Visual and Proprioceptive Information
A System Theoretical Approach
Isual and Proprioceptive Information
in Goal Directed Movements:
A System Theoretical Approach
P R O E F S C H R I F T
ter verkrijging van de graad van doctor in de technische wetenschappen aan de Technische Hogeschool Delft, op gezag van de Rector Magnificus, prof.dr. J. M. Dirken,
in het openbaar te verdedigen ten overstaan van het College van Dckancn
op 19 december 19S5 te 16-00 uur door JACOBUS CORNELIS R U I T E N B E E K , geboren te Rhedcn, elektrotechnisch ingenieur.
TRdiss
1469
Dit proefschrift is goedgekeurd door de promotor Prof.dr.ir. H. G. Stassen. Dr.ir. A. van Lunteren heeft als begeleider in hoge mate bijgedragen aan het totstandkomen van het proefschrift. Het College van Dekanen heeft hem als zodanig aangewezen.
This research was sponsored by the Netherlands Organization for the Advance ment of Pure Research (ZWO).
The contribution of the Stichting Nationaal Revalidatie Fonds to purchase part of the equipment is acknowledged.
"An i m p o r t a n t limitation in seeking to understand the control of human movement is that of being confined by necessity to observations about motor output from which to infer the nature of the underlying processes".
J.A. Scott Kelso et al.,
The role of proprioception in the perception and control of human movement, Percept ion and Psychophysics, Vol. 28, No. 1, 45-52, 19S0.
CONTENTS Samenvatting / Summary I. 1.1. 1.2. 1.3. 1.4. Introduction Research aims Research approach Layout of the thesis References
2. Models and methods
2.1. Hierarchical motor control structure 2.2. A two-level scheme
2.3. A model for the two-level scheme 2.4. Methods
2.4.1. Strategy
2.4.2. The describing function model for goal directed 2.5. References
3. System identification 3.1. Introduction
3.2. Step response identification
3.3. Identification of the describing function model 3.4. Numerical aspects
3.5. Evaluation of the method 3.6. References
4. Experimental setup 4.1. Experimental considerations 4.2. General system description 4.3. Detailed system description 4.4. Operating principles 4.5. References
5. Invariants in loaded goal directed movements 5.1. Introduction 5.2. Desired movements 5.3. Methods 5.3.1. Experimental setup 5.3.2. Experimental conditions 5.4. Data analysis
5.4.1. Validation of the working hypothesis 5.4.2. The describing function model 5.4.3. Data processing
5.5. Results 70 5.6. Discussion 75 5.7. References 76
6. Goal directed movements under various control display relations 79
6.1. Introduction 79 6.2. Control display relations 80
6.3. Methods 85 6.3.1. Experimental setup 85 6.3.2. Motor tasks 85 6.4. Data analysis 86 6.4.1. The describing function model 86
6.4.2. Data processing 87 6.5. Results 87 6.6. Concluding remarks 92
6.7. References 93 Adaptation in goal directed movements 95
Introduction 95 Adaptive control 96 Measures 98 Experiments 101 Data processing 101 Results 102 Concluding remarks 107 References 108 8. Final remarks 109 8.1. Discussion and conclusions 109
8.1.1. Recapitulation 109 8.1.2. I n v a r i a n t properties 110 8.1.3. The two-level model 112
8.1.4. Methods 116 8.2. Recommendations 118 8.2.1. The two-level model 118 8.2.2. A d a p t a t i o n 120 8.2.3. System identification 120 8.3. Technical applications 121 8.4. Summarized conclusions 122 8.5. References 122 Curriculum Vitac Nawoord
Visuele en proprioceptieve informatie bij doelgerichte bewegingen: Een systeemtheoretische benadering
Samenvatting
In dit proefschrift wordt ingegaan op de rol van visuele en proprioceptieve informatie bij de uitvoering van doelgerichte armbewegingen door de mens. De aandacht richt zich d a a r b i j met name op de vraag naar de invloed van beide vormen van informatie bij de adaptatie van de interne representatie van de uit te voeren taak.
De interne representatie omvat het totaal aan ervaringen en i n d r u k k e n met betrekking tot deze taak waarover de mens op een zeker moment beschikt. Bij doelgerichte bewegingen bestaat de interne representatie ondermeer uit kennis over het te bereiken doel, de af te leggen afstand, de strategieën die gevolgd kunnen worden om het doel te bereiken en over de dynamica van het systeem waarmee de beweging uitgevoerd moet worden.
Omdat de rol van visuele en proprioceptieve informatie bij de adaptatie van de interne representatie n a u w verbonden is met de s t r u c t u u r van de regeling van doelgerichte bewegingen, wordt deze vraag bestudeerd binnen een model van deze structuur.
Uitgaande van een synthese van verschillende regelconcepten die in de l i t e r a t u u r beschikbaar zijn, wordt een schema bestaande uit twee niveaus voorgesteld. Verondersteld wordt dat in het eerste niveau aan de hand van de interne representatie een zgn. voorgenomen beweging gegenereerd wordt. In het tweede niveau wordt deze voorgenomen beweging omgezet in de werkelijke beweging. De belangrijkste aspecten van dit schema en van de rol van de afferente informatie worden vervolgens samengevat in een functioneel model. Op basis van dit model, dat eveneens een tweetal niveaus bevat, wordt de a d a p t a t i e van de interne representatie experimenteel onderzocht aan de hand van de voorgenomen bewe ging. Deze beweging kan geschat worden uit de uitgevoerde bewegingen wanneer deze volledig voor-geprogrammeerd zijn.
In de eerste serie experimenten worden geoefende bewegingen, uitgevoerd met behulp van een manipulator met verschillende eigenschappen, bestudeerd. In de tweede serie experimenten worden geoefende bewegingen onderzocht wanneer de relatie tussen de uitgevoerde beweging en de visueel waargenomen beweging gewijzigd is. D a a r n a a s t worden verkennende experimenten beschreven w a a r i n de aandacht op het adaptatieproces zelf gericht is.
De experimentele opstelling bestaat uit een lineaire hydraulische motor en een beeldscherm. Ter vereenvoudiging van het experimentele onderzoek en ter verho
ging van de betrouwbaarheid van de geregistreerde meetgegevens is deze opstelling verregaand geautomatiseerd.
Tijdens de analyse wordt elke geregisteerdc beweging volledig geïdentificeerd met behulp van een model gebaseerd op de beschrijvende functie methode. De nauw-keurigheidsaspecten van de identificatiemethoden, die toegepast worden om de modelparameters te schatten, worden zowel langs theoretische als langs experimen tele weg onderzocht.
