Octopuses use a human-like strategy to control precise point-to-point arm movements

One of the key problems in motor control is mastering or reducing the number of degrees of freedom (DOFs) through coordination. This problem is especially prominent with hyper-redundant limbs such as the extremely flexible arm of the octopus. Several strategies for simplifying these control problems have been suggested for human point-to-point arm movements. Despite the evolutionary gap and morphological differences, humans and octopuses evolved similar strategies when fetching food to the mouth. To achieve this precise point-to-point-task, octopus arms generate a quasi-articulated structure based on three dynamic joints. A rotational movement around these joints brings the object to the mouth . Here, we describe a peripheral neural mechanism-two waves of muscle activation propagate toward each other, and their collision point sets the medial-joint location. This is a remarkably simple mechanism for adjusting the length of the segments according to where the object is grasped. Furthermore, similar to certain human arm movements, kinematic invariants were observed at the joint level rather than at the end-effector level, suggesting intrinsic control coordination. The evolutionary convergence to similar geometrical and kinematic features suggests that a kinematically constrained articulated limb controlled at the level of joint space is the optimal solution for precise point-to-point movements.     

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.     

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.     

The effect of the partially restricted sit-to-stand task on biomechanical variables in subjects with and without Parkinson’s disease

The aim of this study was to explore the electromyographic, kinetic and kinematic patterns during a partially restricted sit-to-stand task in subjects with and without Parkinson’s disease (PD). If the trunk is partially restricted, different behavior of torques and muscle activities could be found and it can serve as a reference of the deterioration in the motor performance of subjects with PD. Fifteen subjects participated in this study and electromyography (EMG) activity of the tibialis anterior (TA), soleus (SO), vastus medialis oblique (VMO), biceps femoris (BF) and erector spinae (ES) were recorded and biomechanical variables were calculated during four phases of the movement. Subjects with PD showed more flexion at the ankle, knee and hip joints and increased knee and hip joint torques in comparison to healthy subjects in the final position. However, these joint torques can be explained by the differences in kinematic data. Also, the hip, knee and ankle joint torques were not different in the acceleration phase of movement. The use of a partially restricted sit-to-stand task in PD subjects with moderate involvement leads to the generation of joint torques similar to healthy subjects. This may have important implications for rehabilitation training in PD subjects.     

Robot-based methodology for a kinematic and kinetic analysis of unconstrained,but reproducible upper extremity movement

Although arm movements play an important role in everyday life, there is still a lack of procedures for the analysis of upper extremity movement. The main problems for standardizing the procedure are the variety of arm movements and the difficult assessment of external hand forces. The first problem requires the predefinition of motions, and the second one is the prerequisite for calculation of net joint forces and torques arising during motion. A new methodology for measuring external forces during prespecified, reproducible upper extremity movement has been introduced and validated. A robot-arm has been used to define the motion and 6 degrees of freedom (DoF) force sensor has been attached to it for acquiring the external loads acting on the arm. Additionally, force feedback has been used to help keeping external loads constant. Intra-individual reproducibility of joint angles was estimated by using correlation coefficients to compare a goal-directed movement with robot-guided task. Inter-individual reproducibility has been evaluated by using the mean standard deviation of joint angles for both types of movement. The results showed that both inter- and intra-individual reproducibility have significantly improved by using the robot. Also, the effectiveness of using force feedback for keeping a constant external load has been shown. This makes it possible to estimate net joint forces and torques which are important biomechanical information in motion analysis.     

Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.     

