Trajectory formation of arm movement by cascade neural network model based on minimum torque-change criterion

We proposed that the trajectory followed by human subject arms tended to minimize the time integral of the square of the rate of change of torque (Uno et al. 1987). This minimum torque-change model predicted and reproduced human multi-joint movement data quite well (Uno et al. 1989). Here, we propose a neural network model for trajectory formation based on the minimum torque-change criterion. Basic ideas of information representation and algorithm are(i) spatial representation of time,(ii) learning of forward dynamics and kinetics model and(iii) relaxation computation based on the acquired model. The model can resolve ill-posed inverse kinematics and inverse dynamics problems for redundant controlled object as well as ill-posed trajectory formation problems. By computer simulation, we show that the model can produce a multi-joint arm trajectory while avoiding obstacles or passing through viapoints.     

Estimation of dynamic joint torques and trajectory formation from surface electromyography signals using a neural network model

In this study, human arm movement was re-constructed from electromyography (EMG) signals using a forward dynamics model acquired by an artificial neural network within a modular architecture. Dynamic joint torques at the elbow and shoulder were estimated for movements in the horizontal plane from the surface EMG signals of 10 flexor and extensor muscles. Using only the initial conditions of the arm and the EMG time course as input, the network reliably reconstructed a variety of movement trajectories. The results demonstrate that posture maintenance and multijoint movements, entailing complex via-point specification and co-contraction of muscles, can be accurately computed from multiple surface EMG signals. In addition to the model's empirical uses, such as calculation of arm stiffness during motion, it allows evaluation of hypothesized computational mechanisms of the central nervous system such as virtual trajectory control and optimal trajectory planning.     

When Kinesthesia Becomes Visual: A Theoretical Justification for Executing Motor Tasks in Visual Space

Several experimental studies in the literature have shown that even when performing purely kinesthetic tasks, such as reaching for a kinesthetically felt target with a hidden hand, the brain reconstructs a visual representation of the movement. In our previous studies, however, we did not observe any role of a visual representation of the movement in a purely kinesthetic task. This apparent contradiction could be related to a fundamental difference between the studied tasks. In our study subjects used the same hand to both feel the target and to perform the movement, whereas in most other studies, pointing to a kinesthetic target consisted of pointing with one hand to the finger of the other, or to some other body part. We hypothesize, therefore, that it is the necessity of performing inter-limb transformations that induces a visual representation of purely kinesthetic tasks. To test this hypothesis we asked subjects to perform the same purely kinesthetic task in two conditions: INTRA and INTER. In the former they used the right hand to both perceive the target and to reproduce its orientation. In the latter, subjects perceived the target with the left hand and responded with the right. To quantify the use of a visual representation of the movement we measured deviations induced by an imperceptible conflict that was generated between visual and kinesthetic reference frames. Our hypothesis was confirmed by the observed deviations of responses due to the conflict in the INTER, but not in the INTRA, condition. To reconcile these observations with recent theories of sensori-motor integration based on maximum likelihood estimation, we propose here a new model formulation that explicitly considers the effects of covariance between sensory signals that are directly available and internal representations that are ‘reconstructed’ from those inputs through sensori-motor transformations.     

A Real-Time Brain-Machine Interface Combining Motor Target and Trajectory Intent Using an Optimal Feedback Control Design

Real-time brain-machine interfaces (BMI) have focused on either estimating the continuous movement trajectory or target intent. However, natural movement often incorporates both. Additionally, BMIs can be modeled as a feedback control system in which the subject modulates the neural activity to move the prosthetic device towards a desired target while receiving real-time sensory feedback of the state of the movement. We develop a novel real-time BMI using an optimal feedback control design that jointly estimates the movement target and trajectory of monkeys in two stages. First, the target is decoded from neural spiking activity before movement initiation. Second, the trajectory is decoded by combining the decoded target with the peri-movement spiking activity using an optimal feedback control design. This design exploits a recursive Bayesian decoder that uses an optimal feedback control model of the sensorimotor system to take into account the intended target location and the sensory feedback in its trajectory estimation from spiking activity. The real-time BMI processes the spiking activity directly using point process modeling. We implement the BMI in experiments consisting of an instructed-delay center-out task in which monkeys are presented with a target location on the screen during a delay period and then have to move a cursor to it without touching the incorrect targets. We show that the two-stage BMI performs more accurately than either stage alone. Correct target prediction can compensate for inaccurate trajectory estimation and vice versa. The optimal feedback control design also results in trajectories that are smoother and have lower estimation error. The two-stage decoder also performs better than linear regression approaches in offline cross-validation analyses. Our results demonstrate the advantage of a BMI design that jointly estimates the target and trajectory of movement and more closely mimics the sensorimotor control system.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

Formation and control of optimal trajectory in human multijoint arm movement

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.     

