718Internal models for motor control and trajectory planning
Mitsuo Kawato
A number of internal model concepts are now widespread inneuroscience and cognitive science. These concepts aresupported by behavioral, neurophysiological, and imaging data;
furthermore, these models have had their structures andfunctions revealed by such data. In particular, a specific theory
on inverse dynamics model learning is directly supported byunit recordings from cerebellar Purkinje cells. Multiple paired
forward inverse models describing how diverse objects andenvironments can be controlled and learned separately haverecently been proposed. The ‘minimum variance model’ isanother major recent advance in the computational theory of
motor control. This model integrates two furiously disputed
approaches on trajectory planning, strongly suggesting thatboth kinematic and dynamic internal models are utilized inmovement planning and control.

modelers, connectionists and neurophysiologists [2–4]),
and have been studied increasingly seriously as one of the
major theories of motor control and learning in neuroscience and cognitive science. Accordingly, in the past few
years, much more direct and convincing data than everbefore have been accumulated. Such data can alreadyshow the existence, structures, learning, functions andanatomy of internal models. Of particular importance, wehave seen significant theoretical advances in elucidation of
the generalization, multiplicity and switching of internal
models, and their possible use in trajectory planning.

Abbreviations
DLPN
dorsolateral pontine nucleus
MST
medial superior temporal
OFR
ocular following responses
VPFL
ventral paraflocculus

In this review, I will discuss data supporting the existenceof internal models. It has been shown that the behavioral
paradigms in use are diverse and include adaptation to force
fields, posture control, grip-force–load-force coupling, oculomanual coordination, and the vestibular system. An
explanation will be given on points of controversy between
the equilibrium point control hypothesis and the internal
model hypothesis, and some clues towards their resolution
will be presented. Recent neurophysiological and imaging
studies that suggest that the cerebellar cortex is a major siteof internal models will also be discussed. Furthermore,structures of internal models will be explored by ‘generalization’ experiments; modularity and multiplicity aresuggested by the data obtained. Finally, two major
approaches to trajectory planning will be reviewed and a
new theory will be introduced to integrate them.

Introduction

Existence of internal models

Internal models are neural mechanisms that can mimic the
input/output characteristics, or their inverses, of the motor
apparatus. Forward internal models can predict sensory
consequences from efference copies of issued motor commands. Inverse internal models, on the other hand, cancalculate necessary feedforward motor commands fromdesired trajectory information.
Fast and coordinated arm movements cannot be executedsolely under feedback control, since biological feedback
loops are slow and have small gains (Figure 1a). Thus, theinternal model hypothesis (Figure 1b) proposes that thebrain needs to acquire an inverse dynamics model of theobject to be controlled through motor learning, after which
motor control can be executed in a pure feedforward manner. In theory, a forward model of the motor apparatus
embedded in an internal feedback loop can approximate
an inverse model.

When subjects first undertake point-to-point arm reaching
movements under force fields which effectively change
dynamic characteristics of the arm, their hand trajectories
are distorted compared with the normal, roughly straightpaths; also, the end point errors are large, especially in the
direction of the applied force. The force fields generated
predetermined forces which depended on the state spacepoint (position, velocity), and were produced by a robot
manipulandum [5] or by a rotating room [6,7•]. After
repeated trials, the hand trajectories gradually become normal, straight paths, and the end point errors decrease insize. However, when the force fields are removed suddenly after this adaptation has occurred, the trajectories
become distorted and the end-point errors become large inthe opposite direction to the previously applied force.
Such an occurrence can readily be explained as follows by
the adaptation of the inverse dynamics model of the arm to
the applied force field (see Figure 1b).

The internal model concept has its origin in control theory
and robotics, but Ito [1] proposed almost 30 years ago thatthe cerebellum contains forward models of the limbs andother brain regions. More recently, internal models haveattracted a broader range of specialists (e.g. neural network

Under normal conditions, the inverse dynamics model calculates motor commands which appropriately compensate
the arm dynamics. Under the altered dynamics conditions,in contrast, the motor commands are insufficient to compensate for the applied force, and this leads to distortions

Addresses
ATR Human Information Processing Research Laboratories and
Kawato Dynamic Brain Project, ERATO, JST, 2-2 Hikaridai, Seika-cho,
Soraku-gun, Kyoto 619-0288, Japan; e-mail: kawato@hip.atr.co.jp
Current Opinion in Neurobiology 1999, 9:718–727
0959-4388/99/$ — see front matter © 1999 Elsevier Science Ltd.
All rights reserved.