De resultaten van de experimenten geven aan dat de spatiele component van de visueel waargenomen beweging in de verschillende experimentele omstandigheden nagenoeg i n v a r i a n t is. De temporele component, die de snelheid van de beweging vastlegt, lijkt vrij gekozen te zijn.
Binnen het model van de s t r u c t u u r van de regeling van doelgerichte bewegingen kan dan geconcludeerd worden dat de interne representatie v a n de taak op basis van de visuele en proprioceptive informatie geadapteerd wordt. In het bijzonder kan vastgesteld worden dat de interne representatie van het te besturen systeem volledig a d a p t e e r t aan de werkelijke dynamica van het te besturen syteem en dat de regelaar, die de generatie van de voorgenomen beweging beheerst, zodanig adapteert dat de i n v a r i a n t i e in de spatiele component g e h a n d h a a f d wordt.
Visual and proprioceptive information in goal directed movements: A system theoretical approach.
SUMMARY
In this thesis, we consider the role of visual and proprioceptive information in the generation and control of goal directed arm movements in man. In p a r t i c u l a r , wc focus on the role of both types of information in the a d a p t a t i o n of the internal representation of the task.
This internal representation embodies the knowledge of the subject about the outer world. For goal directed movements, it includes knowledge about the target to be reached, the distance to be covered, the strategies t h a t can be adopted to reach the target and the dynamics of the controlled system.
As these questions are directly related to the structure of the control of goal directed movements, the role of visual and proprioceptive information in the a d a p t a t i o n of the internal representation is studied w i t h i n the context of a model of the control structure.
Based on a synthesis of various control schemes presented in literature, wc propose a two-level scheme for the control of goal directed movements. In this scheme, the upper level is assumed to generate an intended movement on the basis of the internal representation. In the lower level, the intended movement is thought to be transformed into the resulting movement.
To summarize the two-level scheme and the role of the afferent information in a concise manner, an attempt is made to describe the main aspects of the two-level scheme from a functional point of view by means of a two-level model. Within this model, we investigate the a d a p t a t i o n of the internal representation by considering the intended movement. This movement can be estimated from the executed movements when the executed movements are preprogrammed.
Within this framework, the a d a p t a t i o n of the internal representation is studied experimentally. In the first series of experiments, well-trained movements executed by means of a manipulator with various dynamics are considered. In the second series, we study well-trained movements made under d i f f e r e n t control display relations. In addition, explorative experiments arc reported in which the adapta tion process itself is considered.
The experimental setup applied consists of a linear, h y d r a u l i c motor and a display
system. To facilitate experimenting and to improve d a t a integrity, this setup is highly automated.
For the analysis, each movement is identified by means of a describing function model. This method takes the entire movement into account. T h e accuracy of the identification techniques, applied to estimate the model parameters, is studied both theoretically and experimentally.
The results of the experiments show t h a t the spatial course of the visually perceived movements in the various experimental conditions is almost invariant. The temporal course, which specifies the velocity of the movement, seems to be selected freely.
Within the context of the two-level model we, therefore, conclude that the internal representation of the task is adapted on the basis of visual and proprioceptive information. In particular, we conclude that the internal representation of the controlled system is fully adapted to the actual dynamics of the controlled system and that the controller, which governs the generation of the intended movement, is adapted in such a manner that the invariance in the spatial course is preserved.
C H A P T E R ONE I N T R O D U C T I O N
It is a widely held notion that man has but five senses, whereas in truth he has a great many more. The role of these "hidden" senses in everyday life often only emerges when their contribution to the regulation and control of the body is disturbed.
In this thesis wc will focus on the role of vision and proprioception in the control of h u m a n arm movements. Vision, just like hearing, belongs to the class of exteroceptivc senses. It provides the organism with i n f o r m a t i o n from the outside world. In proprioception, one of the "hidden" senses, the stimuli to the receptors are delivered by the organism itself. Sherrington (1906) chose the prefix "proprio" (from the Latin proprius: "one's own") to indicate the sense of movement, along with the forces and tensions, the relative positions of the body segments and the orientation and movement of the body in space (Schmidt, 1971). The primary receptors for proprioception are the proprioccptors, such as the muscle spindles (Mc Closkcy, 1978; Matthews, 1982).
To point out the importance of visual and proprioceptive information in the control of movements, we will present some examples from the field of rehabilita tion engineering and man-machine systems.
The loss of arm and hand means, among other things, the loss of some i m p o r t a n t motor functions. Although the application of an artificial device, such as an arm prosthesis, may provide partial restauration of the lost motor f unction, the control of these devices by the wearer is in general hampered. T h i s is caused by the fact that the loss of an arm also implies the loss of important sensory information such as proprioception. The full sensation of a normal arm and h a n d is a very complex quality (Mobcrg, 1964), which does not lend itself easily to replacement by an artificial device. As a consequence, visual and auditory i n f o r m a t i o n are most often essential in the control of the prosthesis, in order to circumvent the lacking sensory information. In many cases, part of the proprioceptive system is still present, for instance in the muscles which, before the amputation, operated the hand. There fore, part of the research in rehabilitation engineering is directed to increased utilisation of the remaining proprioceptive mechanisms in the prosthesis feedback system (Herberts and Korner, 1979), Various techniques, such as 'extended proprio ceptive feedback', proposed by Simpson (1969, '974), (Doubler and Childress, 1984a, 1984b) and p a t t e r n recognition (Herberts et al., 1973; Tomovic, 1984) are applied to improve the generation of suitable control modes of the prosthesis and to reduce the use oï visual information in the control of the movement.
Also in the general field of man-machine systems, the importance of proprio-ception is recognized. In a discussion on human operator control behaviour for predictable inputs, McRuer and Krendel (1974), for instance, stated "The pilot acts as if the only signals he requires, once he is fully familiar with the input and controlled element and knows when to begin, are those generated by the proprio-ceptors involved in his control movements". Another example is found in flight simulators for aircraft control training. As proprioceptive information, obtained from the flight control device, is a main source in pilot's decision making, a complete control device fidelity in the flight simulator is an i m p o r t a n t require ment (Wierda, 1984).
