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     

Mutual influences of upper and lower extrimities during cyclic movements

The possibility of muscle activation of passive arm during its cyclic movements, imposed by active movements of contralateral arm or by experimenter was studied, as well as the influence of lower extremities cyclic movements onto arm muscles activity. In addition to that the activity of legs muscles was estimated in dependence on motor task condition for arms. Ten healthy supine subjects carried out opposite movements of arms with and without stepping-like movements of both legs. The experiment included three conditions for arm movements: 1) the active movements of both arms; 2) the active movements of one arm, when other entirely passive arm participated in the movement by force; 3) passive arm movement caused by experimenter. In the condition 2) additional load on active arm was applied (30 N and 60 N). In all three conditions the experiment was carried out with arms movements only or together with legs movements. The capability of passive moving arm muscles activation depended on increasing afferent inflow from muscles of contralateral arm was demonstrated. Emerging electrical activity was modulated in the arms movements cycle and depended on the degree of active arm loading. During combined active movements of arms and legs the reduction of activity in the flexor muscles of shoulder and forearm was observed. Concomitant arms movements increased the magnitude ofelectromiographic bursts during passive stepping-like movements in the most of recorded muscles, and the same increasing was only observed in biceps femoris and tibialis anterior muscles during active legs movement. The increasing of loading of one arm caused essential augmentation of EMG-activity in the majority of recording legs muscles. The data obtained are the additional proof of existence of functionally significant neuronal interaction both between arms and between upper and lower extremities, which is evidently depend on the intraspinal neuronal connections.     

A numerical simulation of muscle spindle ensemble encoding during planar movement of the human arm

We address the issue of what proprioceptive information, regarding movement of the human arm, may be provided to the central nervous system by proprioceptors located within muscles of this limb. To accomplish this we developed a numerical simulation which could provide estimates of the length regimes experienced by a set of model receptors located within some of the principal muscles of the human arm during planar movement of this limb. These receptors were assumed to have characteristics analogous to those associated with a simple model of muscle spindle signalling of movement. To this end each spindle had proprioceptive ‘channels’ associated with it. These corresponded to primary and secondary spindle afferent fibers which could provide independent afferent output regarding the parent muscle the spindle monitored. The angles of the shoulder and elbow joints attained by subjects performing a task requiring movement of the right arm in a horizontal plane to a static visual target were recorded. For this angular data the lengths and rates of change of lengths experienced by muscle fascicles, and hence the model spindles, during movement were calculated by means of the numerical simulation. The discharge rates of the simulated spindles during the movement were calculated to derive a measure of the depth of modulation, induced by the movement, for each spindle. These values were then summed for all spindles to provide a first-order approximation of spindle ensemble coding of the movement. Significant correlations (0.0001, Spearman's rank order) were found between the resulting ensemble encodings and, in order of significance, the angular velocity of the shoulder joint (), the tangential velocity of the hand (), and the angular velocity of the elbow joint (). Correlations between the angular positions of the shoulder () and elbow () were lower. These findings indicate that the ensemble profiles of the simulated muscle spindles, encode information regarding kinematic parameters of movements related to both intrinsic and extrinsic coordinate systems. This suggests that motor structures capable of deriving such an ensemble encoding would be in a position to perform the sensory-motor transformations between intrinsic and extrinsic frames of reference necessary for controlling movements planned in extrinsic coordinates. Received: 12 August 1994 / Accepted in revised form: 17 June 1996     

1998 ISEK Congress Keynote Lecture: Multi-muscle control in human movements

It has been suggested that the coordination of the activity of multiple muscles results from the comparison of the actual configuration of the body with a referent configuration specified by the nervous system so that the recruitment and gradation of the activity of each skeletal muscle depend on the difference between these two configurations. Active movements may be produced by the modification of the referent configuration. The hypothesis predicts the existence of a global minimum in electromyographic (EMG) activity of multiple muscles during movements involving reversals in direction. This prediction was tested in five subjects by analysing movements resembling the act of reaching for an object placed beyond one's reach from a sitting position. In such movements, initially sitting subjects raise their body to a semi-standing position and then return to sitting. Consistent with the hypothesis is the observation of a global minimum in the surface EMG activity of 16 muscles of the arm, trunk and leg at a specific phase of the movement. When the minimum occurred, EMG activity of each muscle did not exceed 2–7% of its maximal activity during the movement. As predicted, global EMG minima occurred at the phase corresponding to the reversal in movement direction, that is, during the transition from raising to lowering of the body. The global EMG minimum may represent the point at which temporal matching occurs between the actual and the referent body configurations. This study implies a specific link between motor behavior and the geometric shape of the body modified by the brain according to the desired action.     

