Gregor Schöner

The uncontrolled manifold concept: identifying control variables for a functional task

Abstract The degrees of freedom problem is often posed by asking which of the many possible degrees of freedom does the nervous system control? By implication, other degrees of freedom are not controlled. We give an operational meaning to ”controlled” and ”uncontrolled” and describe a method of analysis through which hypotheses about controlled and uncontrolled degrees of freedom can be tested. In this conception, control refers to stabilization, so that lack of control implies reduced stability. The method was used to analyze an experiment on the sit-to-stand transition. By testing different hypotheses about the controlled variables, we systematically approximated the structure of control in joint space. We found that, for the task of sit-to-stand, the position of the center of mass in the sagittal plane was controlled. The horizontal head position and the position of the hand were controlled less stably, while vertical head position appears to be no more controlled than joint motions.

Motor control strategies revealed in the structure of motor variability.

LATASH, M.L., J.P. SCHOLZ, and G. SCHÖNER. Motor control strategies revealed in the structure of motor variability. Exerc. Sport Sci. Rev., Vol. 30, No. 1, pp 26–31, 2002. We describe an uncontrolled manifold hypothesis, which suggests a particular solution for the notorious problem of motor redundancy. A body of recent experiments supports the uncontrolled manifold hypothesis and shows its ability to discover biological strategies of the coordination of apparently redundant motor systems. The hypothesis and associated computational apparatus have great potential for application in the areas of motor rehabilitation and motor skill acquisition.

Dynamic field theory of movement preparation.

A theoretical framework for understanding movement preparation is proposed. Movement parameters are represented by activation fields, distributions of activation defined over metric spaces. The fields evolve under the influence of various sources of localized input, representing information about upcoming movements. Localized patterns of activation self-stabilize through cooperative and competitive interactions within the fields. The task environment is represented by a 2nd class of fields, which preshape the movement parameter representation. The model accounts for a sizable body of empirical findings on movement initiation (continuous and graded nature of movement preparation, dependence on the metrics of the task, stimulus uncertainty effect, stimulus-response compatibility effects, Simon effect, precuing paradigm, and others) and suggests new ways of exploring the structure of motor representations.

Dynamics of behavior : theory and applications for autonomous robot architectures

Abstract Limitations both for the further development as well as for the actual technical application of autonomous robots arise from the lack of a unifying theoretical language. We propose three concepts for such a language: (1) Behaviors are represented by variables, specific constant values of which correspond to task demands; (2) Behaviors are generated as attractors of dynamical systems; (3) Neural field dynamics lift these dynamic principles to the representation of information. We show how these concepts can be used to design autonomous robots. Because behaviors are generated from attractor states of dynamical systems, design of a robot architecture addresses control-theoretic stability. Moreover, flexibility of the robot arises from bifurcations in the behavioral dynamics. Therefore techniques from the qualitative theory of dynamical systems can be used to design and tune autonomous robot architectures. We demonstrate these ideas in two implementations. In one case, visual sensory information is integrated to achieve target acquisition and obstacle avoidance in an autonomous vehicle minimizing the known problem of spurious states. In a second implementation of the same behavior, a neural dynamic field endows the system with a form of obstacle memory. A critical discussion of the approach highlights strengths and weaknesses and compares to other efforts in this direction.

Structure of motor variability in marginally redundant multifinger force production tasks.

Abstract. The framework of the uncontrolled manifold hypothesis (UCM hypothesis) was applied to the analysis of the structure of finger force variability during oscillatory force production tasks. Subjects produced cycles of force with one, two (index and middle), or three (index, middle, and ring) fingers acting in parallel against force sensors mounted inside a small frame. The frame could be placed on the top of a table (stable conditions) or on a 4-mm-wide supporting surface (unstable conditions). Subjects were less variable when they used two fingers than when using one finger; adding the third finger did not change indices of variability of the performance. Components of finger force variance that did (VUN) or did not (VCOMP) change the value of a particular functional variable were computed for two control hypotheses: (1) at each time, the subjects tried to stabilize the total value of force (force-control); and (2), at each time, the subjects tried to stabilize the total moment produced with respect to an axis parallel to the hand/forearm (moment-control). Most subjects showed selective stabilization of moment and destabilization of force throughout most of the force cycle, in both stable and unstable conditions. The shapes of VUN and VCOMP suggested a possibility of selective compensation of timing errors across fingers within force cycles. One subject showed different relations between VUN and VCOMP, suggesting that these relations did in fact reflect particular central strategies of solving the tasks. The UCM method is applicable to force production tasks. It allows the comparison of control hypotheses in a quantitative way and unveils central strategies of control of redundant motor systems. Within this approach, redundancy (rather, abundance) is not a problem but an inherent part of a solution for natural motor tasks.

Learning as change of coordination dynamics: theory and experiment.

Learning of coordination patterns was investigated theoretically from the point of view of a dynamic theory of biological coordination and with reference to recent experiments on the learning of relative timing patterns. The theory is based on theoretical and experimental work showing that coordinated movement is characterized not only by the actually performed pattern of coordination but by an entire dynamics of coordination. Theoretically, such dynamics are captured as equations of motion of relevant collective variables. Experimentally, signatures of these underlying dynamics can be found in the temporal stability of coordination patterns, which can be assessed through various stability measures as well as through processes of pattern change. We argue that not only intrinsic coordination tendencies, but also specific behavioral requirements, be they perceived, memorized, or intended, must be expressed in terms of such dynamics. The concept of behavioral information captures such requirements as part of the coordination dynamics. We expound two hypotheses on the nature of learning in this framework. First, we assume that at each point during the learning process the system is governed by a well-defined coordination dynamics. This equation of motion evolves with learning so as to acquire an attractor solution near the to-be-learned pattern. Second, we hypothesize that this change of the coordination dynamics, captured by the time course of memorized behavioral information, can itself be ascribed to an additional layer of dynamics, the slower learning dynamics. Testable consequences of these views are discussed in the light of recent experimental findings on the learning of a relative phase in rhythmic movement: (a) Learning affects dynamic properties of performed coordination patterns, in particular, their stability; (b) the change of the coordination dynamics due to learning leads to specific changes of behavior also under conditions other than the learned condition, namely, to systematic deviation toward the learned patterns; (c) learning may lead to instabilities in the coordination behavior if initial and learned performance differ sufficiently; and (d) the dynamic properties of the performed coordination patterns are distinct on the two time scales of learning and of performance.

