinematic model of cyclical arm movements derived in the present study analytically demonstrates that all three kinematic invariants can be predicted from a two-joint approximation of the kinematic structure of the arm and from sinusoidal joint motions. With this approach, explicit expressions for two kinematic invariants, the two-thirds power law during drawing movements and the velocity profile during point-to-point movements are obtained as functions of arm segment lengths and joint motion parameters. Additionally, less recognized kinematic invariants are also derived from the model. The obtained analytical expressions are further validated with experimental data. The high accuracy of the predictions confirms practical utility of the model, showing that the model is relevant to human performance over a wide range of movements. The results create a basis for the consolidation of various existing interpretations of kinematic invariants. In particular, optimal control is discussed as a plausible source of invariant characteristics of joint motions and movement trajectories.     

Evolutionary optimization for robust hierarchical computation of the rotation centres of kinematic chains from reduced ranges of motion the lower spine case

A novel technique based on evolutionary optimization is proposed here to compute the average rotation centres (RCs) of ball joints linked into kinematic chains using 3D trajectories of the markers attached to the external surface of the corresponding articulated structures. The chain is hierarchically solved by iteratively minimizing the variance of the marker distances from the actual RC through an evolutional strategy method (ESM) from proximal to distal joints. In particular, the technique is compared to the non-rigid sphere-fitting method, recently proposed in literature and implemented through a closed-form solution (CFS), in conditions of random and systematic noise superimposed to the marker coordinates. Results from simulated motions showed that, in case of small range of motion (5°, 10°) the performance of CFS is really unreliable whereas ESM provided satisfactory accuracy. Error propagation along the kinematic chain was found to be negligible. Also in the case of systematic errors, ESM provides an accuracy that is sensibly better than that of the CFS. As a case study, ESM was applied to the in vivo computation of the RCs of the vertebrae in the lower spine region using a specific marker protocol. A set of spine movements by a normal adult male, recorded by an optoelectronic motion capture system, were processed with the developed method. The variability of the estimated average RCs was small (few millimeters) in agreement with the literature data from cadaveric studies and X-ray imaging.     

The effects of unsupervised movement training with visual feedback on upper limb kinematic in persons with shoulder impingement syndrome

Persons with shoulder impingement syndrome (SIS) present impairments that can be improved following supervised movement training with feedback; however, retention is low. The purpose of this study was to evaluate if kinematic changes observed following supervised training can be maintained using unsupervised training with visual feedback. Thirty-three subjects with SIS participated in two visits, one day apart. Kinematic patterns of the upper limb were evaluated once during the first visit, immediately after supervised training; they were evaluated twice during the second visit, before and immediately after unsupervised training. Kinematic patterns were characterized by total excursion and final position during reaching. Unsupervised training consisted of reaching movements performed in front of a mirror. The day after supervised training, subjects with SIS used significantly larger trunk rotation and finished reaching with the trunk more rotated as compared to immediately after supervised training. Following unsupervised training, kinematics of the trunk was back to the level observed immediately after supervised training. Subjects who presented the largest kinematic deficits also significantly improved their shoulder and clavicular movements. Unsupervised training appears to be a good complement to supervised training in order to normalize the kinematic impairments of persons with SIS as compared to healthy subjects.     

Three-dimensional kinematic analysis of influence of hand orientation and joint limits on the control of arm postures and movements