Internal models for motor control and trajectory planning Kawato719

Figure 1
Feedback and feedforward control using an
inverse model of a controlled object. (a) In
feedback control, the realized trajectory iscompared with the desired trajectory, and theerror is computed. The feedback motor
command is generated from this error using a
relatively simple algorithm, such as aproportional, integral and derivative feedback
controller. In robotics, almost all practicalapplications depend solely on feedback
controls. This is because feedback delays in
artificial systems can be made small; hence,
sampling and control frequencies can be quite
high (from 500–10000 Hz). In biological motor
control, however, the delay is very large. For
visual feedback on arm movements, the delay
ranges from 150–250 ms. Relatively fast spinal
feedback loops still require 30–50 ms timedelays. These are very large compared with the
movement duration of very fast (150 ms) tointermediate (500 ms) movements. Because
time delay occupies a large proportion of
movement execution time, and feedback gains
cannot be set high because of instability due tolarge delays, fast and smooth movements
cannot be executed depending solely on
feedback control. Muscle intrinsic mechanicalproperties produce proportional (stiffness) and
derivative (viscosity) gains without delay.
However, these viscoelasticities are small forwell-trained movements [21,23•]. (b) If an(a)

Stiffness, viscosity
Feedback
motor
commandDesiredtrajectory +Gain–Controlled
objectRealized
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Delay

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Current Opinion in Neurobiology

inverse dynamics model is serially-connectedwith the controlled object, the serial systemgives a mathematical identity function. That is,
the output (i.e. the realized trajectory) is
identical to the input (i.e. the desired trajectory).
Thus, the inverse model, if it exists and can belearned, becomes an ideal feedforward
controller. In biological systems with large

in the trajectories and large end-point errors. During
repeated trials, the inverse dynamics model changes to theinverse of the combined arm dynamics and the applied
force field. Then, normal trajectories reappear and theend-point errors are reduced. This adaptation is assumed
to involve plastic changes of the synaptic efficacy of neurons constituting the inverse dynamics model. With thesudden removal of the applied force field, however, theinverse dynamics model continues to generate the motor
commands to compensate for the arm dynamics, as well as
the non-existing force field, and this leads to distortions in
the trajectories in the opposite direction.
The most convincing set of data for the existence of forward
models comes from studies on coordination between reaching and grasping. When an object is held with the tips of theindex finger and thumb on either side (Figure 2a), the grip
force is precisely controlled (Figure 2b) so that, under normal conditions, it is just slightly greater than the minimum
grip force needed to prevent slip [8]; this is also so when thearm dynamics is altered by a robot [9]. Such a gripforce–load-force coupling is explained by a framework that
contains both the inverse and forward models of the arm, as
shown in Figure 2c. Functional magnetic resonance imaging(fMRI) studies have revealed cerebellar activity specific togrip-force–load-force coupling [10•], suggesting the existence of forward models in the cerebellum. In principle, thescheme shown in Figure 2c can be generalized to the coordination of any combined movements (e.g. eye and hand

feedback delays and small feedback gains,internal models are the only computational
possibility for fast and well coordinatedmovements. Even for artificial robotic systems,
if reduction gears are not used (e.g. direct drive
motors, artificial muscles, hydraulic actuators),
inverse models are required (see, for example,
the URL http://www.erato.atr.co.jp/DB/).

movement, or right-hand movement and left-hand movement) in any part of the body. Oculomanual coordination[11••], and bi-manual tracking (E Nakano, DM Wolpert,
personal communications) are examples.
Internal models were also studied in the sensory system forprocesses other than motor control. The vestibular system
is composed of semicircular canals, which report any angular acceleration, and otolith organs, which respond to any
linear acceleration. Because the otolith responds to boththe occurrence of linear acceleration and gravity, it is computationally difficult to analyse the ambiguous sensory
information [12]. Through the use of dexterously designed
vestibular stimuli and the examination of resulting eye
movements in monkeys [13] and humans [14], internal
models have been suggested to estimate linear acceleration and gravity from the canal and otolith outputs. This
internal model can be classified as an inverse model of thesensor physics with acceleration and gravity as its inputs.
The necessity for internal models in motor control has been
one of the central issues of debate in relation to equilibrium-point control. Muscle and peripheral reflex loops havespring-like properties that pull joints back to their equilibrium positions by generating a restoring force against
external perturbations. This viscoelasticity can be regarded
as peripheral feedback control gain, which is adjustable byregulating the associated muscle co-contraction level andreflex gain. It has been hypothesized that by exploiting this720