Thumb postures and physical loads during mobile phone use – A comparison of young adults with and without musculoskeletal symptoms

The aim of this study was to evaluate thumb postures, thumb movements and muscle activity when using mobile phones for SMS messaging and to determine whether there were differences in these exposures (a) across various mobile phone tasks, (b) between gender and (c) between subjects with and without musculoskeletal symptoms in shoulders and upper extremities. Fifty-six young adults (15 healthy and 41 with musculoskeletal symptoms) performed a series of distinct tasks on a mobile phone. Muscular load in four forearm/hand muscles in the right arm and the right and left trapezius muscles were measured using electromyography (EMG). Thumb movements were registered using an electrogoniometer. The results showed that postures (sitting or standing) and the type of mobile phone task (holding the phone versus texting) affected muscle activity and thumb positions. Females compared to males had higher muscle activity in the extensor digitorum and the abductor pollicis longus when entering SMS messages and tended to have greater thumb abduction, higher thumb movement velocities and fewer pauses in the thumb movements. Subjects with symptoms had lower muscle activity levels in the abductor pollicis longus and tended to have higher thumb movement velocities and fewer pauses in the thumb movements compared to those without symptoms.     

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     

Mutual influences of upper and lower extremities during cyclic movements

The possibility for the activation of muscles in a passive arm during its cyclic movements imposed by active movements of the contralateral arm or by an experimenter and the effect that the movements of lower extremities have on the activity of the arm muscles have been studied. In addition, the activity of the leg muscles was studied as dependent on the motor task performed by the arms. Ten healthy subjects performed antiphase arm movements with and without stepping-like movements of both legs in the supine position. The experiment was performed under three conditions for the arm movements: (1) both arms performed active movements; (2) one arm performed active movements, and the contralateral arm, being entirely passive, was forced to participate in movements; (3) the movement of the passive arm was caused by an experimenter. Under condition (2), additional loadings of 30 and 60 N were applied to the active arm. Under all conditions, the arm movements were performed with and without leg movements. The possibility for the activation of muscles in the arm performing passive movements has been demonstrated. To a large extent, this is possible due to an increase in the afferent inflow from the muscles of the contralateral arm. The electrical activity was modulated during cyclic arm movements and depended on the level of loading of the active arm. During the combined active movements of the arms and legs, the reduction in the activity of the flexor muscles of the shoulder and forearm was observed. In the case of passive stepping-like movements, the concomitant arm movements increased the magnitude of electromyographic bursts in most of the examined leg muscles. During active leg movements, a similar increase in electromyographic bursts was observed only in the m. biceps femoris (BF) and the anterior tibial muscle. An increase in the loading of one arm caused a significant increase in the EMG activity in most examined muscles of the legs. The data obtained provide additional proof for the existence of a functionally significant neuronal interaction between the arms, as well as between the upper and lower extremities, which is probably due to intraspinal neuronal connections.     

Correction for skin displacement errors in movement analysis of the horse

In movement analysis of the horse, large errors result from movements of the skin with respect to the underlying bones. A generally applicable, two-dimensional, method for correction of these skin-movement errors in kinematic data has been developed. It was tested on a kinematic analysis of the hindlimb in a walking pony. The results indicate that without correction for skin-movement errors, misreadings of up to 15 degrees in the knee angle and 30% in the moment arm of the gastrocnemius muscle can be expected.     

Effect of Tendon Vibration on Hemiparetic Arm Stability in Unstable Workspaces

Sensory stimulation of wrist musculature can enhance stability in the proximal arm and may be a useful therapy aimed at improving arm control post-stroke. Specifically, our prior research indicates tendon vibration can enhance stability during point-to-point arm movements and in tracking tasks. The goal of the present study was to investigate the influence of forearm tendon vibration on endpoint stability, measured at the hand, immediately following forward arm movements in an unstable environment. Both proximal and distal workspaces were tested. Ten hemiparetic stroke subjects and 5 healthy controls made forward arm movements while grasping the handle of a two-joint robotic arm. At the end of each movement, the robot applied destabilizing forces. During some trials, 70 Hz vibration was applied to the forearm flexor muscle tendons. 70 Hz was used as the stimulus frequency as it lies within the range of optimal frequencies that activate the muscle spindles at the highest response rate. Endpoint position, velocity, muscle activity and grip force data were compared before, during and after vibration. Stability at the endpoint was quantified as the magnitude of oscillation about the target position, calculated from the power of the tangential velocity data. Prior to vibration, subjects produced unstable, oscillating hand movements about the target location due to the applied force field. Stability increased during vibration, as evidenced by decreased oscillation in hand tangential velocity.     