An improved localization algorithm based on genetic algorithm in wireless sensor networks

Wireless sensor network (WSN) are widely used in many applications. A WSN is a wireless decentralized structure network comprised of nodes, which autonomously set up a network. The node localization that is to be aware of position of the node in the network is an essential part of many sensor network operations and applications. The existing localization algorithms can be classified into two categories: range-based and range-free. The range-based localization algorithm has requirements on hardware, thus is expensive to be implemented in practice. The range-free localization algorithm reduces the hardware cost. Because of the hardware limitations of WSN devices, solutions in range-free localization are being pursued as a cost-effective alternative to more expensive range-based approaches. However, these techniques usually have higher localization error compared to the range-based algorithms. DV-Hop is a typical range-free localization algorithm utilizing hop-distance estimation. In this paper, we propose an improved DV-Hop algorithm based on genetic algorithm. Simulation results show that our proposed algorithm improves the localization accuracy compared with previous algorithms.     

A model of handwriting

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.     

Disruption of state estimation in the human lateral cerebellum

The cerebellum has been proposed to be a crucial component in the state estimation process that combines information from motor efferent and sensory afferent signals to produce a representation of the current state of the motor system. Such a state estimate of the moving human arm would be expected to be used when the arm is rapidly and skillfully reaching to a target. We now report the effects of transcranial magnetic stimulation (TMS) over the ipsilateral cerebellum as healthy humans were made to interrupt a slow voluntary movement to rapidly reach towards a visually defined target. Errors in the initial direction and in the final finger position of this reach-to-target movement were significantly higher for cerebellar stimulation than they were in control conditions. The average directional errors in the cerebellar TMS condition were consistent with the reaching movements being planned and initiated from an estimated hand position that was 138 ms out of date. We suggest that these results demonstrate that the cerebellum is responsible for estimating the hand position over this time interval and that TMS disrupts this state estimate.     

A computer algorithm for representing spatial-temporal structure of human motion and a motion generalization method

Inspired by the generalized motor program (GMP) theory, this study presents a symbolic motion structure representation (SMSR) algorithm that identifies a basic spatial-temporal structure of a human motion. The algorithm resolves each joint angle-time trajectory of a multi-joint motion into a sequence of elemental motion segments and labels each motion segment with a symbol representing its shape ("U": monotonically increasing; "D": monotonically decreasing; "S": stationary). By concatenating symbols according to their order in time, the spatial-temporal structure of a joint angle-time trajectory is represented as a symbolic string. The structure of a multi-joint motion is then represented as a set of symbolic strings. A sample motion, whose structure is identified by the SMSR algorithm, can be generalized to produce an infinite number of similar motion variants. To generate a variant of a sample motion, segment boundary points of the sample motion are first relocated to new locations in the angle-time space, and then individual motion segments of the original joint angle trajectories are shifted and proportionally rescaled to fit the new segment boundary points. This motion generalization method provides a basis for developing GMP-based motion simulation models, and exploring ideas and hypotheses related to the GMP theory through simulation. As an application of the motion generalization method, a motion modification (MoM) algorithm is presented, which adapts existing reach motions for new target locations. Some examples generated by the MoM algorithm are illustrated.     