Motor systems

Figure 2(a)(b)
Load force
Grip force

Force
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Time (s)(c)

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Current Opinion in Neurobiology

viscoelasticity, the brain can control the limbs simply bycommanding a series of stable equilibrium positionsaligned along the desired movement trajectory (i.e. theequilibrium-point control hypothesis) [15–17,18•]. In particular, it was once advocated that internal models are notnecessary provided that the brain utilizes equilibrium control. This theory, however, requires that viscoelastic forces
increase as the movement speeds up because the dynamic
forces acting on the multijoint links grow in rough proportion to the square of the velocity. On the other hand, thealternative hypothesis (i.e. the internal model control,
shown in Figure 1b), proposes the realization of a fast andaccurate movement even with low viscoelastic forces. A
point of controversy here is whether the CNS relies on highviscoelastic forces without internal models [15–17,18•] or
utilizes acquired internal models with low viscoelastic
forces [19–21,22•]. Recent observations of a relatively low
stiffness during well-trained movements have supported
the existence of internal models [21,23•].
Reports showing that the electromyogram (EMG) is higher in a novel environment than in a normal environment

Coordination of grip force and load force, and acomputational model based on internal forward
and inverse models. (a) When an object is heldwith the tips of the index finger and thumb oneither side, the normal grip force on the contact
surface allows for the development of africtional force, which prevents the object fromslipping. (b) The grip force is precisely
controlled so that it is just slightly greater thanthe minimum grip force needed to prevent slip.
(c) This grip-force–load-force coupling is
explained by a framework that contains boththe inverse and forward models of the arm.
Take, for example, a point-to-point arm-reaching
movement that takes place while the hand isgrasping an object. The inverse model of the
combined dynamics of the arm, hand andobject calculates the necessary motor
commands from the desired trajectory of thearm. These commands are sent to the arm
muscles as well as to the forward dynamics
model as the efference copy. Then, the forward
model can predict an arm trajectory that isslightly in the future. Given the predicted arm
trajectory, the load force is calculated; then, by
multiplying a friction coefficient and a safety
factor, the necessary minimum level of grip
force can be calculated. To realize this grip
force time course, motor commands are sent tohand muscles. This model predicts that threedifferent computational elements are necessary
for grip-force–load-force coupling: the inverse
model for arm reaching; the forward model forarm trajectory prediction; and the grip force
controller for grip execution. Tamada et al.
(T Tamada et al., personal communication) haverecently identified three fMRI active locicorresponding to these three elements.

[24], however, have supported the empirical observationthat any stiffness at the beginning of learning may not be
as low as that after extensive training. Computationalmodels have suggested that there is an advantage to integrating the muscle viscoelasticity and internal models for
efficient learning of internal models [25,26]. Accordingly,
one of the major future experimental objectives is to elucidate how these two schemes are integrated; Osu, Katoand Gomi have obtained new data suggesting a specificscheme of integration (R Osu, H Kato, H Gomi, personalcommunication).

Internal models in the cerebellum
It is conceivable that internal models are located in allbrain regions having synaptic plasticity, provided thatthey receive and send out relevant information for their
input and output. We have good reason to believe that atleast some internal models are acquired and stored in the
cerebellar cortex. For example, there is a new computational theory [27••] that allocates supervised learning,
reinforcement learning, and unsupervised learning to the
cerebellum, the basal ganglia and the cerebral cortex,