Moving just like you: motor interference depends on similar motility of agent and observer

Recent findings in neuroscience suggest an overlap between brain regions involved in the execution of movement and perception of another's movement. This so-called "action-perception coupling" is supposed to serve our ability to automatically infer the goals and intentions of others by internal simulation of their actions. A consequence of this coupling is motor interference (MI), the effect of movement observation on the trajectory of one's own movement. Previous studies emphasized that various features of the observed agent determine the degree of MI, but could not clarify how human-like an agent has to be for its movements to elicit MI and, more importantly, what 'human-like' means in the context of MI. Thus, we investigated in several experiments how different aspects of appearance and motility of the observed agent influence motor interference (MI). Participants performed arm movements in horizontal and vertical directions while observing videos of a human, a humanoid robot, or an industrial robot arm with either artificial (industrial) or human-like joint configurations. Our results show that, given a human-like joint configuration, MI was elicited by observing arm movements of both humanoid and industrial robots. However, if the joint configuration of the robot did not resemble that of the human arm, MI could longer be demonstrated. Our findings present evidence for the importance of human-like joint configuration rather than other human-like features for perception-action coupling when observing inanimate agents.     

A new non-orthogonal decomposition method to determine effective torques for three-dimensional joint rotation

This paper describes a new non-orthogonal decomposition method to determine effective torques for three-dimensional (3D) joint rotation. A rotation about a joint coordinate axis (e.g. shoulder internal/external rotation) cannot be explained only by the torque about the joint coordinate axis because the joint coordinate axes usually deviate from the principal axes of inertia of the entire kinematic chain distal to the joint. Instead of decomposing torques into three orthogonal joint coordinate axes, our new method decomposes torques into three "non-orthogonal effective axes" that are determined in such a way that a torque about each effective axis produces a joint rotation only about one of the joint coordinate axes. To demonstrate the validity of this new method, a simple internal/external rotation of the upper arm with the elbow flexed at 90 degrees was analyzed by both orthogonal and non-orthogonal decomposition methods. The results showed that only the non-orthogonal decomposition method could explain the cause-effect mechanism whereby three angular accelerations at the shoulder joint are produced by the gravity torque, resultant joint torque, and interaction torque. The proposed method would be helpful for biomechanics and motor control researchers to investigate the manner in which the central nervous system coordinates the gravity torque, resultant joint torque, and interaction torque to control 3D joint rotations.     

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.     

Sensitivity to Differences in the Motor Origin of Drawings: From Human to Robot

This study explores the idea that an observer is sensitive to differences in the static traces of drawings that are due to differences in motor origin. In particular, our aim was to test if an observer is able to discriminate between drawings made by a robot and by a human in the case where the drawings contain salient kinematic cues for discrimination and in the case where the drawings only contain more subtle kinematic cues. We hypothesized that participants would be able to correctly attribute the drawing to a human or a robot origin when salient kinematic cues are present. In addition, our study shows that observers are also able to detect the producer behind the drawings in the absence of these salient kinematic cues. The design was such that in the absence of salient kinematic cues, the drawings are visually very similar, i.e. only differing in subtle kinematic differences. Observers thus had to rely on these subtle kinematic differences in the line trajectories between drawings. However, not only motor origin (human versus robot) but also motor style (natural versus mechanic) plays a role in attributing a drawing to the correct producer, because participants scored less high when the human hand draws in a relatively mechanical way. Overall, this study suggests that observers are sensitive to subtle kinematic differences between visually similar marks in drawings that have a different motor origin. We offer some possible interpretations inspired by the idea of “motor resonance”.     

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.     

Development of an Anthropomorphic Robotic Arm and Hand for Interactive Humanoids

Humanoid robots are designed and built to mimic human form and movement.Ultimately,they are meant to resemble the size and physical abilities of a human in order to function in human-oriented environments and to work autonomously but to pose no physical threat to humans.Here,a humanoid robot that resembles a human in appearance and movement is built using powerful actuators paired with gear trains,joint mechanisms,and motor drivers that are all encased in a package no larger than that of the human physique.In this paper,we propose the construction of a humanoid-applicable anthropomorphic 7-DoF arm complete with an 8-DoF hand.The novel mechanical design of this humanoid arm makes it sufficiently compact to be compatible with currently available narrating-model humanoids,and to be sufficiently powerful and flexible to be functional; the number of degrees of freedom endowed in this robotic arm is sufficient for executing a wide range of tasks,including dexterous hand movements.The developed humanoid arm and hand are capable of sensing and interpreting incoming external force using the motor in each joint current without conventional torque sensors.The humanoid arm adopts an algorithm to avoid obstacles and the dexterous hand is capable of grasping objects.The developed robotic arm is suitable for use in an interactive humanoid robot.     

