Control of Three- and Four-Joint Arm Movement: Strategies for a Manipulator With Redundant Degrees of Freedom

Control of arm movements when the number of joints exceeds the degrees of freedom necessary for the task requires a strategy for selecting specific arm configurations out of an infinite number of possibilities. This report reviews strategies used by human subjects to control the shoulder, elbow, and wrist (three degrees of freedom) while moving a pointer to positions in a horizontal plane (two degrees of freedom). Analysis of final arm configurations assumed when the pointer was at the target showed the following: (a) Final arm configurations were virtually independent of the configuration at the start of the pointing movement, (b) subjects avoided configurations subjectively felt to be uncomfortable (e.g., those with extreme flexion or extension of the wrist), and (c) the results could be simulated by assigning hypothetical cost functions to each joint and selecting the arm configuration that minimized the sum of the costs. The fitted cost functions qualitatively agreed with psychophysically determined comfort; they appeared to depend on joint angle and on muscular effort. Simple neural networks can learn implicit representations of these cost functions and use them to specify final arm configurations. The minimum cost principle can be extended to movements that use the fingers as a fourth movable segment. For this condition, however, experiments showed that final configurations of the arm depended upon initial configurations. Analysis of movement trajectories for arms with three degrees of freedom led to a control model in which the minimum cost principle is augmented by a mechanism that distributes required joint movements economically among the three joints and a mechanism that implements a degree of mass-spring control.     

The Organization of Multisegmental Pulls Made by Standing Humans: II. Submaximal Pulls

Previously, an autonomous oscillator model with three parameters was derived that describes the relationship between anterior-posterior center of mass motions and pulling force for near-maximal, bimanual pulls made by standing subjects (Michaels, Lee, Pai, 1993). The present study evaluated the extent to which a full range of pulling forces could be fit by the model and how the model's three parameters changed with intended pulling force. How much variation in force each parameter could contribute was determined by simulating the model. Qualitative and quantitative analyses of pulls made by 6 well-practiced subjects at 5prcent;, 10prcent;, 20prcent;, 40prcent;, 60prcent;, 80prcent;, and 95prcent; of their maximum pulling force revealed that the model holds well, except for the least forceful pulls of some subjects. Two parameters appeared to be controlled; one, related to the position of the center of pressure, varied most among less forceful pulls; the second, related to the position of the center of mass at the time of handle-force onset, varied most among more forceful pulls. How these parameters might be set is discussed.     

The Organization of Multisegmental Pulls Made by Standing Humans: II. Submaximal Pulls

Previously, an autonomous oscillator model with three parameters was derived that describes the relationship between anterior-posterior center of mass motions and pulling force for near-maximal, bimanual pulls made by standing subjects (Michaels, Lee, & Pai, 1993). The present study evaluated the extent to which a full range of pulling forces could be fit by the model and how the model's three parameters changed with intended pulling force. How much variation in force each parameter could contribute was determined by simulating the model. Qualitative and quantitative analyses of pulls made by 6 well-practiced subjects at 5%, 10%, 20%, 40%, 60%, 80%, and 95% of their maximum pulling force revealed that the model holds well, except for the least forceful pulls of some subjects. Two parameters appeared to be controlled; one, related to the position of the center of pressure, varied most among less forceful pulls; the second, related to the position of the center of mass at the time of handle-force onset, varied most among more forceful pulls. How these parameters might be set is discussed.     

Change in the organization of degrees of freedom with learning

The authors examined the effects of learning on the change in the organization of the mechanical and dynamical degrees of freedom in 5 men who performed a ski-simulator task. A 3-dimensional analysis of the motion of the total-body center of mass and the segmental centers of mass (head, torso, thighs, and shanks) over practice showed that the recruitment of mechanical degrees of freedom was strongly influenced by anatomical and task constraints. Principal components analysis of the body segments' motions revealed that practice shifted their relative contributions but did not change the number of principal components. The present findings show that there can be independence in the patterns of change in the mechanical and dynamical degrees of freedom that arise from practice.     