Several studies have been conducted aiming to improve manual control perfor mance of the human operator by making use of proprioceptive feedback. As in many cases the human operator output interface is a manipulator, the dynamics of t h e manipulator can be perceived proprioccptively from the displacement and the exerted forces. Provided that a suitable relation between the dynamics of the m a n i p u l a t o r and the dynamics of the system to be controlled exists, this additional feedback may improve his control performance. Examples of these studies arc those of McRuer and Magdalcno (1966), Herzog (1969), Kraiss (1970), Merhav (1976), Kruger (1978), Doctsch (1979), Bejczy and Salisburg (1983) and Rcppcrgcr (1984).
Apart from these application oriented studies, also the research on the structure of human movement control as such has received more attention over the last years. As the dexterity of human arms in real time is generally superior to that of c u r r e n t l y available robots (Bcnati et al., 1980a), despite the greater number of degrees of freedom in the human arm and the considerable time delays of the nervous system, attemps are made to apply knowledge on how human achieves coordinated control of the limbs in designing robot control systems (Chandler et al., 1981; Hanaf i et al., 1984). However, concepts as used in robot control also inspired the research of human movement control, as these may provide plausible biological mechanisms to accomplish part of the control of the human arm (Raibert, 1978; Hinton, 1984).
Areas of research in common to human movement control and robotic control systems are the multi-level structure in which a coarse c h a r a c t e r i z a t i o n of the movement to be executed is refined into specific control signals for the various segments of the multi-link arm (Saltzman, 1979), the planning (Lozano-Perez, 1982) and control of a movement to follow a predefined reference in the presence of disturbances and the (de)coupling of the control of multi-link segments, such as in resolved rate motion control (Whitney, 1972). Other areas include the study of inverse kinematic control (Benati et al., 1982), d y n a m i c factors such as the masses of the segments and interactive effects (e.g. Coriolis forces) (Luh et al., 1980; Hollerbach and Flash, 1982), impedance control (Hogan, 1980, 1984; Bcnati et al., 1980b) and hybrid position/force control (Raibert and Craig, 1981; Mason, 1981).
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1.1. Research aims
In this thesis, we will focus on goal directed arm movements. This type of movements is common to everyday movement as it appears in pointing and reaching towards objects. To distinguish goal directed or voluntary movements from continuously tracking movements, in which a continuously changing target has to be tracked, Pew (1974) gives the following characteristics of a goal directed movement:
The path of the movement is less important than the goal that is achieved; the conduct of the movement is paced largely by the subject and not driven by an external forcing function;
the pattern of the movement is largely formulated internally on the basis of a backlog of experience with movements designed to achieve similar goals. With respect to the generation and control of goal directed movements, the first characteristic deals with the static aspect of the movement. It emphasizes the aim of the movement i.e. to arrive at the target. The remaining two characteristics consider the d y n a m i c aspects of the control: the timing of the movement and the generation of the pattern or trajectory to reach the goal.
To introduce the aims of the research reported in this thesis we will first present a brief overview of some themes in the research on the role of visual and proprioceptive information in goal directed movements, as reported in l i t e r a t u r e . For convenience, we will classify these themes according to the characteristics of goal directed movements given by Pew.
Early research as reported by e.g. Weiss (1954) and Bahrick et al. (1955), mainly focused on the first characteristic. The influences of various types of propriocep tive information, achieved by applying a manipulator with adjustable dynamics, such as spring loadings and attached masses, were studied by investigating the final positioning accuracy of the goal directed movement. Related research considered the reproduction of location and the reproduction of distance u n d e r normal, i n t e r r u p t e d or disrupted proprioceptive information, obtained by e.g. d e a f f e r e n t a t i o n or mechanical vibration of the muscles, (e.g. Angel et al., 1971; Goodwin et al., 1972; Tomlinson, 1972; Bossom, 1974; Scott Kelso et al., 1980; Van Bcekum, 1980; Worringham and Stelmach, 1984).
V/ith respect to the control of the movement, especially how the final position is achieved, several d e a f f e r e n t a t i o n studies (Bizzi et al., 1976; Polit and Bizzi, 1978; T a u b et al., I975) and those in which the executed movement was unexpectedly disturbed (Schmidt, 1980; Schmidt and Me Gown, 19S0) provided evidence for a mass-spring mechanism in end point control. In this view, the movement is elicited by activation of agonist and antagonist muscles, thus defining the force-length relations of these muscles. As a result, the arm moves towards a position w h e r e the moments exerted by the agonist and antagonist are balanced. As noted by various
authors (e.g. Hinton, 1984), however, this view can not be correct because it docs not allow to control the dynamics of the movement i.e. the trajectory and the timing.
Apart from the studies in which the role of visual and proprioceptive information is mainly analyzed in terms of the final positioning accuracy, other studies also incorporated the timing aspects of the goal directed movements. Fitts (1954) suggested that the relation between the duration and the accuracy of the movement is determined by the information conveyed by a movement of a given accuracy. This information theoretical approach, extended by Wclford (I960) and K n i g h t and Dagnall (1967) led to the notion of a maximum channel capacity of the human sensori-motor system. Other studies (Kecle and Posner, 1968; Poulton, 1974;Carlton and Ncwell, 1979; Smith and Bowcn, 1980; Carlton, 1981) analyzed the timing of the movement and the final accuracy, aiming to establish the time needed to process visual and proprioceptive information (Chernikoff and Taylor, 1952; Wadman et al., 1979).
This issue received a good deal of attention since it is directly related to the relative contribution of peripheral and central mechanisms in the control of a goal directed movement. Long processing delays have been used to argue for the existence of central mechanisms that structure movements and guide them without feedback involvement (Schmidt, 1976). The general concept of prcstructured motor commands has been termed "motor program". It dates back to the work of Lashley (1917). The concept suggests that the movements are initially controlled in an open loop manner, whereas feedback information may be used in a later phase to correct latter parts of the movement (KLlapp, 1975).The existence of an open loop component raised questions about the characteristics of the central mechanism in the control of the movement. On the one hand, it initatcd research on the (in)variant properties in the programming of the movement (Glencross, 1973; Schmidt, 1975; Shapiro et al., 1981; Soechting and Lacquaniti, 1981). On the other, it concerned the cognitive and memory function in the generation of the movement patterns as a backlog of the experiences from the execution of similar movements (Magill, 1983). These experiences include the visual a n d proprioceptive informa tion obtained from former movements.