Identification of neuromuscular synergies in natural upper-arm movements

 In this paper we study a natural upper-arm movement composed of sequential phases of reaching, grasping, and retrieval in the horizontal plane; in the present context, natural means that the spatiotemporal constraints active in the execution of the movement are low. The proposed method of quantitative analysis, which is applied to data obtained from healthy subjects, combines quantification of arm kinematics and kinesiologic electromyography assessment of neuromuscular control for each subject; to this aim, we propose using factor analysis. Despite the existence of a time-profile invariance of velocity traces, the identified factors may differ in the muscles that load on them; the interpretation is that different neuromuscular synergies are involved in the execution of the movement, which leads to cluster the subjects into two distinct groups. Compared with group-2 subjects, group-1 subjects present a more lateral hand path direction and a less smooth hand trajectory in their approach to the grasped object. To explain the identified factors and the kinematic findings, it is hypothesized that the feedforward motor commands involved in trajectory planning are different. Received: 28 June 2001 / Accepted in revised form: 6 November 2001     

A Unified Model of Heading and Path Perception in Primate MSTd

Self-motion, steering, and obstacle avoidance during navigation in the real world require humans to travel along curved paths. Many perceptual models have been proposed that focus on heading, which specifies the direction of travel along straight paths, but not on path curvature, which humans accurately perceive and is critical to everyday locomotion. In primates, including humans, dorsal medial superior temporal area (MSTd) has been implicated in heading perception. However, the majority of MSTd neurons respond optimally to spiral patterns, rather than to the radial expansion patterns associated with heading. No existing theory of curved path perception explains the neural mechanisms by which humans accurately assess path and no functional role for spiral-tuned cells has yet been proposed. Here we present a computational model that demonstrates how the continuum of observed cells (radial to circular) in MSTd can simultaneously code curvature and heading across the neural population. Curvature is encoded through the spirality of the most active cell, and heading is encoded through the visuotopic location of the center of the most active cell''s receptive field. Model curvature and heading errors fit those made by humans. Our model challenges the view that the function of MSTd is heading estimation, based on our analysis we claim that it is primarily concerned with trajectory estimation and the simultaneous representation of both curvature and heading. In our model, temporal dynamics afford time-history in the neural representation of optic flow, which may modulate its structure. This has far-reaching implications for the interpretation of studies that assume that optic flow is, and should be, represented as an instantaneous vector field. Our results suggest that spiral motion patterns that emerge in spatio-temporal optic flow are essential for guiding self-motion along complex trajectories, and that cells in MSTd are specifically tuned to extract complex trajectory estimation from flow.     

The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off

In primates, it is well known that there is a consistent relationship between the duration, peak velocity and amplitude of saccadic eye movements, known as the ‘main sequence’. The reason why such a stereotyped relationship evolved is unknown. We propose that a fundamental constraint on the deployment of foveal vision lies in the motor system that is perturbed by signal-dependent noise (proportional noise) on the motor command. This noise imposes a compromise between the speed and accuracy of an eye movement. We propose that saccade trajectories have evolved to optimize a trade-off between the accuracy and duration of the movement. Taking a semi-analytical approach we use Pontryagin’s minimum principle to show that there is an optimal trajectory for a given amplitude and duration; and that there is an optimal duration for a given amplitude. It follows that the peak velocity is also fixed for a given amplitude. These predictions are in good agreement with observed saccade trajectories and the main sequence. Moreover, this model predicts a small saccadic dead-zone in which it is better to stay eccentric of target than make a saccade onto target. We conclude that the main sequence has evolved as a strategy to optimize the trade-off between accuracy and speed.     

Drifting towards a diffuse control model of exploratory motor learning: A comparison of global and within-trial performance measures

 Accurate measurement is crucial for understanding the processes that underlie exploratory patterns in motor learning. Accordingly, measures of learning should be sensitive to the changes that take place during skill acquisition. Most studies, however, use trial-based global measures that assess performance but do not actually measure gradual changes taking place within trials. The present study attempted to remedy this shortcoming by analysing a visual adaptation task, and comparing traditional global measures of learning with new, within-trial measures. Movement time was the only global measure sensitive to changes in the movement trajectory during learning. Three new measures were expected to reveal changes to the movement trajectory that are associated with learning: (i) the length of runs, (ii) change of trajectory angle in relation to the target, and (iii) drift (change in distance from the target). All three measures were sensitive to learning and indicated a gradual straightening of the movement trajectories over trials. Furthermore, three different methods to partition trajectories into segments were examined. The new within-trial measures, irrespective of partitioning method, prove promising for the development of a diffuse control model of exploratory learning. Received: 5 February 2001 / Accepted in revised form: 16 January 2002     

Real-time tumor tracking with an artificial neural networks-based method: A feasibility study