Kinematic, kinetic and EMG patterns during downward squatting.

The aim of this study was to investigate the kinematic, kinetic, and electromyographic pattern before, during and after downward squatting when the trunk movement is restricted in the sagittal plane. Eight healthy subjects performed downward squatting at two different positions, semisquatting (40 degrees knee flexion) and half squatting (70 degrees knee flexion). Electromyographic responses of the vastus medialis oblique, vastus medialis longus, rectus femoris, vastus lateralis, biceps femoris, semitendineous, gastrocnemius lateralis, and tibialis anterior were recorded. The kinematics of the major joints were reconstructed using an optoelectronic system. The center of pressure (COP) was obtained using data collected from one force plate, and the ankle and knee joint torques were calculated using inverse dynamics. In the upright position there were small changes in the COP and in the knee and ankle joint torques. The tibialis anterior provoked the disruption of this upright position initiating the squat. During the acceleration phase of the squat the COP moved posteriorly, the knee joint torque remained in flexion and there was no measurable muscle activation. As the body went into the deceleration phase, the knee joint torque increased towards extension with major muscle activities being observed in the four heads of the quadriceps. Understanding these kinematic, kinetic and EMG strategies before, during and after the squat is expected to be beneficial to practitioners for utilizing squatting as a task for improving motor function.     

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.     

Inverse dynamic investigation of voluntary leg lateral movements in weightlessness: a new microgravity-specific strategy

This study deals with the quantitative assessment of exchanged forces and torques at the restraint point during whole body posture perturbation movements in long-term microgravity. The work was based on the results of a previous study focused on trunk bending protocol, which suggested that the minimization of the torques exchanged at the restraint point could be a strategy for movement planning in microgravity (J. Biomech. 36(11) (2003) 1691). Torques minimization would lead to the optimization of muscles activity, to the minimization of energy expenditure and, ultimately, to higher movement control capabilities. Here, we focus on leg lateral abduction from anchored stance. The analysis was based on inverse dynamic modelling, leading to the estimation of the total angular momentum at the supporting ankle joint. Results agree with those obtained for trunk bending movements and point out a consistent minimization of the torques exchanged at the restraint point in weightlessness. Given the kinematic features of the examined motor task, this strategy was interpreted as a way to master the rotational dynamic effects on the frontal plane produced by leg lateral abduction. This postural stabilizing effects was the result of a multi-segmental compensation strategy, consisting of the counter rotation of the supporting limb and trunk accompanying the leg raising. The observed consistency of movement-posture co-ordination patterns among lateral leg raising and trunk bending is put forward as a novel interpretative issue of the adaptation mechanisms of the motor system to sustained microgravity, especially if one considers the completely different kinematics of the centre of mass, which was observed in weightlessness for these two motor tasks.     

Age causes a redistribution of joint torques and powers during gait.

At self-selected walking speeds, elderly compared with young adults generate decreased joint torques and powers in the lower extremity. These differences may be actual gait-limiting factors and neuromuscular adaptations with age or simply a consciously selected motor pattern to produce a slower gait. The purpose of the study was to compare joint torques and powers of young and elderly adults walking at the same speed. Twelve elderly and fourteen young adults (ages 69 and 21 yr) walked at 1.48 m/s over a force platform while being videotaped. Hip, knee, and ankle torques and powers were calculated from the reaction force and kinematic data. A support torque was calculated as the sum of the three joint torques. Extensor angular impulse during stance and positive work at each joint were derived from the torques and powers. Step length was 4% shorter and cadence was 4% higher in elderly adults (both P < 0.05) compared with young adults. Support angular impulse was nearly identical between groups, but elderly adults had 58% greater angular impulse and 279% more work at the hip, 50% less angular impulse and 39% less work at the knee, and 23% less angular impulse and 29% less work at the ankle compared with young adults (t-test, all P < 0.05). Age caused a redistribution of joint torques and powers, with the elderly using their hip extensors more and their knee extensors and ankle plantar flexors less than young adults when walking at the same speed. Along with a reduction in motor and sensory functions, the natural history of aging causes a shift in the locus of function in motor performance.     