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.     

On the possibility of linear modelling the human arm neuromuscular apparatus

It has been widely claimed that linear models of the neuromuscular apparatus give very inaccurate approximations of human arm reaching movements. The present paper examines this claim by quantifying the contributions of the various non-linear effects of muscle force generation on the accuracy of linear approximation. We performed computer simulations of a model of a two-joint arm with six monarticular and biarticular muscles. The global actions of individual muscles resulted in a linear dependence of the joint torques on the joint angles and angular velocities, despite the great non-linearity of the muscle properties. The effect of time delay in force generation is much more important for model accuracy than all the non-linear effects, while ignoring this time delay in linear approximation results in large errors. Thus, the viscosity coefficients are rather underestimated and some of them can even be paradoxically estimated to be negative. Similarly, our computation showed that ignoring the time delay resulted in large errors in the estimation of the hand equilibrium trajectory. This could explain why experimentally estimated hand equilibrium trajectories may be complex, even during a simple reaching movement. The hand equilibrium trajectory estimated by a linear model becomes simple when the time delay is taken into account, and it is close to that actually used in the non-linear model. The results therefore provide a theoretical basis for estimating the hand equilibrium trajectory during arm reaching movements and hence for estimating the time course of the motor control signals associated with this trajectory, as set out in the equilibrium point hypothesis. Received: 17 February 1999 / Accepted in revised form: 22 October 1999     

Trunk Muscle Activation at the Initiation and Braking of Bilateral Shoulder Flexion Movements of Different Amplitudes

The aim of this study was to investigate if trunk muscle activation patterns during rapid bilateral shoulder flexions are affected by movement amplitude. Eleven healthy males performed shoulder flexion movements starting from a position with arms along sides (0°) to either 45°, 90° or 180°. EMG was measured bilaterally from transversus abdominis (TrA), obliquus internus (OI) with intra-muscular electrodes, and from rectus abdominis (RA), erector spinae (ES) and deltoideus with surface electrodes. 3D kinematics was recorded and inverse dynamics was used to calculate the reactive linear forces and torque about the shoulders and the linear and angular impulses. The sequencing of trunk muscle onsets at the initiation of arm movements was the same across movement amplitudes with ES as the first muscle activated, followed by TrA, RA and OI. All arm movements induced a flexion angular impulse about the shoulders during acceleration that was reversed during deceleration. Increased movement amplitude led to shortened onset latencies of the abdominal muscles and increased level of activation in TrA and ES. The activation magnitude of TrA was similar in acceleration and deceleration where the other muscles were specific to acceleration or deceleration. The findings show that arm movements need to be standardized when used as a method to evaluate trunk muscle activation patterns and that inclusion of the deceleration of the arms in the analysis allow the study of the relationship between trunk muscle activation and direction of perturbing torque during one and the same arm movement.     

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.     

Motor commands for fast point-to-point arm movements are customized for small changes in inertial load

For repeated point-to-point arm movements it is often assumed that motor commands are customized in a trial-to-trial manner, based on previous endpoint error. To test this assumption, we perturbed movement execution without affecting the endpoint error by using a modest manipulation of inertia. Participants made point-to-point elbow flexion and extension movements in the horizontal plane, under the instruction to move as fast as possible from one target area to another. In selected trials the moment of inertia of the lower arm was increased or decreased by 25%. First, we found that an unexpected increase or decrease of inertia did not affect the open loop controlled part of the movement path (and thus endpoint error was not affected). Second, we found that when the increased or decreased inertia was presented repeatedly, after 5-11 trials motor commands were customized: the first 100ms of agonistic muscle activity in the smoothed and rectified electromyographic signal of agonistic muscles was higher for the high inertia compared to the low inertia. We conclude that endpoint error is not the only parameter that is used to evaluate if motor commands lead to movements as planned.     