The problems related to kinematic redundancy in both task and joint space were investigated for arm prehension movements in this paper. After a detailed analysis of kinematic redundancy of the arm, it is shown that the redundancy problem is ill posed only for the control of hand orientation. An experiment was then designed to investigate the influence of hand orientation on the control of arm movements. Since movements must be made within the limits of the joints, the influence of these limits was also analyzed quantitatively. The results of the experiment confirm that the increase of movement time because of the change of object orientation is due to the lengthening of the deceleration phase disproportionately to the rest of the movement. The variation of hand path due to the change of object orientation was observed as being surprisingly small for some subjects as opposed to the large range of object orientation, implying that hand path and hand orientation could be controlled separately, thus simplifying the computational problem of inverse kinematics. Moreover, the observations from the present experiment strongly suggest that a functional segmentation of the proximal and distal joints exists and that the control of wrist motion is dissociated from the rest of joint motions. The contribution of each joint in the control of arm movements could be determined through the principle of minimum energy and minimum discomfort under the constraints of the joint limits. A simplified inverse kinematics model was tested. It shows that these hypotheses can be easily implemented in a geometric algorithm and be used to predict arm prehension postures reasonably well under the constraints of joint limits. Received: 6 August 1998 / Accepted in revised form: 16 December 1998     

Motor control of voluntary arm movements

The motor control of pointing and reaching-to-grasp movements was investigated using two different approaches (kinematic and modelling) in order to establish whether the type of control varies according to modifications of arm kinematics. Kinematic analysis of arm movements was performed on subjects' hand trajectories directed to large and small stimuli located at two different distances. The subjects were required either to grasp and to point to each stimulus. The kinematics of the subsequent movement, during which subject's hand came back to the starting position, were also studied. For both movements, kinematic analysis was performed on hand linear trajectories as well as on joint angular trajectories of shoulder and elbow. The second approach consisted in the parametric identification of the black box (ARMAX) model of the controller driving the arm movement. Such controller is hypothesized to work for the correct execution of the motor act. The order of the controller ARMAX model was analyzed with respect to the different experimental conditions (distal task, stimulus size and distance). Results from kinematic analysis showed that target distance and size influenced kinematic parameters both of angular and linear displacements. Nevertheless, the structure of the motor program was found to remain constant with distane and distal task, while it varied with precision requirements due to stimulus size. The estimated model order of the controller confirmed the invariance of the control law with regard to movement amplitude, whereas it was sensitive to target size.     

Three-dimensional model to predict muscle forces and their relation to motor variances in reaching arm movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.     

Assessing Movement Factors in Upper Limb Kinematics Decoding from EEG Signals

The past decades have seen the rapid development of upper limb kinematics decoding techniques by performing intracortical recordings of brain signals. However, the use of non-invasive approaches to perform similar decoding procedures is still in its early stages. Recent studies show that there is a correlation between electroencephalographic (EEG) signals and hand-reaching kinematic parameters. From these studies, it could be concluded that the accuracy of upper limb kinematics decoding depends, at least partially, on the characteristics of the performed movement. In this paper, we have studied upper limb movements with different speeds and trajectories in a controlled environment to analyze the influence of movement variability in the decoding performance. To that end, low frequency components of the EEG signals have been decoded with linear models to obtain the position of the volunteer’s hand during performed trajectories grasping the end effector of a planar manipulandum. The results confirm that it is possible to obtain kinematic information from low frequency EEG signals and show that decoding performance is significantly influenced by movement variability and tracking accuracy as continuous and slower movements improve the accuracy of the decoder. This is a key factor that should be taken into account in future experimental designs.     

Kinematics of the Coordination of Pointing during Locomotion

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

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

The generation of handwriting with delta-lognormal synergies

This paper presents a handwriting generation model that takes advantage of the asymptotic impulse response of neuromuscular networks to produce and control complex two-dimensional synergistic movements. A parametric definition of a ballistic stroke in the context of the kinematic theory of rapid human movements is given. Two types of parameters are used: command and system parameters. The first group provides a representation of the action plan while the second takes into account the temporal properties of the neuromuscular systems executing that plan. Handwriting is described as the time superimposition of basic discontinuous strokes that results in a continuous summation of delta-lognormal velocity vectors. The model leads to trajectory reconstruction, both in the spatial and in the kinematic domain. According to this new paradigm, the angular velocity does not have to be controlled independently and continuously; it naturally emerges from the vectorial summation process. Several psychophysical phenomena related to two-dimensional movements are explained and analyzed in the context of the model: the speed/accuracy trade-offs, spatial scaling, the isochrony principle, the two-thirds power law, effector independence, etc. The overall approach also shows how basic handwriting characteristics (dimension, slant, baseline, shape, etc.) are affected and controlled using an action plan made up of virtual targets fed into a neuromuscular synergy that is governed by a delta-lognormal law. Received: 22 July 1996 / Accepted in revised form: 15 September 1997     

