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.     

The Effects of Rhythmicity and Amplitude on Transfer of Motor Learning

We perform rhythmic and discrete arm movements on a daily basis, yet the motor control literature is not conclusive regarding the mechanisms controlling these movements; does a single mechanism generate both movement types, or are they controlled by separate mechanisms? A recent study reported partial asymmetric transfer of learning from discrete movements to rhythmic movements. Other studies have shown transfer of learning between large-amplitude to small-amplitude movements. The goal of this study is to explore which aspect is important for learning to be transferred from one type of movement to another: rhythmicity, amplitude or both. We propose two hypotheses: (1) Rhythmic and discrete movements are generated by different mechanisms; therefore we expect to see a partial or no transfer of learning between the two types of movements; (2) Within each movement type (rhythmic/discrete), there will be asymmetric transition of learning from larger movements to smaller ones. We used a learning-transfer paradigm, in which 70 participants performed flexion/extension movements with their forearm, and switched between types of movement, which differed in amplitude and/or rhythmicity. We found partial transfer of learning between discrete and rhythmic movements, and an asymmetric transfer of learning from larger movements to smaller movements (within the same type of movement). Our findings suggest that there are two different mechanisms underlying the generation of rhythmic and discrete arm movements, and that practicing on larger movements helps perform smaller movements; the latter finding might have implications for rehabilitation.     

A dynamic theory of coordination of discrete movement

The concepts of pattern dynamics and their adaptation through behavioral information, developed in the context of rhythmic movement coordination, are generalized to describe discrete movements of single components and the coordination of multiple components in discrete movement. In a first step we consider only one spatial component and study the temporal order inherent in discrete movement in terms of stable, reproducible space-time relationships. The coordination of discrete movement is captured in terms of relative timing. Using an exactly solvable nonlinear oscillator as a mathematical model, we show how the timing properties of discrete movement can be described by these pattern dynamics and discuss the relation of the pattern variables to observable end-effector movement. By coupling several such component dynamics in a fashion analogous to models of rhythmic movement coordination we capture the coordination of discrete movements of two components. We find the tendency to synchronize the component movements as the discrete analogon of in-phase locking and study its breakdown when the components become too different in their dynamic properties. The concept of temporal stability leads to the prediction that remote compensatory responses occur such as the restore synchronization when one component is perturbed. This prediction can be used to test the theory. We find that the discrete analogon to antiphase locking in rhythmic movement is a tendency to move sequentially, a finding that can also be subjected to empirical test.     

A behavior-based inverse kinematics algorithm to predict arm prehension postures for computer-aided ergonomic evaluation.

In this paper, the computational problem of inverse kinematics of arm prehension movements was investigated. How motions of each joint involved in arm movements can be used to control the end-effector (hand) position and orientation was first examined. It is shown that the inverse kinematics problem due to the kinematic redundancy in joint space is ill-posed only at the control of hand orientation but not at the control of hand position. Based upon this analysis, a previously proposed inverse kinematics algorithm (Wang et Verriest, 1998a) to predict arm reach postures was extended to a seven-DOF arm model to predict arm prehension postures using a separate control of hand position and orientation. The algorithm can be either in rule-based form or by optimization through appropriate choice of weight coefficients. Compared to the algebraic inverse kinematics algorithm, the proposed algorithm can handle the non-linearity of joint limits in a straightforward way. In addition, no matrix inverse calculation is needed, thus avoiding the stability and convergence problems often occurring near a singularity of the Jacobian. Since an end-effector motion-oriented method is used to describe joint movements, observed behaviors of arm movements can be easily implemented in the algorithm. The proposed algorithm provides a general frame for arm postural control and can be used as an efficient postural manipulation tool for computer-aided ergonomic evaluation.     

Characterizing and Predicting Submovements during Human Three-Dimensional Arm Reaches

We have demonstrated that 3D target-oriented human arm reaches can be represented as linear combinations of discrete submovements, where the submovements are a set of minimum-jerk basis functions for the reaches. We have also demonstrated the ability of deterministic feed-forward Artificial Neural Networks (ANNs) to predict the parameters of the submovements. ANNs were trained using kinematic data obtained experimentally from five human participants making target-directed movements that were decomposed offline into minimum-jerk submovements using an optimization algorithm. Under cross-validation, the ANNs were able to accurately predict the parameters (initiation-time, amplitude, and duration) of the individual submovements. We also demonstrated that the ANNs can together form a closed-loop model of human reaching capable of predicting 3D trajectories with VAF >95.9% and RMSE ≤4.32 cm relative to the actual recorded trajectories. This closed-loop model is a step towards a practical arm trajectory generator based on submovements, and should be useful for the development of future arm prosthetic devices that are controlled by brain computer interfaces or other user interfaces.     