Impaired agonists recruitment during voluntary arm movements in patients affected by spasmodic torticollis

We have investigated the electromyographic (EMG) and kinematic characteristics of horizontal arm extension movements in patients affected by idiopathic cervical dystonia (ICD) as well as in normal subjects. In spite of the lack of an overt dystonic involvement of the muscles acting at upper arm level, all these patients were considerably bradykinetic. Although the degree of bradykinesia observed was comparable to that previously reported for the body segment directly affected by this patholgy (21,15,8), the EMG analysis of the agonist muscles indicated a specific pathophysiological mechanism. In particular, the recruitment of the posterior deltoid (pD) in ICD patients was severely impaired within the initial phase (130 ms) of the movement. On the other hand, within the same time span, the activation of the mD, a muscle that plays a more important postural role than the pD, was not significantly different between patients and normal subjects. This reduced recruitment in the initial phase of the AG1 appears responsible of the slowness of voluntary movements.     

Normalization of electromyogram in the neck-shoulder region

Linear and curvilinear electromyogram (EMG) normalization methods were compared among ten healthy men during a simulated work cycle demanding attention and static holding of the arm (Solitaire test). Maximal voluntary contractions (MVC) and gradually increasing contractions up to 70% of MVC were used for normalization in different arm postures. The test contractions studied included inward and outward rotations, abduction, shoulder elevation, and flexion in different arm positions. The shoulder load moment was calculated for the flexion tests using a simple two-dimensional model. The effect of arm posture on the EMG versus shoulder load moment relationship was studied on the following muscles: supraspinatus, infraspinatus, trapezius (three parts), deltoid (two parts) and pectoralis major. All muscles participated in the MVC tests performed, and its was not possible to suggest a single recommended test for each muscle. Differences in normalized EMG median values ranging up to 30% of MVC were found between linear and curvilinear normalization methods. Short-term repeatability of normalization based on a contraction with gradually increasing force was good. Arm posture affected the relationships between shoulder load moment and EMG activity of all muscles studied. Arm posture did not, however, have a significant effect on the estimated amplitude probability distribution functions during the simulated work task. Therefore, at least for the tasks studied, the principle of normalizing in the middle position of the range of movement was deemed acceptable.     

Effects of head position on errors in 3-D pointing to remembered locations

The accuracy of pointing movements performed under different head positions to remembered target locations in 3-D space was studied in healthy persons. The subjects fixated a visual target, then closed their eyes and after 1.0 sec performed the targeted movement with their right arm. The target (a point light source) was presented in random order by a programmable robot arm at one of five space locations. The accuracy of pointing movements was examined in a spherical coordinate system centered in respect with the shoulder of the responding arm. The pointing movements were most accurate under natural eye-head coordination. With the head fixed in the straight-ahead position, both the 3-D absolute error and its standard deviation increased significantly. At the same time, individual components of spatial error (directional and radial) did not change significantly. With the head turned to the rightmost or leftmost position, the pointing accuracy was disturbed within larger limits than under head-fixed condition. The main contributors to the 3-D absolute error were the changes in the azimuth error. The latter depended on the direction of the head-turn: the rightmost turn either increased leftward or decreased rightward shift, and conversely, the left turn increased rightward shift or decreased leftward shift of the target-directed movements.It is suggested that the increased inaccuracy of pointing under head-fixed condition reflected the impairment of the eye-head coordination underlying gaze orientation, and increased inaccuracy under the head-turned condition may be explained by changes in the internal representation of the head and target position in space.Neirofiziologiya/Neurophysiology, Vol. 26, No. 2, pp. 122–131, March–April, 1994.     

Optimization and evaluation of a proportional derivative controller for planar arm movement

In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.     

Changes in limb dynamics during the practice of rapid arm movements

In our study we examined Bernstein's hypothesis that practice alters the motor coordination among the muscular and passive joint moments. In particular, we conducted dynamical analyses of a human multisegmental movement during the practice of a task involving the upper extremity. Seven male human volunteers performed maximal-speed, unrestrained vertical arm movements whose upward and downward trajectories between two target endpoints required the hand to round a barrier, resulting in complex shoulder, elbow, and wrist joint movements. These movements were recorded by high-speed ciné film, and myopotentials from selected upper-extremity muscles were recorded. The arm was modeled as interconnected rigid bodies, so that dynamical interactions among the upper arm, forearm, and hand could be calculated. With practice, subjects achieved significantly shorter movement times. As movement times decreased, all joint-moment components (except gravity) increased, and the moment-time and EMG profiles were changed significantly. Particularly during reversals in movement direction, the changes in moment-time and EMG profiles were consistent with Bernstein's hypothesis relating practice effects and intralimb coordination: with practice, motor coordination was altered so that individuals employed reactive phenomena in such a way as to use muscular moments to counterbalance passive-interactive moments created by segment movements.