As an example, we consider the effects of displaced visual information in goal directed hand movements as reported by Smith and Bowen (1980). They compared the final positioning accuracy in the cases when subjects had an undisturbed and a disturbed view. T h e latter condition was achieved by applying a pair of goggles with a base-left prism, which displaced the subject's visual field to the right. After practice of the movements in the undisturbed case, the prism distortion induced significant inaccuracies in reaching the target. With practice, this effect diminish ed until the original accuracy was achieved. Upon w i t h d r a w a l of the distortion, again inaccuracies occured which dissipated with repeated undisturbed move ments.
The distortion of the wedge prism implies t h a t the felt h a n d position no longer matches the visually perceived position of the hand. Hence the experienced relation from the undisturbed view is no longer a p p r o p r i a t e in the disturbed case. Based on the information perceived in the disturbed case, the visuo-motor relation is adapted to reach the target accurately. This adaptation is not instantaneously, but requires practice in repeated movements.
The various ideas on the generation and the control of goal directed movements led to a concept which is commonly referred to as the internal representation (Sommerhoff, 1974). It is thought to contain the knowledge about the outer world, the task to be performed, the strategies t h a t can be adopted and the experiences and sensory information as obtained from similar task executions. Based on the internal representation, the movement is initiated by specifying a motor program which guides and controls the actual movement. A detailed discussion of this concept will be provided in Ch. 2.
As may be clear from this overview, the role of the visual and proprioceptive information in the control of goal directed movement is essentially twofold. First, it contributes to the direct control of the movement in order to arrive at the target. Second, it also contributes to the internal representation about the task to be performed e.g. as embodied in the experiences from former task executions. Whereas the first part can be considered as an error correction function, the second part constitutes an a d a p t i v e function as it may adjust the internal representation in order to generate a p p r o p r i a t e movement patterns.
The research, reported in this thesis, deals with the second part i.e. the role of the visual and proprioceptive information in the internal representation of the goal directed movement. In p a r t i c u l a r , the attention will be focused on how a n d to what extent the internal representation is adapted when visual and proprioceptive information are m a n i p u l a t e d externally. We will not deal with the physiological properties of the i n d i v i d u a l receptors involved or the neural processing of the information, but study the problem from a functional point of view. However, as these questions are directly related to the structure of the control of goal directed movements as such, the adaptation of the internal representation will be studied within the context of a formal model of the control of goal directed movements.
1.2. Research approach
A major d r a w b a c k of the various schemes proprosed to describe the functional aspects of the control system in goal directed movements is t h a t these schemes are mostly of a verbal n a t u r e . Especially in the models discussed in the field of experimental psychology, the d y n a m i c behaviour of d i f f e r e n t parts of the models is often vaguely described. Moreover, causal relations are sometimes ill defined, hence leaving room for misinterpretation a n d confusion. As a consequence, 5
experimental results arc hard to interpret in terms of the model, as the q u a n t i t a t i v e contribution of d i f f e r e n t parts of the model, due to the verbal nature, can not be distinguished appropriately (Kearny and Munter, I982).
To arrive at a dynamic description of the goal directed movements, as a major tool in the analysis of the current problems, we have adopted an approach based on system and control theory.
This approach allows to investigate the movements as a function of input stimuli by means of a mathematical model. Provided that an adequate structure of the model can be obtained, in which the main relations which are supposed to govern the system are expressed, various techniques such as parameter estimation and simulation can be used to study the system in detail. F u r t h e r m o r e , it allows to investigate the functional behaviour of the system from a control theoretical point of view.
Although the use of mathematical models is widely accepted in physiological research (Bekey and Bcneken, 1978), estimation of model parameters from recorded data finds more limited application, (Bekey, 1985; O'Lcary, 1985). This may be caused by the fact that the number of model parameters that can be estimated accurately is in general less then the number of parameters that can be distinguish ed from a physiological point of view.
In the present study, this problem becomes more severe as the parameters of the model applied to characterize the goal directed movements, have to be estimated from a limited set of observations. Various physiologically i n t e r p r e t a t i e para meters are merged into a small set of model parameters in order to allow an accurate estimation. As a consequence, a rigid physiological i n t e r p r e t a t i o n m a y b e limited. However, the accurate parameterization of the movement as executed allows a system theoretical analysis and interpretation towards a q u a n t i t a t i v e search for functional principles.
In the present research, the system theoretical approach resulted into the following steps.
The various schemes on the control of goal directed movements, as reported in literature, arc analyzed from a functional point of view.
On the basis of this analysis, a formal model is proposed. Its structure contains the main functional aspects of the control of goal directed movements. This model provides the framework in which the role of the visual and proprioccptive information is studied.
Within this model structure, the various research methods, such as a describing function method to characterize the goal directed movements, and the requirements to investigate and quantify the effects of visual and proprioccptive information in an experimental setting arc derived. In this way, a condensed framework to study the role of the visual and proprioccptive information in the internal representation is achieved.
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1.3. Layout of the thesis
The thesis is organized in the following manner.
In Ch. 2 we develop a two-level scheme, representing some functional aspects in the generation and control of goal directed movements. Based on this two-level scheme, we propose a s t r u c t u r a l model for the control of goal directed movements, which provides the framework for the reported research.
In Ch. 3 we consider the various techniques applied to process recorded movements into accurate values of the model parameters of the describing function model. In Ch. 4 we describe the setup applied to manipulate the visual and the proprioceptive information in the experiments and to measure the executed movements.
Ch. 5 reports the results of the experiments when the proprioceptive information, conceived by varying the dynamics of the m a n i p u l a t o r by which the movements are executed, is changed.
In Ch. 6 we investigate the role of the visual information when the relation between the executed and the visually perceived movements is changed. The experiments reported in Ch. 5 and 6 were performed after the subjects were able to adapt their control with respect to the various experimental conditions. In Ch. 7 we report some results of an explorative study in which we focus on the description of the adapation in the control itself.
In Ch. 8 the methods applied and the results of the experiments reported in the previous chapters arc discussed with respect to the proposed model for goal directed movements.
The research reported in Ch. 4 and 5 has already been published (Ruitenbeek and Jansseji, 19S4; Ruitenbeek, 19S4). The work described in Ch. 6 will be submitted for publication.
1.4. References
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Bahrick, H.P., W.F. Bennett and P.M. Fitts, Accuracy of positioning responses as a function of spring loading in a control, Journ. of Exp. Psych., Vol.49, No. 6, 437-444, 1955.
Bcekum, W.T. van, Muscle spindles in human position sense, Ph.D. thesis, Utrecht, 1980.