Modeling discrete and rhythmic movements through motor primitives: a review

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.     

Distinct timing mechanisms produce discrete and continuous movements

The differentiation of discrete and continuous movement is one of the pillars of motor behavior classification. Discrete movements have a definite beginning and end, whereas continuous movements do not have such discriminable end points. In the past decade there has been vigorous debate whether this classification implies different control processes. This debate up until the present has been empirically based. Here, we present an unambiguous non-empirical classification based on theorems in dynamical system theory that sets discrete and continuous movements apart. Through computational simulations of representative modes of each class and topological analysis of the flow in state space, we show that distinct control mechanisms underwrite discrete and fast rhythmic movements. In particular, we demonstrate that discrete movements require a time keeper while fast rhythmic movements do not. We validate our computational findings experimentally using a behavioral paradigm in which human participants performed finger flexion-extension movements at various movement paces and under different instructions. Our results demonstrate that the human motor system employs different timing control mechanisms (presumably via differential recruitment of neural subsystems) to accomplish varying behavioral functions such as speed constraints.     

Rhythm Patterns Interaction - Synchronization Behavior for Human-Robot Joint Action

Interactive behavior among humans is governed by the dynamics of movement synchronization in a variety of repetitive tasks. This requires the interaction partners to perform for example rhythmic limb swinging or even goal-directed arm movements. Inspired by that essential feature of human interaction, we present a novel concept and design methodology to synthesize goal-directed synchronization behavior for robotic agents in repetitive joint action tasks. The agents’ tasks are described by closed movement trajectories and interpreted as limit cycles, for which instantaneous phase variables are derived based on oscillator theory. Events segmenting the trajectories into multiple primitives are introduced as anchoring points for enhanced synchronization modes. Utilizing both continuous phases and discrete events in a unifying view, we design a continuous dynamical process synchronizing the derived modes. Inverse to the derivation of phases, we also address the generation of goal-directed movements from the behavioral dynamics. The developed concept is implemented to an anthropomorphic robot. For evaluation of the concept an experiment is designed and conducted in which the robot performs a prototypical pick-and-place task jointly with human partners. The effectiveness of the designed behavior is successfully evidenced by objective measures of phase and event synchronization. Feedback gathered from the participants of our exploratory study suggests a subjectively pleasant sense of interaction created by the interactive behavior. The results highlight potential applications of the synchronization concept both in motor coordination among robotic agents and in enhanced social interaction between humanoid agents and humans.     

A hybrid genetic algorithm and expectation maximization method for global gene trajectory clustering

Clustering time-course gene expression data (gene trajectories) is an important step towards solving the complex problem of gene regulatory network modeling and discovery as it significantly reduces the dimensionality of the gene space required for analysis. Traditional clustering methods that perform hill-climbing from randomly initialized cluster centers are prone to produce inconsistent and sub-optimal cluster solutions over different runs. This paper introduces a novel method that hybridizes genetic algorithm (GA) and expectation maximization algorithms (EM) for clustering gene trajectories with the mixtures of multiple linear regression models (MLRs), with the objective of improving the global optimality and consistency of the clustering performance. The proposed method is applied to cluster the human fibroblasts and the yeast time-course gene expression data based on their trajectory similarities. It outperforms the standard EM method significantly in terms of both clustering accuracy and consistency. The biological implications of the improved clustering performance are demonstrated.     

MORE: Mixed Optimization for Reverse Engineering-An Application to Modeling Biological Networks Response via Sparse Systems of Nonlinear Differential Equations

Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.     