Internal models for motor control and trajectory planning Kawato

respectively. This is partially based on previous cerebellar learning theories [28–30,31 ••]. The learning
acquisition of internal models is best performed bysupervised learning, and accordingly, the cerebellar cortex seems the most appropriate location as the storagesite of internal models.
The most convincing neurophysiological data for internal
models were obtained for eye movements. Kawano and hiscolleagues [32] studied neural circuits involved in controlling ocular following responses (OFR), which are reflex eye
movements with a short latency. These circuits stabilize
retinal images and are driven by large visual field movements. It is known that they involve the MST (medial
superior temporal) area, dorsolateral pontine nucleus(DLPN), and the ventral paraflocculus (VPFL) of the cerebellum [32]. Figure 3 summarizes neural networks for OFR
based on [32]; a similarity to the feedback–error–learningmodel [30] is suggested. In accordance with the theory, theclimbing fiber inputs to Purkinje cells during OFR carryerror signals in the motor command coordinates, andaccordingly, their temporal waveforms can be well reproduced by the inverse dynamics model of the eye [33••]. In
Figure 3, the simple spikes of the Purkinje cells during
OFR are well fitted by the inverse dynamics model of theeye, but share an approximate mirror image relationshipwith the climbing fiber inputs. For both the climbing fibers
and simple spikes, the position coefficients have the opposite sign to the real inverse dynamics model of the eye[34,35••], suggesting that the VPFL comprises a major,
dynamic part of the inverse dynamics model, and also that
other brain regions complement it. The data from monkeys
could be strengthened by recording in the flocculus of catsduring optokinetic responses [36•]. In particular, the negative sign of the position coefficient was confirmed, evenwith the inclusion of the slide term.

721

which neural firings are encoded [40]. Accordingly, examining inverse dynamics representations is very difficult.
However, strong physiological evidence suggests that the
climbing fiber inputs also work to encode error signals forarm movements [41••]. In addition, imaging, physiologicaland lesion studies have demonstrated that the cerebellum is
at least one of the possible sites for internal models for arm
movements [42••,43••,44•,45•]. A theoretical model — thatthe cerebellum constitutes a major part of the parallel
inverse models of the arm has been proposed [46••].
The most frustrating missing link in the cerebellar learning
hypothesis is the computational clarification of peculiar
physiological and anatomical characteristics of inferior
olive neurons [47]. A compartmental biophysical model ofinferior olive neurons electrically coupled by gap junctions
has been found to reproduce many such physiological data
both in vivo and in vitro [48••]. Furthermore, there has
been a suggestion that there is ‘desynchronization’ of coupled neurons by gap junctions [48••]. This theoretical work
may in fact provide an important clue towards elucidating
the computational significance of the above missing link
(N Schweighofer, K Doya, M Kawato, unpublished data).

Structures of internal models

The MST area and DLPN send visual information to the
VPFL [37], and drastic changes of neural codes occur at
the parallel fiber Purkinje cell synapses. That is, in thearea MST and DLPN, population coding is used: the optimum directions of the visual stimuli cover the entire 360°
and the optimum velocities are widespread, and many different temporal waveforms of firings can be observed[32,37]. On the other hand, temporal rate coding is used for
Purkinje cells: either downward or ipsilateral visual motion
is optimal, the firing rate increases with the stimulus velocity, and the temporal waveform is stereotypicallyreconstructed by the inverse dynamics model. Computer
simulations based on the feedback–error–learning theory[38,39] have shown that changes to neural codes, as well as
the learning acquisition of the inverse dynamics model,
can be reproduced based on the known synaptic plasticityof Purkinje cells, that is, long-term depression, long-term
potentiation, and rebound potentiation.

The functional structures of internal models can be probed by
the so-called ‘generalization experiment’ [49–52,53•,54,55•].
Humans or animals are trained for a specific set of movement
trajectories with an altered kinematic or dynamic perturbation. After sufficient learning, the organism’s ability to copewith different trajectories or movements in a different part of
the workspace in which the motor apparatus can move is
examined. If ‘generalization’ is considered perfect, new trajectories are controlled precisely from the beginning. If
generalization is considered to not exist, the performance of
subjects undergoing new experiences is as poor as those withno prior learning. The brain does not memorize a simple association between movement instances and motor commands.
Rather, it has an internal memory of the motor apparatus andthe external world in the form of an inverse dynamics modelwith state–space representations. The motor commands ateach instance are calculated by a functional map from thestate–space input point, including the acceleration, velocity,and position of the desired trajectory [51,52]. If generalizationof learning is perfect, the inverse dynamics model after learning is very precise over the entire state–space, and must
therefore take the form of a parametric and analytical model.
In contrast, if there is no generalization apart from the experienced trajectory, the inverse dynamics model is a local
table-look-up map. The experimental data [49–52,53•,54,55•]
suggests neither is the case. Instead, an intermediate generalization level has been consistently reported. It is possible,
therefore, that internal models in the brain are similar to artificial neural networks or connectionist models in theirgeneralization capability.