Quantitative analysis of finger motion coordination in hand manipulative and gestic acts

This article reports an experimental study that aimed to quantitatively analyze motion coordination patterns across digits 2-5 (index to little finger), and examine the kinematic synergies during manipulative and gestic acts. Twenty-eight subjects (14 males and 14 females) performed two types of tasks, both right-handed: (1) cylinder-grasping that involved concurrent voluntary flexion of digits 2-5, and (2) voluntary flexion of individual fingers from digit 2 to 5 (i.e., one at a time). A five-camera opto-electronic motion capture system measured trajectories of 21 miniature reflective markers strategically placed on the dorsal surface landmarks of the hand. Joint angular profiles for 12 involved flexion-extension degrees of freedom (DOF's) were derived from the measured coordinates of surface markers. Principal components analysis (PCA) was used to examine the temporal covariation between joint angles. A mathematical modeling procedure, based on hyperbolic tangent functions, characterized the sigmoidal shaped angular profiles with four kinematically meaningful parameters. The PCA results showed that for all the movement trials (n = 280), two principal components accounted for at least 98% of the variance. The angular profiles (n = 2464) were accurately characterized, with the mean (+/-SD) coefficient of determination (R2) and root-mean-square-error (RMSE) being 0.95 (+/-0.12) and 1.03 degrees (+/-0.82 degrees ), respectively. The resulting parameters which quantified both the spatial and temporal aspects of angular profiles revealed stereotypical patterns including a predominant (87% of all trials) proximal-to-distal flexion sequence and characteristic interdependence--involuntary joint flexion induced by the voluntarily flexed joint. The principal components' weights and the kinematic parameters also exhibited qualitatively similar variation patterns. Motor control interpretations and new insights regarding the underlying synergistic mechanisms, particularly in relation to previous findings on force synergies, are discussed.     

The visual perception of rigid motion from constant flow fields

Four experiments investigated observers’ judgments of rigidity for different types of optical motion. The depicted structural deformations were of two types: (1) those with nonparallel image trajectories that are detectable from the first-order spatiotemporal relations between pairs of views; and (2) those with parallel image trajectories that can only be detected from higher order relations among three or more views. Patterns were composed of smooth flow fields in Experiments 1 and 3, and of wire frame figures in Experiments 2 and 4. For both types of display, the nonrigidity detectable from the first-order spatiotemporal structure of the motion sequence was much more salient than the deformation detectable only from the higher order spatiotemporal structure. These results indicate that observers’ judgments of rigidity are based primarily on a two-view analysis, but that some useful information can be obtained under appropriate circumstances from higher order spatiotemporal relations among three or more views.     

A simulation study of the degrees of freedom of movement in reaching and grasping

The question of independently controlled components in the act of reaching and grasping has attracted interest experimentally and theoretically. Data from 35 studies were recently found consistent with simulated kinematic finger and thumb trajectories optimised for minimum jerk. The present study closely reproduces those trajectories using a discrete-time model based on minimum acceleration. That model was further used to generate two-dimensional trajectories for finger and thumb to reach and grasp an elliptical object with varying position and/or orientation. Orthogonalisation of these four trajectories revealed one degree of freedom when direction of reach was constant and two degrees of freedom when direction of reach varied, irrespective of object distance and orientation. These simulations indicate that reach and grasp movements contain redundancy that is removable by formation of task-dependent synergies. As skilled movement can be planned and executed in a low dimension workspace, control of these independent components lessens central workload.     

A comparison of the effects of spatial separation on apparent motion in the auditory and visual modalities

In the present investigation, the effects of spatial separation on the interstimulus onset intervals (ISOIs) that produce auditory and visual apparent motion were compared. In Experiment 1, subjects were tested on auditory apparent motion. They listened to 50-msec broadband noise pulses that were presented through two speakers separated by one of six different values between 0 degrees and 160 degrees. On each trial, the sounds were temporally separated by 1 of 12 ISOIs from 0 to 500 msec. The subjects were instructed to categorize their perception of the sounds as "single," "simultaneous," "continuous motion," "broken motion," or "succession." They also indicated the proper temporal sequence of each sound pair. In Experiments 2 and 3, subjects were tested on visual apparent motion. Experiment 2 included a range of spatial separations from 6 degrees to 80 degrees; Experiment 3 included separations from .5 degrees to 10 degrees. The same ISOIs were used as in Experiment 1. When the separations were equal, the ISOIs at which auditory apparent motion was perceived were smaller than the values that produced the same experience in vision. Spatial separation affected only visual apparent motion. For separations less than 2 degrees, the ISOIs that produced visual continuous motion were nearly equal to those which produced auditory continuous motion. For larger separations, the ISOIs that produced visual apparent motion increased.     