EMG reaction in muscles about the knee to passive velocity,acceleration, and jerk manipulations

Twenty subjects, ten adults and ten children were tested in this study. Each test consisted of applying an ensemble of velocities to the lower limb using a torque motor in such a way that the entire range of motion of the knee was traversed. Eight velocities between 60°/s and 280°/s were reached at 2–3 different acceleration rates and 1–2 different rates of jerk. EMG from three muscles, vastus, rectus, and hamstring were recorded during each move. Regression and correlation coefficients between EMG and kinematic parameters indicated different reactions in both muscle groups and age groups to each of the three kinematic parameters. Adult muscle was dominated by a reaction to the velocity kinematic while children’s muscles were dominated by either acceleration or jerk. The extensor muscles of adults seem to be slightly more sensitive to acceleration and jerk than the flexors. In the muscle responses of children the exact opposite pattern is seen. The small sample size in this study does not allow for a meaningful statistical analysis.     

Kinematic study of reaching-grasping movements

The experiment was conducted to investigate, by using kinematic parameters, the influence of the type of prehension on the transportation component in reaching-grasping movements. The main question was whether the transportation component is influenced by the type of prehension besides the distance of the object. The experiment was carried out on eight subjects who performed reaching-grasping movements toward objects located at different distances. Two types of prehension were examined: whole hand prehension and precision grip. The following kinematic parameters of the transportation component (wrist movement) were studied: movement times, profiles of velocity and accelerations. Our results have shown that the transportation component is affected by the two factors. However the kinematic parameters were influenced differently by the distance and the type of prehension. Our conclusion is that, although distance and type of prehension affect the transportation component, they are computed separately in programming this component.     

Neuronal correlates of kinematics-to-dynamics transformation in the supplementary motor area

It is widely acknowledged that movements are planned at the level of the kinematics. However, the central nervous system must ultimately transform kinematic plans into dynamics-related commands. How, when, and where the kinematics-to-dynamics (KD) transformation is processed represent fundamental and unanswered questions. We recorded from the supplementary motor area (SMA) of two monkeys as they executed visually instructed reaching movements. We specifically analyzed a delay period following the instruction but prior to the go signal (motor planning). During the delay, a group of neurons in the SMA progressively came to reflect the dynamics rather than the desired kinematics of the upcoming movement. This finding suggests that some neurons in the SMA participate in the KD transformation.     

The point of no return in planar hand movements: an indication of the existence of high level motion primitives

Previous psychophysical studies have sought to determine whether the processes of movement engagement and termination are dissociable, whether stopping an action is a generic process, and whether there is a point in time in which the generation of a planned action is inevitable (“point of no return”). It is not clear yet, however, whether the action of stopping is merely a manifestation of low level, dynamic constraints, or whether it is also subject to a high level, kinematic plan. In the present study, stopping performance was studied while nine subjects, who generated free scribbling movements looking for the location of an invisible circular target, were requested unexpectedly to impede movement. Temporal analysis of the data shows that in 87% of the movements subsequent to the ‘stop’ cue, the tangential motion velocity profile was not a decelerating function of the time but rather exhibited a complex pattern comprised of one or more velocity peaks, implying an unstoppable motion element. Furthermore, geometrical analysis shows that the figural properties of the path generated after the ‘stop’ cue were part of a repetitive geometrical pattern and that the probability of completing a pattern after the ‘stop’ cue was correlated with the relative advance in the geometrical plan rather than the amount of time that had elapsed from the pattern initiation. Altogether, these findings suggest that the “point of no return” phenomenon in humans may also reflect a high level kinematic plan and could serve as a new operative definition of motion primitives.