Bejczy, A.K. and J.K. Salisbury, Controlling remote m a n i p u l a t o r s through kinesthe-tic coupling, Comp. in Mech. Eng., Vol. 1, No. 1, 48-60, 1983.
Bekey, G.A, Identification of neuro-muscular systems, Preprints IFAC Identif. and Syst. Param. Estim., York, 69-76, 1985.
Bekey, G.A. and J.E.W. Beneken, Identification of biological system: A survey, Automatica, Vol. 14, 41-47, i978.
Benati, M., S. Gaglio, P. Morasso, V. Tagliasco and Z. Zaccaria, Anthropomorphic Robots, 1. Representing mechanical complexity, Biol. Cybern., 38, 125-140, 1980 (a).
Benati, M., S. Gaglio, P. Morasso, V. Tagliasco and Z. Zaccaria, Anthropomorphic Robots, 2. Analysis of manipulator dynamics and the output motor impe dance, Biol. Cybern., 38, 141-150, 1980 (b).
Benati, M., P. Morasso and V. Tagliasco, The inverse kinematic problem for anthropomorphic manipulator arms, Trans. ASME, 110-113, 1982. Bizzi, E., A. Polit and P. Morasso, Mechanisms underlying achievement of final
head position, J. Neurophys., 39, 435-444, 1976.
Bossom, J., Movement w i t h o u t proprioception, Brain Res. 71, 285-296, 1974. Carlton, L.G., Processing visual feedback information for movement control, J.
Exp. Psych., Vol. 7, No. 5, 1019-1030, 1981.
Carlton, M.J. and K.M. Newel], On the relationship between response initiation and response outcome, J. of Hum. Movem. Studies, 5, 90-103, 1979. Chernikoff, R. and F.V. Taylor, Reaction time to kinesthetic stimulation resulting
from sudden arm displacement, J. of Exp. Psych., 43, 1-8, 1952.
Chandler, C.S., J,R. Hewit and J.S.G. Miller, Dynamic control of robotic and human limbs, IEE Colloq. Neuromusc. Control Systems, St. Thomas Hospital, Lon don, 1981.
Doetsch, K.H. and W. Roger, The transfer of control and guidance information to the pilot through the mainipulator forces, Proc. 15th Ann. Conf. on Manual Control, 430-444, Ohio, 1979.
Doubler, J.A. and D.S. Childress, Analysis of extended physiological proprioception as prothesis-control technique, Journ. of Rehab, and Devel., Vol. 21, No. 1,5-18, 1984 (a).
Doubler, J.A. and D.S. Childress, Design and evaluation of a prosthesis control system based on the concept of extended physiological proprioception, Journ. of R e h a b . Res. and Devel., Vol. 21, No. 1, 19-31, 1984 (b).
Fitts, P.M., The information capacity of the human motor system in controlling the amplitude of movement, J.Exp.Psych. 47, 381-391, 1954.
Glencross, D.J., Temporal organization in a repetitive speed skill, Ergonom. 16, 765-776, 1972.
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12
CHAPTER TWO
MODELS AND METHODS
In this chapter the framework will be outlined in which the role of visual and proprioceptive information in the generation and control of goal directed move ments is studied.
First of all we will focus on some general aspects of the structure of human movement control. Second, we will propose a control scheme which allows to describe the role of visual and proprioceptive information in more detail. The scheme includes two major levels which arc hierarchically ordered. T h e first level is assumed to provide the intended movement. The second level is assumed to transform the intended movement into the actual movement.
Based on this control scheme and a model of the main aspects, the methods adopted to measure these aspects will be outlined and discussed.
2 1. The hierarchical motor control structure.
Any general theory or model of the control of voluntary human movements faces the problem of the existence of a surplus of degrees of freedom in the skeletal system. T h e r e are more joints in the human body than seem to be necessary for anyone task. Moreover, each joint is typically affected by more muscles than seems to be necessary. This raises two kinds of questions.
First, due to the flexibility of the system, there are more degrees of freedom in the way the body can move than there are constraints. As an example we consider the shoulder-arm-hand system. The position of the hand relative to a reference is given by six degrees of freedom, which describe the position and the orientation of the hand. However, as the shoulder-arm-hand system has many more degrees of freedom, the solution of the attitude problem is not u n i q u e . T h e r e f o r e , additional constraints have to be imposed in order to arrive at a unique solution for this particular case. By contrast, in the control of robotic arms, this problem is circumvented by limiting the number of degrees of freedom by design (Paul, 1981; but: V u k o b r a t o v i c and K i r c a n s k i , 1984). Provided that these constraints can be selected and that it can be decided what to do with each joint and each muscle, than, as the second question, we face the problem of the coordination and the synchronization of their activities when the h a n d has to be moved.
For any central mechanism, the task to control and coordinate all individual muscles directly, to monitor all joint orientations directly and to cope with disturbances is 'liable to swamp' (Hinton, 19S4) the central mechanism, as the complexity of the system is too large.
A conceptual method in what manner the control system would be able to handle this complexity was proposed by Bernstein (1967). He postulated "...A scries of hierarchical levels, each of them, inevitably, having a degree of qualitative independence...". For a given motor task, the control scheme would consist of hierarchically ordered subsystems. Each of these subsystems would have many degrees of freedom which are controlled by a central mechanism, having only a few degrees of freedom (Greene, 1972; Gelfand et al., 1971). The postulated hierarchical structure implies that the task of the higher levels is more or less relieved by the lower levels. The direct control of all variables by a central mechanism is replaced by a distributed control structure (Findeiscn et al., I980). Higher levels arc thought to function in a more abstract manner, specifying the global characteristics of the movement. The lower levels, tuned and adjusted by higher levels, are supposed to transform these global characteristics into more specific actions which, at the lowest level, control the muscle or pairs of muscles of a selected effector system.
This structure embodies a fundamental hypothesis in movement control theory. It states that coordinated movements are not represented in the higher levels as joint-muscle schemes, but rather exist as topologically oriented engrams that can be translated into different joint-muscle sets (Bernstein, 1967). An example of the latter is the similarity of the movement patterns in writing on a blackboard, using the whole arm compared to writing on a paper, using only the muscles of the fingers (Merton, 1972). Bernstein's concepts provided and still provide a rationale for many studies on movement control. His ideas are studied in many disciplines, ranging from neuroscience (e.g. Kots, 1977), physiology (e.g. Arbib, 1981), and (bio)mathematics to control theory (Greene 1972, 1982; Kohout, 1976; Vossius, 1981; Hinton 1984a, 1984b). Also recent motor control theories in experimental psychology (Schmidt, 1975, 1976, 1980; Glencross, 1977; Jeannerod and Prablanc, 1983) are essentially based on the hierarchical organization.