Effect of a terminal constraint on control of balance during sit-to-stand

The speed at which sit-to-stand (STS) motions are performed and the subsequent terminal constraint upon upright stance can present subjects with contradictory goals. Previous findings suggested that subjects might adopt a strategy of limiting the peak horizontal momentum of the center of mass (CM), and perhaps of body segments as well, regardless of the speed of ascent. The primary purpose of this study was to test the hypothesis that the limitation in CM momentum is related to the constraint on upright stance at the termination of the task. The secondary purpose was to describe the contribution of the shank, thigh, and upper body (head-arm-trunk) to the peak horizontal momentum of the CM under each test condition. Nine healthy adult males rose from a seated position under the following three conditions: (a) at natural speeds (natural STS); (b) as fast as possible (fast STS); and (c) as fast as possible, followed by falling forward while keeping the feet fixed and using the arms on a support bar to stop the fall (fast STS+fall). The results showed that the peak horizontal momentum of the CM did not change substantially from the natural to fast STS, but increased significantly from the fast STS to the fast STS+fall. These findings are consistent with the hypothesis that limiting peak horizontal momentum of the CM may reflect a movement control strategy related to maintaining equilibrium at the termination of the voluntary task of rising from a chair. The momentum profile of the upper body, but not of the thigh or shank, remained constant across all experimental conditions, suggesting that the motion of the upper body may be tightly controlled in STS, regardless of the altered constraint on balance.     

Free(z)ing Degrees of Freedom in Skill Acquisition

This study reports an empirical investigation into Bernstein's (1967) ideas that in the early stages of the acquisition of a movement skill the coordination problem is reduced by an initial freezing out of degrees of freedom, followed later in the learning process by the release of these degrees of freedom and their incorporation into a dynamic, controllable system. “Freezing” degrees of freedom was made operational both as a rigid fixation of individual degrees of freedom and as the formation of rigid couplings between multiple degrees of freedom. Five subjects practiced slalom-like ski movements on a ski apparatus for 7 consecutive days. Results showed that at the early phases of learning, the joint angles of the lower limbs and torso displayed little movement, as expressed by their standard deviations and ranges of angular motion, whereas joint couplings were high, as shown by the relatively high cross correlations between joint angles. Over practice, angular movement significantly increased in all joint angles of the lower limbs and torso, although the cross correlations decreased. Support for the processes of freezing and releasing degrees of freedom was thus given at both levels of operationalization. In addition, a consistent change from laterally symmetric to laterally asymmetric cross-correlation patterns were observed as a function of practice. Overall, the findings provide empirical support for Bernstein's ideas regarding the mastery of redundant degrees of freedom in the acquisition of coordination.     

Auditory apparent motion under binaural and monaural listening conditions

This investigation examined the ability of listeners to perceive apparent motion under binaural and monaural listening conditions. Fifty-millisecond broadband noise sources were presented through two speakers separated in space by either 10 degrees, 40 degrees, or 160 degrees, centered about the subject's midline. On each trial, the sources were temporally separated by 1 of 12 interstimulus onset intervals (ISOIs). Six listeners were asked to place their experience of these sounds into one of five categories (single sound, simultaneous sounds, continuous motion, broken motion, or successive sounds), and to indicate either the proper temporal sequence of presentation or the direction of motion, depending on whether or not motion was perceived. Each listener was tested at all spatial separations under binaural and monaural listening conditions. Motion was perceived in the binaural listening condition at all spatial separations tested for ISOIs between 20 and 130 msec. In the monaural listening condition, motion was reliably heard by all subjects at 10 degrees and 40 degrees for the same range of ISOIs. At 160 degrees, only 3 of the 6 subjects consistently reported motion. However, when motion was perceived in the monaural condition, the direction of motion could not be determined.     