Coupling of fingertip somatosensory information to head and body sway

Abstract Light touch contact of a fingertip with a stationary surface can provide orientation information that enhances control of upright stance. Slight changes in contact force at the fingertip provide sensory cues about the direction of body sway, allowing attenuation of sway. In the present study, we asked to which extent somatosensory cues are part of the postural control system, that is, which sensory signal supports this coupling? We investigated postural control not only when the contact surface was stationary, but also when it was moving rhythmically (from 0.1 to 0.5 Hz). In doing so, we brought somatosensory cues from the hand into conflict with other parts of the postural control system. Our focus was the temporal relationship between body sway and the contact surface. Postural sway was highly coherent with contact surface motion. Head and body sway assumed the frequency of the moving contact surface at all test frequencies. To account for these results, a simple model was formulated by approximating the postural control system as a second-order linear dynamical system. The influence of the touch stimulus was captured as the difference between the velocity of the contact surface and the velocity of body sway, multiplied by a coupling constant. Comparison of empirical results (relative phase, coherence, and gain) with model predictions supports the hypothesis of coupling between body sway and touch cues through the velocity of the somatosensory stimulus at the fingertip. One subject, who perceived movement of the touch surface, demonstrated weaker coupling than other subjects, suggesting that cognitive mechanisms introduce flexibility into the postural control scheme.

Temporal stability of the action-perception cycle for postural control in a moving visual environment

When standing human subjects are exposed to a moving visual environment, the induced postural sway forms a stable temporal relationship with the visual information. We have investigated this relationship experimentally with a new set-up in which a computer generates video images which correspond to the motion of a 3D environment. The suggested mean distance to a sinusoidally moving wall is varied and the temporal relationship to induced sway is analysed (1) in terms of the fluctuations of relative phase between visual and sway motion and (2) in terms of the relaxation time of relative phase as determined from the rate of recovery of the stable relative phase pattern following abrupt changes in the visual motion pattern. The two measures are found to converge to a well-defined temporal stability of the action-perception cycle. Furthermore, we show that this temporal stability is a sensitive measure of the strength of the action-perception coupling. It decreases as the distance of the visual scene from the observer increases. This fact and the increase of mean relative phase are consistent with predictions of a linear second-order system driven by the visual expansion rate. However, the amplitude of visual sway decreases little as visual distance increases, in contradiction to the predictions, and is suggestive of a process that actively generates sway. The visual expansion rate on the optic array is found to decrease strongly with visual distance. This leads to the conclusion that postural control in a moving visual environment cannot be understood simply in terms of minimization of retinal slip, and that dynamic coupling of vision into the postural control system must be taken into account.

Understanding finger coordination through analysis of the structure of force variability

Abstract. Most common motor acts involve highly redundant effector systems. Understanding how such systems are controlled by the nervous system is a long-standing scientific challenge. Most proposals for solving this problem are based on the assumption that a particular solution, which optimizes additional constraints, is selected by the nervous system out of the many possible solutions. This study attempts to address this question in the context of coordinating individual finger forces to produce a controlled total force oscillation between 5% and 35% of each subjects maximum force of voluntary contraction, under two different combinations of four fingers. The structure of variability of individual finger forces was evaluated with respect to hypotheses that, at each instance in time, subjects attempt to: (1) stabilize the value of total force and (2) stabilize the total moment created by the fingers about the long axis passing through the forearm and midline of the hand. The results provide evidence that a range of goal-equivalent finger force combinations is generated to stabilize the values of total force and the total moment. The control of total force was specified explicitly by the task. However, it was stabilized only near the time of peak force. In contrast, the total moment was stabilized throughout most of the force cycle. The results lead to the suggestion that successful task performance is achieved, not by selecting a single optimal solution, but by discovering an appropriate control law that selectively stabilizes certain combinations of degrees of freedom relevant to the task while releasing from control other combinations.

Frequency dependence of the action-perception cycle for postural control in a moving visual environment: relative phase dynamics

When standing human subjects are exposed to a moving visual environment, the induced postural sway displays varying degrees of coherence with the visual information. In our experiment we varied the frequency of an oscillatory visual display and analysed the temporal relationship between visual motion and sway. We found that subjects maintain sizeable sway amplitudes even as temporal coherence with the display is lost. Postural sway tended to phase lead (for frequencies below 0.2 Hz) or phase lag (above 0.3 Hz). However, we also observed at a fixed frequency, highly variable phase relationships in which a preferred range of phase lags is prevalent, but phase jumps occur that return the system into the preferred range after phase has begun drifting out of the preferred regime. By comparing the results quantitatively with a dynamical model (the sine-circle map), we show that this effect can be understood as a form of relative coordination and arises through an instability of the dynamics of the action-perception cycle. Because such instabilities cannot arise in passively driven systems, we conclude that postural sway in this situation is actively generated as rhythmic movement which is coupled dynamically to the visual motion.