Some aspects of Bernstein's hierarchy have come under closer scrutiny. In consequence to the concept of levels, one faces the problem how to define boundaries between the various levels and how to understand the communication between these levels (Boylls and Greene, 1984). Moreover, questions are raised how parallel activities should be understood as the hierarchical s t r u c t u r e suggests a serial way of action in which the activities of a level depend upon the proper completion of its antecedents. These general questions, which are linked to the actual implementation of the control structure, arc still open.
14
2.2. A two-level scheme
In nearly all models or schemes for the generation and control of voluntary movements, as proposed in recent years, two functionally distinct, hierarchically ordered levels can be distinguished.
The upper level is thought to specify the characteristics of the movement to be executed. The lower level is the executive part. In this level, the characteristics of the movement specified by the upper level are transformed into the resulting movement.
In several proposed models, this distinction is made explicitly. In the generalized motor program scheme (Schmidt, 1975, 1976, 1980; Pew, 1974), as a first stage it is assumed that a motor program must be prepared. From this motor program, in the second stage, the patterns to activate the muscles of a selected effector system arc derived. After reviewing the evidence related to the "centralist"' and the "peri-pheralist" hypotheses on the control of movements, Glencross (1977) also proposes a "two-stage" model consisting of an open loop program component and a closed loop executive system.
Van Dijk (1979) discusses a control scheme in which an intended movement is prescribed in time and space by higher brain levels. In the executive part of his scheme, the intended movement, as internally simulated by the brain, is t r a n s formed into effector specific control signals. In arm trajectory formation, as described by Morasso (1981, 1983; Morasso and Mussa Ivaldi, 1982), preprogram ming of the position trajectory prior to the transformation into the required joint positions and torques to achieve the actual movement is assumed. Also J e a n n e r o d and Prablanc (1983) describe a central programming of the movement based on visual input at the top level. The lower level involves the processing of the generated program by a peripheral loop.
The description of each level varies from a u t h o r to author. Also different view points about the implementation, such as which muscle variables are controlled (Stein, 1982), exist.
Functionally, however, these theories share a two-level s t r u c t u r e in which the first level provides a crude and possibly incorrect version of the required motor response which, on the basis of afferent information, is corrected and refined into more specific activations by the second level (Arbib, 1980).
To clarify the discussion, in the sequel we will refer to the intended movement as the output of the first level, available in some abstract coding.
Prior to the execution of a movement by a subject, the intended movement comes into being on the basis of the internal representation of the task to be executed. This hypothetical concept embodies the knowledge of the outer world, such as the characteristic features of the goal to be reached, and of the strategies on how it can be achieved. F u r t h e r m o r e , it includes the results of practice and experience, as acquired by making other movements.
In most theories on motor control and motor learning, the i n t e r n a l representation is raised in some form or other, though under different names like "internal model" (Pew, 1974), "image" (Sokolov, 1969), "mental image" (Bouisset and Lcstrienne, 1974), "internal memory representation", (Kclso, 1977) or "internal mapping" (Jeannerod and P r a b l a n c , 1983).
From a system theoretical point of view, the internal representation of the task can be considered as an adjustable transfer function which describes the relation between the goal to be reached and the intended movement.
As it specifies a given set of variables, the intendent movement, to follow a set of reference inputs, the goal to be reached, the internal representation constitutes a controller function.
This view resembles the concepts as described by Vincken (1983): the goal to be reached is transformed into a trace which includes the spatial features of the movement to be executed. This trace is scanned at a certain intensity to yield a kind of i m a g i n a r y movement.
As shown by Francis and Wonham (1975) in the context of system and control theory, every controller requires at least some knowledge about the system to be controlled. It implies that the internal representation of the task should contain an i n t e r n a l representation of the controlled system. Hence, when a pointing movement has to be made with e.g. the right arm, some knowledge about the dynamics of this system has to be available. Also, when a movement has to be executed by means of a manipulator, the dynamics of this external system have to be taken into account when the intended movement is generated. In the field of man - machine systems, the internal representation of the system to be controlled has been studied extensively in relation to the ability of the human operator to control the system adequately. (See Rouse and Morris (1984) for a review). Various engineering models, which describe the internal r e p r e s e n t a t i o n of the system either implicitcly (Mc Ruer and Jex, 1967) or explicitely, have been applied to study and to improve the human controller task. Examples of the latter are the models of Senders (1964) and Smallwood (1967) for human sampling behaviour, that of Rouse (1973) for h u m a n prediction behaviour and the optimal control model, as proposed by Baron and K l e i n m a n n (1969),
The function of the intended movement, as derived on the basis of the internal representation, is thought to be manifold. Within the first level, it may be used in the comparison with the goal the subject is trying to reach (Angel, 1976). With respect to the second level, the intended movement specifies the generation of the control signals and the adjustment of the peripheral system to the type of motor task to be executed. However, it also provides a reference for the second level. The sensory inputs of former task executions, as reflected in the intended movement, allow a comparison with the afferent information as obtained d u r i n g the execution 16
of the movement.
In the context of motor learning, (Namikas, 1983), these notions of the intended movement have been described as "memory trace" and "perceptual trace" (Adams, 1971, 1976) or as "recall scheme" and "recognition scheme" (Schmidt, 1975, 1976). Differences between the actual sensory inputs and the expectations are used as momentary inputs to the feedback system in the executive level, in order to correct the ongoing movement (Klapp, 1975). However, these differences are also used to update the reference, as provided by the intended movement, for future task executions. In this way, the afferent information contributes both to the execution of the ongoing movement and to the improvement and adjustment of the internal representation.
To point out the d i f f e r e n t roles of the afferent i n f o r m a t i o n , Paillard (1980) distinguished two distinct "loops": an "error correction loop" for immediate correction of the ongoing movement and an "adaptive loop". The latter operates even after the movement is completed to "tune more accurately the instruction set for the next activation". Also Vincken (1983) distinguished both functions of the afferent information: the contribution to the direct control of the movement while it is being carried out and the use of afferent information for the improvement of the t r a n s f o r m a t i o n from the goal into trace.
The learning of movement is often considered as a process in which increasingly fewer afferent i n f o r m a t i o n is used (Stelmach and Larish, 1980; N a m i k a s , 1983). In view of the outlined two-level scheme, this notion can be interpreted in the following manner.