Modeling inter-human movement coordination: synchronization governs joint task dynamics

Human interaction partners tend to synchronize their movements during repetitive actions such as walking. Research of inter-human coordination in purely rhythmic action tasks reveals that the observed patterns of interaction are dominated by synchronization effects. Initiated by our finding that human dyads synchronize their arm movements even in a goal-directed action task, we present a step-wise approach to a model of inter-human movement coordination. In an experiment, the hand trajectories of ten human dyads are recorded. Governed by a dynamical process of phase synchronization, the participants establish in-phase as well as anti-phase relations. The emerging relations are successfully reproduced by the attractor dynamics of coupled phase oscillators inspired by the Kuramoto model. Three different methods on transforming the motion trajectories into instantaneous phases are investigated and their influence on the model fit to the experimental data is evaluated. System identification technique allows us to estimate the model parameters, which are the coupling strength and the frequency detuning among the dyad. The stability properties of the identified model match the relations observed in the experimental data. In short, our model predicts the dynamics of inter-human movement coordination. It can directly be implemented to enrich human-robot interaction.     

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.     

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.     

Trajectory formation based on physiological characteristics of skeletal muscles

Human arm trajectories in natural unrestricted reaching movements were studied. They have particular properties such that a hand path is a rather simple straight or curved line, and a tangential velocity profile of hand is bell-shaped. Also these properties are invariant, independent of movement duration and hand-held load. In this study, trajectory formation is investigated on the basis of physiological characteristics of skeletal muscles, and a criterion prescribed by a derivative of isometric muscle torque is proposed. Subsequently, optimal trajectories are formulated under various conditions of movement to account for a planning strategy of human arm trajectories. In addition to such a theoretical approach, human arm trajectories are experimentally observed by a measuring system which provides a visual sensor and a target tracking device, enabling totally unrestricted movements. Then, optimal trajectories are quantitatively evaluated in comparison with experimental data in which essential properties of human arm trajectories are demonstrated. These results support the idea that human arm trajectories are planned in order to minimize the proposed criterion which is determined from physiological aspects. Finally, the physiological advantages of human arm trajectories are discussed with regard to the analysis of observed and optimal trajectories. Received: 2 December 1997 / Accepted in revised form: 20 March 1998     

Planning and execution of multijoint movements

This paper reviews some recent studies related to the generation of simple multijoint arm movements. Two principal issues are considered. The first concern is how movements are represented internally by the central nervous system. There are many possible sets of coordinates that could be used to represent arm movements. Two of the possibilities are reviewed: representation in terms of joint angular motions versus representation in terms of motions of the hand in external space coordinates. A second concern is the transformation from intention to action: how is an internal representation of motion expressed by the neuromuscular system? The computational complexity of this problem is reviewed. A way in which the mechanics of the neuromuscular system could be exploited to simplify this problem is discussed.     

Influence of Vibration on Motor Responses in the Upper Arm Muscles under Stationary Conditions and during Voluntary and Evoked Arm Movements under Limb Unloading Conditions

Locomotion of mammals, including humans, is based on the rhythmic activity of spinal cord circuitries. The functioning of these circuitries depends on multimodal afferent information and on supraspinal influences from the motor cortex. Using the method of transcranial magnetic stimulation (TMS) of arm muscle areas in the motor cortex, we studied the motor evoked potentials (MEP) in the upper arm muscles in stationary conditions and during voluntary and vibration-evoked arm movements. The study included 13 healthy subjects under arm and leg unloading conditions. In the first series of experiments, with motionless limbs, the effect of vibration of left upper arm muscles on motor responses in these muscles was evaluated. In the second series of experiments, MEP were compared in the same muscles during voluntary and rhythmic movements generated by left arm m. triceps brachii vibration (the right arm was stationary). Motionless left arm vibration led to an increase in MEP values in both vibrated muscle and in most of the non-vibrated muscles. For most target muscles, MEP was greater with voluntary arm movements than with vibration-evoked movements. At the same time, a similar MEP modulation in the cycle of arm movements was observed in the same upper arm muscles during both types of arm movements. TMS of the motor cortex significantly potentiated arm movements generated by vibration, but its effect on voluntary movements was weaker. These results indicate significant differences in the degree of motor cortex involvement in voluntary and evoked arm movements. We suppose that evoked arm movements are largely due to spinal rather than central mechanisms of generation of rhythmic movements.     