Studying arm movements is much more difficult than studying eye movements with respect to the coordinate frame in

An imperfect generalization of internal models would
strongly suggest the need for modular structures [56]. This

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Figure 3
(a)

(c)
(i)

Firing rate (imp/sec)

400
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Current Opinion in Neurobiology

Change of neural codes and learning of inverse dynamics model inthe cerebellum for OFR. The neurophysiological data shown in (a) and(c) are taken from [32,33••,37] and reproduced with permission.
(a) The firing characteristics of MST, DLPN and VPFL neurons. (b) A
schematic neural circuit for OFR. (c) Temporal firing patterns of VPFL
Purkinje cells in upward eye movements induced by upward visualmotion. (a) (i) Peri-stimulus time graphs of the firing rates of a typicalneuron in each of the three areas. The origin of time is taken as theonset of visual stimulus motion. (ii) Histograms of a number of cells
within a given range of the optimum stimulus speeds. (iii) Polar plotsof optimum stimulus directions. U, C, D and I indicate upward,
contralateral, downward, and ipsilateral, respectively. VPFL Purkinjecells were classified into two groups, vertical cells and horizontal
cells, based on simple spike (green) and complex spike (red) optimum
directions. (b) The circuit can be divided into two main pathways. The
upper part shows the cortico–cortical (the cerebral cortex to the
cerebellar cortex) pathway, which corresponds to the feedforward arcof the feedback–error–learning model. The lower part of the pathway
shows the phylogenetically older feedback pathway containing theaccessory optic system, which corresponds to a crude feedback
controller in the feedback–error–learning scheme. The theory predicts
that the accessory optic system first determines the motor command
coordinates (upward for PT [pretectum], and contralateral for NOT[nucleus of optic tract]). This motor frame of reference is conveyed tothe inferior olive nucleus, and determines the optimum stimulus
directions of the climbing fiber responses, which are reflected incomplex spikes (aiii, red lines). Based on known synaptic plasticity(long-term depression, long-term potentiation, rebound potentiation)of Purkinje cells, it is predicted that the optimum stimulus direction ofeach Purkinje cell for simple spikes and complex spikes is 180°
opposite. (aiii, right shows that this is the case). (c) Accumulated
temporal firing patterns of nine Purkinje cells (black curves) and theirreconstruction based on inverse dynamics model (red and green
curves). The model further predicts that the temporal firing patterns of(i) simple spikes and (ii) complex spikes should be mirror images ofeach other. Kobayashi et al. [33••] confirmed this, and furthermore
reconstructed simple spike as well as complex spike firing waveforms
by the inverse dynamics model. This strongly supports the mostcritical assumption of the feedback–error–learning scheme that the
climbing fiber inputs convey error signals in the motor command
coordinates, and the simple spike firing is learned by being guided bythis error signal through synaptic plasticity. Yamamoto et al. [38,39]
reproduced the dramatic change of neural codes, and the learning
acquisition of simple spike firing patterns, as well as eye movement
waveforms based on Purkinje cell synaptic plasticity. AOS, accessory
optic system; EOMN, extraocular motor neuron; LGN, lateralgeniculate nucleus; MT, middle temporal area; STS, superior
temporal sulcus.

is because a single gigantic internal model with an imperfect generalization capability cannot possibly learn or deal
with a whole range of different behavioral situations.
However, different modules cannot be entirely indepen-

dent from one another because they all exhibit somedegree of generalization. This means that some interference may occur between multiple internal models unlessan efficient computational mechanism exists to regulate

Internal models for motor control and trajectory planning Kawato

723

Figure 4

Responsibility
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Multiple paired forward and inverse models (MPFIMs) [62••] in thecontext of grip-force–load-force coupling for multiple manipulated
objects. The computational scheme shown in Figure 2 is fine as longas only a single object is manipulated. But a single internal modelcannot deal with a large number of objects with different kinematic anddynamic properties. This is because incomplete learning generalization
leads to a catastrophic interference between different learning epochs
and between different motor primitives. MPFIM postulates acomputationally coherent principle to overcome this difficulty. The brain
prepares many modules, each of which comprises three elements: aforward model, an inverse model, and a responsibility predictor.
Learning, switching and blending of these multiple modules are, in
principle, controlled by the relative goodness of predictions made bymany forward models. Furthermore, predictive switching between
modules is performed by responsibility predictors based on contextual
information. In the Bayesian framework, the outputs from theresponsibility predictors determine prior probability about which
module will be recruited for a given environmental situation, and theprediction error of each forward model determines which module islikely to be appropriate for the situation. A soft max function, gathering
all products of the prior probability and the likelihood, finally computes
the responsibility signal (0–1), which specifies the control contributionof the inverse model, as well as the learning responsibility of inverseand forward models within each module. For example, suppose that aperson needs to manipulate one of several objects (see upper inset).