Coordination Patterns in Ball Bouncing as a Function of Skill

By observing the coordination patterns of people of different ages and skill levels bouncing a ball, the authors addressed hypotheses regarding (a) the relative increase and decrease of degrees of freedom with learning and (b) the order of progression in the changing organization of those degrees of freedom with development and learning. The movement patterns of the dominant arm and hand of subjects at various skill levels were contrasted in a cross-sectional design so that the way movement organization changes as a function of practice could be examined. Nine subjects aged between 4 and 22 years bounced a basketball at a preferred rhythm while standing still. Each performance trial was videotaped, and motions of arm and ball were digitized. Statistical analyses were made of linear and angular body motions: pairwise correlations and multiple regressions, amplitude and period variability, phase relations, and spectral and coherency measures. The coordination patterns revealed that (a) the movement patterns of less skilled subjects were more variable than those of more skilled subjects and (b) the motions of the articulators showed directional changes as a function of skill level that began both proximally and distally and moved toward the center of the effector chain with practice. The findings point up the relevance of studying change of system organization for understanding control and coordination.     

Effects of single trial of heart-rate biofeedback on the arterial blood pressure, ventilation volume, and oxygen consumption during ramp bicycling exercise

We examined whether the heart rate attenuation resulting from a single trial of biofeedback during exercise occurs without any changes in oxygen consumption (VO2), ventilation volume (V(E)), and mean arterial blood pressure (M(AP)) although these variables are essential determinants for the heart-rate response during exercise. 35 subjects exercised on a cycle ergometer under two conditions while they exercised only (Control) or were trying to decrease the heart-rate response as low as possible by monitoring their own heart-rate responses as Single trial of biofeedback signals. 17 subjects could attenuate their heart rate (Can group), and their heart-rate reduction during Single trial of biofeedback was 5+/-1 bpm. The remaining subjects were unable to reduce heart rate (Cannot group). The heart-rate attenuation during Single trial of biofeedback in the Can group occurred independently of changes in VO2 and MAP but was accompanied by a significant decrease in V(E) and rating of perceived exertion (RPE). However, there was a similar decrease in V(E) in the Cannot group. These findings suggested that the heart-rate attenuation during Single trial of biofeedback was not induced by the metabolic demand of VO2 and the regulations of M(AP) and V(E) during exercise. Other mechanisms, which are probably related to the reduction of RPE, might play an important role in the heart-rate attenuation during a Single trial of biofeedback.     

The effect of sound on visual apparent movement

Twelve subjects found the longest possible interstimulus interval (ISI) at which they perceived continuous apparent motion of one light instead of partial motion or succession between two lights. In the visual condition, two lights only were presented. In the bimodal conditions, binaurally presented tones were presented synchronously with the lights, and the lights and tones were either spatially congruent (in phase) or incongruent (180 degrees out of phase). Bimodal presentations lowered the upper ISI threshold for the perception of visual apparent motion, and the reduction was greater when the tones and lights were spatially congruent. The threshold reduction may be caused by a perceptual inference about localization of the lights in space or by a change in visual persistence.     

Learning to coordinate redundant degrees of freedom in a dynamic balance task

The present study investigated Bernstein's [The co-ordination and regulation of movements, 1967] proposal regarding the three stages of learning in the changing coordination and control of redundant joint-space degrees of freedom. Six participants practiced maintaining balance on a moving platform that was sinusoidally translated in the anterior-posterior direction for 30 trials on day 1 and 10 trials on day 2. At the beginning of practice, the motion of the torso and limb segments was less coherent in the attempt to compensate for the movement of the support surface in retaining a balanced posture. However, with practice, the organization of a compensatory postural coordination mode became highly coherent and also progressively utilized the passive, inertial forces generated by the movement of the support surface. The findings support the propositions that: (a) the pathway of change over time in the coordination pattern of the torso and joint motions depends on the task goal and constraints to action and (b) the changes in limb and torso motion are in support of the learning of a global body center of mass/platform dynamic.     