On the organizing role of nonmuscular forces during performance of a giant circle in gymnastics

Five elite gymnasts performed giant circles on the high bar under different conditions of loading (without and with 6-kg loads attached to the shoulders, waist or ankles). Comparing the gymnasts' kinematic pattern of movement with that of a triple-pendulum moving under the sole influence of nonmuscular forces revealed qualitative similarities, including the adoption of an arched position during the downswing and a piked position during the upswing. The structuring role of nonmuscular forces in the organization of movement was further reinforced by the results of an inverse dynamics analysis, assessing the contributions of gravitational, inertial and muscular components to the net joint torques. Adding loads at the level of the shoulders, waist or ankles systematically influenced movement kinematics and net joint torques. However, with the loads attached at the level of the shoulders or waist, the load-induced changes in gravitational and inertial torques provided the required increase in net joint torque, thereby allowing the muscular torques to remain unchanged. With the loads attached at the level of the ankles, this was no longer the case and the gymnasts increased the muscular torques at the shoulder and hip joints. Together, these results demonstrate that expert gymnasts skillfully exploit the operative nonmuscular forces, employing muscle force only in the capacity of complementary forces needed to perform the task.     

An optimisation-based model for full-body upright reaching movements

An optimal simulation 3D model for full-body upright reaching movements was developed using graphic-based modelling tools (SimMechanics) to generate an inverse dynamics model of the skeleton and using parameterisation methods for a sensory motor controller. The adaptive weight coefficient of the cost function based on the final motor task error (i.e. distance between end-effector and target at the end of movement) was used to correct motor task error and physiological measurements (e.g. joint power, centre of mass displacement, etc.). The output of the simulation models using various cost functions were compared to experimental data from 15 healthy participants performing full-body upright reaching movements. The proposed method can reasonably predict full-body voluntary movements in terms of final posture, joint power, and movement of the centre of mass (COM) using simple algebraic calculations of inverse dynamics and forward kinematics instead of the complicated integrals of the forward dynamics. We found that the combination of several control strategies, i.e. minimising end-effector error, total joint power and body COM produced the best fit of the full-body reaching task.     

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     

Jerk-cost modulations during the practice of rapid arm movements

We examined how hand-trajectory smoothness changed during the practice of a motor task where smoothness was quantified by jerk-cost. Four human subjects each moved his nondominant arm between an upper target and a lower target, while circumnavigating a barrier that extended outward from the vertical plane of the targets. The two targets and the barrier placed boundary constraints on hand trajectories, but the motion was not restrained in any other way. Arm movements were recorded on high-speed ciné film, and linear and angular kinematical data were obtained for all arm segments. In each of 100 practice trials, subjects attempted to minimize movement time. After the practice trials, subjects repeated the same motor task but at movement times corresponding to the slowest, mid-range and fastest motion that had occurred during practice. Thus, jerk-cost could be compared for movements of different speeds during practice and after practice. Because the movement task contained several changes in hand-path direction, the changes in the vector characteristics of the hand accelerations were expected to be important for explaining the modulations in jerk-cost with practice. Total jerk-cost, therefore, was calculated as well as the separate magnitudinal and directional jerk-cost components. During practice, total movement time decreased, hand paths became more parabolic in shape, and significant changes occurred in hand acceleration magnitude, direction, and timing. Total jerk-cost and the magnitudinal and directional jerk-cost components were significantly less when slowest hand movements were compared after practice versus during practice. The decrease in jerk-cost indicated an increased smoothness of the practiced movements.K. Schneider was supported by the German Research Association (Deutsche Forschungsgemeinschaft)