The purpose of this study was to develop and assess the performance of a tumor tracking method designed for application in radiation therapy. This motion compensation strategy is currently applied clinically only in conventional photon radiotherapy but not in particle therapy, as greater accuracy in dose delivery is required.We proposed a tracking method that exploits artificial neural networks to estimate the internal tumor trajectory as a function of external surrogate signals. The developed algorithm was tested by means of a retrospective clinical data analysis in 20 patients, who were treated with state of the art infra-red motion tracking for photon radiotherapy, which is used as a benchmark. Integration into a hardware platform for motion tracking in particle therapy was performed and then tested on a moving phantom, specifically developed for this purpose.Clinical data show that a median tracking error reduction up to 0.7 mm can be achieved with respect to state of the art technologies. The phantom study demonstrates that a real-time tumor position estimation is feasible when the external signals are acquired at 60 Hz.The results of this work show that neural networks can be considered a valuable tool for the implementation of high accuracy real-time tumor tracking methodologies.     

Computational model of motor learning and perceptual change

Motor learning in the context of arm reaching movements has been frequently investigated using the paradigm of force-field learning. It has been recently shown that changes to somatosensory perception are likewise associated with motor learning. Changes in perceptual function may be the reason that when the perturbation is removed following motor learning, the hand trajectory does not return to a straight line path even after several dozen trials. To explain the computational mechanisms that produce these characteristics, we propose a motor control and learning scheme using a simplified two-link system in the horizontal plane: We represent learning as the adjustment of desired joint-angular trajectories so as to achieve the reference trajectory of the hand. The convergence of the actual hand movement to the reference trajectory is proved by using a Lyapunov-like lemma, and the result is confirmed using computer simulations. The model assumes that changes in the desired hand trajectory influence the perception of hand position and this in turn affects movement control. Our computer simulations support the idea that perceptual change may come as a result of adjustments to movement planning with motor learning.     

Toward the Quantification of a Conceptual Framework for Movement Ecology Using Circular Statistical Modeling

To analyze an animal’s movement trajectory, a basic model is required that satisfies the following conditions: the model must have an ecological basis and the parameters used in the model must have ecological interpretations, a broad range of movement patterns can be explained by that model, and equations and probability distributions in the model should be mathematically tractable. Random walk models used in previous studies do not necessarily satisfy these requirements, partly because movement trajectories are often more oriented or tortuous than expected from the models. By improving the modeling for turning angles, this study aims to propose a basic movement model. On the basis of the recently developed circular auto-regressive model, we introduced a new movement model and extended its applicability to capture the asymmetric effects of external factors such as wind. The model was applied to GPS trajectories of a seabird (Calonectris leucomelas) to demonstrate its applicability to various movement patterns and to explain how the model parameters are ecologically interpreted under a general conceptual framework for movement ecology. Although it is based on a simple extension of a generalized linear model to circular variables, the proposed model enables us to evaluate the effects of external factors on movement separately from the animal’s internal state. For example, maximum likelihood estimates and model selection suggested that in one homing flight section, the seabird intended to fly toward the island, but misjudged its navigation and was driven off-course by strong winds, while in the subsequent flight section, the seabird reset the focal direction, navigated the flight under strong wind conditions, and succeeded in approaching the island.     

High-Accuracy Brain-Machine Interfaces Using Feedback Information

Sensory feedback is very important for movement control. However, feedback information has not been directly used to update movement prediction model in the previous BMI studies, although the closed-loop BMI system provides the visual feedback to users. Here, we propose a BMI framework combining image processing as the feedback information with a novel prediction method. The feedback-prediction algorithm (FPA) generates feedback information from the positions of objects and modifies movement prediction according to the information. The FPA predicts a target among objects based on the movement direction predicted from the neural activity. After the target selection, the FPA modifies the predicted direction toward the target and modulates the magnitude of the predicted vector to easily reach the target. The FPA repeats the modification in every prediction time points. To evaluate the improvements of prediction accuracy provided by the feedback, we compared the prediction performances with feedback (FPA) and without feedback. We demonstrated that accuracy of movement prediction can be considerably improved by the FPA combining feedback information. The accuracy of the movement prediction was significantly improved for all subjects (P<0.001) and 32.1% of the mean error was reduced. The BMI performance will be improved by combining feedback information and it will promote the development of a practical BMI system.