To Switch or Not to Switch: Recruitment of Degrees of Freedom Stabilizes Biological Coordination

Recruitment and suppression processes were studied in the swinging-pendulum paradigm (cf. P. N. Kugler & M. T. Turvey, 1987). The authors pursued the hypothesis that active recruitment of previously unmeasured degrees of freedom serves to stabilize an antiphase bimanual coordination pattern and thereby obviates the need for pattern switching from an antiphase to an in-phase coordination pattern, a key prediction of the H. Haken, J. A. S. Kelso, and H. Bunz (1985) model. In Experiment 1, 7 subjects swung single hand-held pendulums in time with an auditory metronome whose frequency increased. Pendulum motion changed from planar (2D) to elliptical (3D), and forearm motion (produced by elbow flexion-extension) was recruited with increasing movement rate for cycling frequencies typically above the pendulum's eigenfrequency. In Experiment 2, 7 subjects swung paired pendulums in either an in-phase or an antiphase coordinative mode as movement rate was increased. With the systematic increase in movement rate, the authors attempted to induce transitions from the antiphase to the in-phase coordinative pattern, with loss of stability the key mechanism of pattern change. Transitions from the antiphase to the in-phase coordinative mode were not observed. Pattern stability, as defined by the variability of the phase relation between the pendulums, was affected only a little by increasing movement rate. As in the single-pendulum case, pendulum motion changed from planar to elliptical, and forearm motion was recruited with increasing cycling frequency. Those results reveal a richer dynamics than previously observed in the pendulum paradigm and support the hypothesis that recruitment processes stabilize coordination in biomechanically redundant systems, thereby reducing the need for pattern switching.     

The role of motion direction selective extrastriate regions in reading: a transcranial magnetic stimulation study

Why reading ability is correlated with motion processing ability is perplexing. Activity in motion direction processing regions (Area V5/MT+) was perturbed by means of repetitive transcranial magnetic stimulation (rTMS) to examine its effect on reading. A functional probe (significant shortening of the motion aftereffect) was used to identify Area V5/MT+. Right-handed participants (8 m, 8 f) received three 7.5 min blocks of rTMS, after which two phonological and one orthographic reading tasks were administered. Application of rTMS to Area V5/MT+ (as compared to a non-rTMS baseline) significantly decreased performance only during non-word naming. The pattern of naming errors and the absence of deficits on the second phonological task were not consistent with a role for Area V5/MT+ in phonological decoding. Instead, its role in reading may be limited to image stabilization and/or letter localization.     

Development of visual center of mass localization for grasp point selection

Adults assess precisely the center of mass (CM) of single-bodied objects and choose grasping points that span an axis through or close to the center of mass when lifting them. The present study examined how children and adults assess the CM when lifting two-bodied objects (barbells) and how this ability develops. Four- to five-year olds, 6- to 7-year olds, 9- to 11-year olds and adults were required to grasp and lift symmetrically and asymmetrically proportioned miniature barbells and their grasping points were recorded. While the 4- to 5-year olds grasped near the center of the barbell, accuracy of assessing the correct CM improved linearly with age. Although adults grasped close to the CM, their CM determination follows only an approximation of the physical law.     

Constructing naive theories of motion on the fly

People often make erroneous predictions about the trajectories of moving objects. McCloskey (1983a, 1983b) and others have suggested that many of these errors stem from well-developed, but naive, theories of motion. The studies presented here examine the role of naive impetus theory in people’s judgments of motion. Subjects with and without formal physics experience were asked to draw or select from alternatives the trajectories of moving objects that were presented in various manners. Results from two experiments indicate that both trajectory judgments and explanations were affected by specific response and display features of the problem. In addition, these data provide little evidence that naive impetus theory plays a significant role in subjects’ performance; instead, they suggest that motion judgments and explanations are constructed on the fly from contextual cues and knowledge that is not necessarily naive.     

The pigeon's discrimination of movement patterns (Lissajous figures) and contour-dependent rotational invariance

The ability of pigeons to discriminate complex motion patterns was investigated with the aid of moving Lissajous figures. The pigeons successfully learned to differentiate two successively presented cyclic trajectories of a single moving dot. This suggests that they can recognize a movement Gestalt when information about shape is minimal. They also quickly learned a new discrimination between moving-outline stimuli with repetitively changing contour patterns. Contrasting results were obtained when the dot or outline stimuli were axis-rotated through 90 degrees. Rotational invariance of pattern discrimination was clearly demonstrated only when moving contours were visible. Nevertheless, pigeons could discriminate the axis-orientation of a moving-dot or moving-outline pattern when trained to do so. Discrimination did not seem to depend on single parameters of motion but rather on the recognition of a temporally integrated movement Gestalt. The visual system of pigeons, as well as that of humans, may be well adapted to recognize the types of oscillatory movements that represent components of the motor behaviour shown by many living organisms.