By visual information of the object, an appropriate module for, say, aracket could be pre-selected. On actual manipulation of the object, theforward model for the racket module predicts sensory consequence
from the efference copy of issued motor commands. If its prediction isgood, that module will continue to be used. However, if the visual
information is erroneous and the object actually grasped is a fork, theracket module prediction is bad and the fork module prediction isbetter, thus the racket module will be turned off and the fork module
will be turned on after actual movement execution. Haruno et al. [63••]
simulated a simple version of this ‘size–weight illusion’. Contextual
information for the responsibility predictor could be virtually anything
useful, such as vision, audition, tactile information, reasoning, verbal
instruction, sequence of movement elements, outputs from other
responsibility predictors, descending signals from higher brain regions,and so on. This gives versatile cognitive capability to MPFIM. Fromprevious studies on the interference of two learning epochs[51,52,57,58], we infer that if some contextual signal is very unusual
and consequently strong (e.g. a unique combination of tactile andvisual information if an arm is attached to a robotic manipulandum),other contextual signals have smaller influences (e.g. color is too weak,
but posture and time still have discriminating effects). Because MPFIM
introduces a blending of multiple inverse dynamics model (IDM) inputs,
a finite number of modules could in principle deal with a vast numberof different objects (see simulation [63••], as well as supporting
behavioral studies [59,61••]).

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their learning and involvement in a specific situation.
Different internal models do seem to compete with eachother in learning, especially for events involved in temporal proximity [57,58]. Interestingly, it has been found thatmultiple internal models can be mixed in an adaptive way
when necessary [59,60••,61••].
On the basis of the findings described above, a new theory has recently been developed where multiple internal
models can be learned and combined adaptively[62••,63••]. Figure 4 shows how this new theory can beused to explain the manipulation of many different objects
with a finite number of internal model modules, while atthe same time efficiently utilizing contextual informationsuch as the vision of objects, verbal instructions, or thesequence of object presentation.

Trajectory formation
Computational theories on how arm reaching trajectories
are planned have been a central issue in motor control since
it was shown that they involve roughly straight hand paths
and bell-shaped velocity profiles [64]. Many of the different
computational models can be classified into two types:
kinematic models such as the minimum jerk model [65],and dynamic models such as the minimum torque-change
model [66]. Because these two classes of models enable theexperimental testing of qualitatively different predictions,rich data sets are now available for discriminating between
the two types (for kinematic planning and against dynamicplanning, see [67–70]; for dynamic planning and against
kinematic planning, see [71,72•,73•,74••]). However, analyses have been complicated and there remain areas ofcontroversy [75].
The integration of these two approaches has been suggested [76•], and an ingenious theory of integration was recently
proposed by Harris and Wolpert [77••]. Their minimum
variance model also takes the form of an optimization
model, in the tradition of many previous models. The objective for optimization in this model is to minimize the end
point variance, and is therefore a purely kinematic variable.
This variance, however, critically depends on the magnitudeof the motor commands. Consequently, the whole optimization process is completely dynamic — that is, the optimal
trajectory critically depends on the dynamics of the muscles
involved, the motor apparatus, and the environment.
The ‘minimum variance model’ is thus kinematic in its
objective function, but the computational process isdynamic, and the trajectory depends on the dynamics.
This model can be viewed as a version of the minimum
motor command change model [75]. This is because in the
integral of the objective function, the square of the motor
commands is increasingly more heavily weighted as thetime approaches the movement end. Finally, because thecomputational process takes into account both the kinematics and dynamics of the motor task, it is important for

both kinematic and dynamic internal models to be utilized
for the trajectory planning, either implicitly or explicitly.

Conclusions
The concepts concerning internal models have now been
well supported by behavioral studies in the field of sensory motor control. Neurophysiological studies have justbegun but should be fruitful in the next five years.
Theoretically, the concept should be extended from puresensory motor control to cognitive domains as we have aflood of data suggesting cerebellar involvement in higher
cognitive functions such as language [78,79,80••]. This isespecially important because the cerebellar computational
principle can be ubiquitous, on the basis of the uniform
neural circuit of the cerebellar cortex, despite diverse functions of different cerebellar loci. In the near future, theauthor expects major breakthroughs in the concepts andcomputational theories of internal models entering into
cognitive domains such as communication, thinking, andconsciousness, on the basis of their firm foundations insensory motor integration.