At the start of the learning process, the intended movement, as generated on the basis of the internal representation, may be rather inaccurate. Consequently, the role of the afferent information in the proper execution of the movement is stressed. As the afferent information also contributes to the improvement of the internal representation, during practice, the internal representation becomes adjusted. Hence, the accuracy of the intended movement increases and the contribution of the afferent information diminishes. When the movement is learned, the afferent information may no longer be used, except for the case, when disturbances d u r i n g the execution of the movement occur. Essentially, the move ment becomes fully preprogrammed. The afferent i n f o r m a t i o n , as obtained during the execution of the movements in the learning phase, has been used to adapt and adjust the internal representation.
2.3. A model of the two-level scheme
To summarize the discussed two-level scheme and the role of the afferent information in the generation and control of voluntary movements, an attempt was made to describe some main aspects by means of a model.
Y(sl
H,(s)
H7(s) - -Ó
N(s)
Fig. 2.1. A model of the two level scheme
The model is depicted in Fig. 2,1. All signals and systems are supposed to be Laplace transformed to the s-domain. The model describes the functional relation between the step input S (s), which is supposed to initialize the movement towards a given target and the resulting goal directed movement X(s). In this model, which basically consists of a master-slave servo loop, the two distinguished levels arc separated by the dotted line. For simplicity, the model is presented for the single-variable case; the multi-single-variable case, to reflect the multi-link s t r u c t u r e of the arm and hand and the various types of afferent information, is not considered cxplicitcly.
We assume that the internal representation can be modeled. Hence we refer to the intcrnai model of the task as a model for the internal representation of the task.
In the upper part of the model, corresponding to the top level of the two-level scheme, the intended movement X(s) is generated on the basis of the intcrnai model of the task. This internal model is described by the servoloop c o n t a i n i n g the subsystems H (s), H_(s), H (s) and H (s). The lower part of the model, the executive level, transforms the intended movement X(s) into the actual movement X(s).
The transfer function of the subsystem H (s) accounts for the static relation between the intended distance to be covered and the actual distance to be covered. Differences between these two distances may arise when e.g. no visual information about the initial or the final position of the hand is available.
The feedback loop in this part of the model mimics the comparison between the generated intended movement and the intended goal to be reached. T h e transfer function of subsystem H (sj accounts for the control law which governs the loop. This control law represents the strategy as adopted in the execution of the movement. It may vary according to the either internally or externally imposed instruction such as to execute the movement as fast as possible or at a lower velocity.
Subsystem H (s) expresses the intcrnai limitations. The transfer function of subsystem Ff (s) represents the intcrnai model of the system to be controlled. Note
4
that as the control law of the loop also depends on the dynamics of H (s), in 4 general H (s) will be a function of H (s).
2 4 A
The control signals, as generated by the first level arc indicated by Y(s). These signals are related to the intended movement by means of H (s).
4
The lower part of the model contains the peripheral loop. T h e peripheral controller, subsystem H (s), receives as an input the difference between the
5 * reference, as described by the intended movement, X{s), and the executed movement, X(s). Together with the control signal Y(s) and an inherent noise N(s) it forms the i n p u t of Ff (s) which models the dynamics of the system to be controlled. As pointed out in the previous section, the afferent information not only influences the execution of the movement, but also contributes to the improvement and adjustment of the intcrnai representation of the task. In the presented model, this means that the transfer functions Ff (s), Ff (s), H (s) and Ft (s) are adapted on the basis of the afferent information. The mechanism which accounts for this a d a p t a t i o n , however, has not been added to the depicted model.
From the s t r u c t u r e of this model, the following relation between the step i n p u t S(s) and the goal directed movement X(s) can be deduced.
The intended movement X (s) equals:
H (s) H (s) H (s)
X(s) = H (s) . S(s), (2.1) 1+H (S) H (s) H4(s)
and the control signal Y(s) equals:
H (s) H (s)
Y(s) = H (s) .S(s) . (2.2) l + H (s) H , ( s ) H , ( s )
2 3 4 The equation of the peripheral loop yields:
H (s) A H (s) H6(s) A X(s) = Y(s) + X(s) 1 + H Is) HAS) 1 + H (s) H (s) 5 6 5 6 N(s) . (2.3) 1 + H,(s) H (s) 5 O (2.4)
it follows from Eq. (2.3): I + H (s) H (s)
X(s)= H (s) Y ( s ) + N ' ( s ) (2.5) 1 + H (s) H (s)
5 6
where the noise contribution N'(s) to X(s) equals: H i s )
N'(s) = N(s) . (2.6) I + H (s) H (s)
5 D
As can be observed from Eq. (2.5), the noise free part of the goal directed movement depends on the following factors:
The control signal Y(s), generated on the basis of the internal model of the task, as given by Eq. (2.2).
The dynamics of the system to be controlled, H (s).
The ratio of the internal model of the system to be controlled, H (s), and the system to be controlled, H (s). This factor results from the comparison between the intended movement and the executed movement.
20
An i m p o r t a n t case of Eq. (2.5) arises when: I + H i s ) H (s) 4 5 = 1 , (2.7) 1 + II (s) H (s) 5 6 which holds if H (s) = H (s). 4 6 Then, Eq. (2.5) reduces to:
X(s) = Y(s) H (s) + N'(s) . (2.8) 6
This means that the noise-free part of the executed goal directed movement only depends on the control signal Y(s) and the system to be controlled H (s). In this case, the p e r i p h e r a l loop no longer contributes to the executed movement. Con sequently, the goal directed movement is preprogrammed.
As:
(2-9) using H (s) = H (s), Eq. (2.8) is equivalent to:
4 6
X(S)=- X(s) + N'(s) . (2.10) Hence within the presented model, a preprogrammed movement, Eq. (2.8) implies
that the executed movement is equal to the intended movement.
2.4. Methods
Based on the two-level scheme, as modeled according to Fig, 2.1, we will now focus on the methods to characterize the influences of the visual and proprioceptive information.
2.4.1. Strategy
In so far, the role of the visual and proprioceptive information in the internal representation of the task has been described in the context of the two-level scheme. To measure the influences, the following strategy has been adopted. Since visual and proprioceptive information contribute to the a d a p t a t i o n and the adjustment of the internal representation, the effects of both types of information
are reflected in the intended movement. Hence, the influences can be deduced when the intended movements are studied. Direct measurement of the intended movement from the executed movement, however, is hampered, as in general also the peripheral loop contributes to the executed movement, Eq. (2.5]. As shown in the previous section, the contribution of the peripheral loop vanishes when the executed movement is preprogrammed. Then the executed movement equals the intended movement, so that the influences of the visual and proprioceptive information to the internal representation can be established from the executed movement.