Parametric stabilization of biological coordination: a theoretical model

In human coordination studies information from the environment may not only pace rhythmic behavior, but also contribute to the observed dynamics, e.g. aphenomenon known as anchoring in the literature. For the paradigmatic caseof bimanual coordination we study these contributions mathematically and develop a model of the interaction between the limb's intrinsic dynamics and environmental signals from a metronome in terms of oscillator equations. We discuss additive versus multiplicative metronomeimpact and show the latter to be more appropriate.Our model describes single limb-metronome interaction, as well as multilimb-metronome interaction. We establish a parametricstabilization term which preserves the characteristicsof bimanual coordination and additionally explains the varyingstability of movement under different metronome conditions, the frequency dependence of the amplitudes of finger movements, anchoring phenomena andgeometries of phase space trajectories. Predictions of our model are tested against experimental observations.     

Interlimb interactions during cyclic in-phase and antiphase movements of arms and legs and their dependence on afferent influences

Coordinated arm and leg movements imply neural interactions between the rhythmic generators of the upper and lower extremities. In ten healthy subjects in the lying position, activity of the muscles of the upper and lower extremities was recorded during separate and joint cyclic movements of the arms and legs with different phase relationships between the movements of the limbs and under various conditions of the motor task. Antiphase active arm movements were characterized by higher muscle activity than during the inphase mode. The muscle activity during passive arm movements imposed by the experimentalist was significantly lower than muscle activity during passive arm movements imposed by the other arm. When loading one arm, the muscle activity in the other, passively moving, arm increased independently from the synergy of arm movements. During a motor task implementing joint antiphase movements of both upper and lower extremities, compared to a motor task implementing their joint in-phase movements, we observed a significant increase in activity in the biceps brahii muscle, the tibialis anterior muscle, and the biceps femoris muscle. Loading of arms in these motor tasks has been accompanied by increased activity in some leg muscles. An increase in the frequency of rhythmic movements resulted in a significant growth of the muscle activity of the arms and legs during their cooperative movements with a greater rate of rise in the flexor muscle activity of the arms and legs during joint antiphase movements. Thus, both the spatial organization of movements and the type of afferent influences are significant factors of interlimb interactions, which, in turn, determine the type of neural interconnections that are involved in movement regulation.     

A review on directional information in neural signals for brain-machine interfaces

Brain-machine interfaces (BMIs) can be characterized by the technique used to measure brain activity and by the way different brain signals are translated into commands that control an effector. We give an overview of different approaches and focus on a particular BMI approach: the movement of an artificial effector (e.g. arm prosthesis to the right) by those motor cortical signals that control the equivalent movement of a corresponding body part (e.g. arm movement to the right). This approach has been successfully applied in monkeys and humans by accurately extracting parameters of movements from the spiking activity of multiple single-units. Here, we review recent findings showing that analog neuronal population signals, ranging from intracortical local field potentials over epicortical ECoG to non-invasive EEG and MEG, can also be used to decode movement direction and continuous movement trajectories. Therefore, these signals might provide additional or alternative control for this BMI approach, with possible advantages due to reduced invasiveness.     

Rhythmic movement and rhythmic auditory cues enhance anticipatory postural adjustment of gait initiation

Abstract

The purpose of this study was to determine whether the rhythmic movements or cues enhance the anticipatory postural adjustment (APA) of gait initiation. Healthy humans initiated gait in response to an auditory start cue (third cue). A first auditory cue was given 8?s before the start cue, and a second auditory cue was given 3?s before the start cue. The participants performed the rhythmic medio-lateral weight shift (ML-WS session), rhythmic anterior-posterior weight shift (AP-WS session), or rhythmic arm swing (arm swing session) in the time between the first and second cues. In the rhythmic cues session, rhythmic auditory cues with a frequency of 1?Hz were given in this time. In the stationary session, the participants maintained stationary stance in this time. The APA and initial step movement preceded by those rhythmic movements or cues were compared with those in the stationary session. The temporal characteristics of the initial step movement of the gait initiation were not changed by the rhythmic movements or cues. The medio-lateral displacement of the APA in the ML-WS and arm swing sessions was significantly greater than that in the stationary session. The anterior–posterior displacement of the APA in the rhythmic cues and arm swing sessions was significantly greater than that in the stationary session. Taken together, the rhythmic movements and cues enhance the APA of gait initiation. The present finding may be a clue or motive for the future investigation for using rhythmic movements or cues as the preparatory activity to enlarge the small APA of gait initiation in the patients with Parkinson’s disease.