A s t r a i g h t f o r w a r d method to study these influences is to compare executed movements when the visual a n d / o r proprioceptive information is manipulated. Provided that the executed movements arc preprogrammed, which can be achieved by training, the effects of the manipulated information can be established by comparing the executed movements.
The application of this method in an experimental setting raises some additional problems. First of all, it should be noted, that the goal directed movement not only depends on the visual and proprioceptive information, as reflected in the internal representation, but also depends on the imposed task. Different instructions about the movement to be executed give rise to d i f f e r e n t internal representations of the task. Consequently, the intended movements will also differ. Within the presented model, this was indicated by the different control laws which govern the loop. As these differences limit the comparison of the executed movements made under various conditions, the instruction about the movement to be executed should be the same for all considered conditions.
Second, it is well known, that in a given experimental condition, even after practice, some variability in successive, executed movements remains. If external disturbances can be excluded, the variability in executed movements can be a t t r i b u t e d to a variability in the intended movements. This implies that within the presented model, the internal model of the task should be considered as a stochastic r a t h e r than a deterministic process. Then the intended movements are in fact realisations of this stochatic process, when triggered by the step input.
Hence, a comparison of executed movements made under various conditions should not be performed between single movements but between the ensemble of movements, as made in each condition. As a characterization of the ensemble, we will consider the mean and standard deviation. To stipulate the difference between the ensemble of movements and this c h a r a c t e r i z a t i o n , the latter will be r e f e r r e d to as the desired movement.
Therefore, the comparison of the executed movements made under various conditions will be performed by comparing the desired movement of each experimental condition.
To perform the comparison, an adequate description of the desired movements is 22
required. This can be conceived by means of a describing function model for goal directed movements.
2.4.2. The describing function model for goal directed movements
A commonly reported method (e.g. Megaw 1972; Carlton, 1981) to describe a goal directed movement is to characterize the movement by means of measures like the reaction time, the movement time, the maximum velocity and the final positioning accuracy. These measures, however, describe the dynamical behaviour of the movement only partly. Hence information as contained in e.g. the shape of the movement will be lost.
To overcome these drawbacks, an attempt was made to develop a model based description of the movement, which takes the entire movement into account. Requirements for this model were, on the one hand, a reasonably accurate description of the movement and, on the other, the feasibility for robust identi fication. The latter requirement implies that the model should be parsimonious i.e. r e d u n d a n c y of parameters should be avoided.
The model applied is a describing function model. This type of model consists of a linear relationship between input and output, represented by a transfer function, and a remnant which represents that part of the output which can not be obtained by a linear operation on the input (Gelb and Vandevelde, 1968).
Consequently, the model is only valid for the given input.
N(s)
H([s)
Fig. 2.2. The describing function model for goal directed movements
The describing function model for goal directed movements is depicted in Fig. 2.2. All signals and systems arc Laplace transformed. Its structure resembles to the upper part of the model for the two-level scheme as discussed in Sect. 2.3. T h e model describes the relation between the step input S(s) and the output X(s) of the controlled system H (s). Its order was established from the physical relation between the step i n p u t and the acceleration of the executed movements. As the latter increases gradually from zero, the model should at least be of order three.
Apart from its structure, the model is characterized by the parameters (K , K , T , d e e T , a , a ). The gain factor K accounts for the d i l f c r e n c c between the intended distance to be covered, as given by the amplitude of the step i n p u t S(s) and the actually covered distance, as obtained from X(s). The time delay outside the loop models part of the reaction time between the a p p e a r a n c e of the step input and the start of the executed movement.
The feedback control law is given by: K 1
C - T S
H (s) - e e . (2.11)
C s H (s) c
Bandwidth limitations are modeled by the second order system, which contains the parameters a and a . The noise N(s) represents the r e m n a n t of the describing function model.
A l t e r n a t i v e model structures aiming e.g. to reduce the number of parameters by merging the time delays T and T into one time delay inside the loop, have been studied and reported elsewhere (Van Lunteren et al., 1983; Sparreboom and Van L u n t e r c n , 1984). The presented model was found to be most preferable both with respect to the accuracy of the description of the goal directed movement and the number of parameters.
The various methods necessary to process the recorded goal directed movements into a c c u r a t e parameter values will be presented in Ch. 3.
T h e application of this describing function model causes some restrictions to the class of movements that can be characterized accurately. Movements which are not continuously d i f f e r e n t i a t e on the interval of the entire movement can not be parameterized properly. An example of the latter arises when the goal is actually reached in two or more distinct movements. An accurate description of this type of movement would only be achievable when the single step input of the model would also be separated into a corresponding number of discrete step signals. Moreover, it would r e q u i r e a considerable extension of the model structure.
It can be argued, however, that after practice this type of movement will not occur, so t h a t the presented model is a p p r o p r i a t e to describe the well t r a i n e d movements as will be considered in the experiments.
2.5. References
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Adams, J.A., Issues for a closed-loop theory of motor learning. In: G.E. Stelmach (Ed.), Motor control: issues and trends, Academic Press, 1976.
Angel, R.W., Efferencc copy in the control of movement, Neurology, 1164-1168, 1976.
Arbib, M.A., I n t e r a c t i n g schemas for motor control, In: G.E. Stelmach and J. Requin (Eds.), Tutorials in motor behaviour, North-Holland, Amsterdam, 1980. Arbib, M.A., Perceptual structures and distributed motor control, In: V.A. Brooks
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Francis, B.A. and W.M. Wonham, T h e internal model principle of linear control theory, Proc. 6th World Congress, Boston, USA, 1975.
Findeisen, W., F.N. Bailey et al., Control and coordination in hierarchical systems, Wiley, London, 1980.
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Gelfand, I.M., V.S G u r f i n k e l , MX. Tsetlin and M.L. Shill, Some problems in the analysis of movements, In: Gelfand, I.M, and M.L. Tsetlin (Eds.), Models of the structural-functional organization of certain biological systems, MIT-press, 1971.
Glencross, D.J., Control of skilled movements, Psych. Bull,, Vol. 84, No. 1, 14-29, 1977.