Acknowledgements
I wish to thank my collaborators in ATR and in the ERATO Dynamic Brain
Project as well as those outside, especially, Daniel Wolpert, Chris Miall andRandy Flanagan. This research was partially supported by HFSP grants,
special coordination funds of promotion of science.

References and recommended reading
Papers of particular interest, published within the annual period of review,
have been highlighted as:• of special interest•• of outstanding interest
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2.

Kawato M, Furawaka K, Suzuki R: A hierarchical neural networkmodel for the control and learning of voluntary movements. Biol
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3.

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10. Tamada T, Miyauchi S, Imamizu H, Yoshioka T, Kawato M: Activation•of the cerebellum in grip force and load force coordination: an
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27. Doya K: What are the computations of cerebellum, basal ganglia,•• and cerebral cortex? Neural Networks 1999, 12:961-974.
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grip–force–load–force coupling. In the figure, the grip force controller
should be replaced by the smooth pursuit controller.

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30. Kawato M, Gomi H: The cerebellum and VOR/OKR learningmodels. Trends Neurosci 1992, 15:445-453.
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This is a review of the author’s brilliant contributions to the elucidation of
cerebellar functions in motor learning and coordination. A proposed cerebellar theory of coordination between different degrees of freedom by theuse of long parallel fibers was a large leap forward from the classicalMarr–Albus–Ito theory, and is very closely related to internal model theories
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The simple spike firing patterns of Purkinje cells were well reconstructed froma linear combination of acceleration, velocity and position of eye movement
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Takemura A, Inoue Y, Gomi H, Kawato M, Kawano K: Analysis ofneuronal activities during ocular following responses in alertmonkeys. Tech Rep IEICE 1999, NC99-22:77-84.

38. Yamamoto K, Kobayashi Y, Takemura A, Kawano K, Kawato M: A
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Motor systems

the beginning of movement can also be interpreted as the predicted error fora default movement response, as simulated in [46••].
42. Imamizu H, Miyauchi S, Tamada T, Sasaki Y, Takino R, Putz B,•• Yoshioka T, Kawato M: Human cirebellar activity reflecting anaquired internal model of a novel tool. Nature 1999, in press.
Previous neuroimaging studies reported a decrease in cerebellar activities
along with motor or cognitive learning. These results have often been interpreted as suggesting that the cerebellum is important only in the early phaseof learning and that it is not the memory site. In these interpretations, theinternal models are not located in the cerebellum. The authors showed that
cerebellar activity remains even after sufficient learning by dexterously equalizing error levels between the test and control conditions.
43. Blakemore SJ, Wolpert DM, Frith CD: Central cancellation of self•• produced tickle sensation. Nat Neurosci 1998, 1:635-640.
Self-produced tickling is not as amusing as tickling by others. The authors
found decreased cerebellar activity during tickling by oneself than during thesame movements which did not produce tickling, and further decreased
activity compared with externally produced tickling. Cancellation of the sensory inputs by predictions of sensory consequences from the efference copyof the motor commands using the forward model is suggested. This is attractive since complex spikes, probably the most energy-demanding processes
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events but not by physically equivalent but predictable events. It is still puzzling why the cerebellar activity during self-produced tickling is lower than
the rest condition. Simple cancellation can explain activity negation, but cannot explain activity reduction.
44. Miall RC, Keating JG, Malkmus M, Thach WT: Purkinje cell complex•
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statistically larger than background. This could be interpreted in the framework of the forward model predicting sensory consequences. The simple
spikes make predictions about future sensory events, and these are compared with the real sensory feedback after a 150 ms sensory time delay; theirconsequences are represented as complex spikes.
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46. Schweighofer N, Spoelstra J, Arbib MA, Kawato M: Role of the•• cerebellum in reaching quickly and accurately. II. A detailed modelof the intermediate cerebellum. Eur J Neurosci 1998, 10:95-105.
This is a simulation study of the learning inverse dynamics model of the armin the intermediate cerebellum based on the feedback–error–learning model.
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48. Schweighofer N, Doya K, Kawato M: Electrophysiological properties•• of inferior olive neurons: a compartmental model. J Neurophysiol
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60. Blakemore SJ, Goodbody SJ, Wolpert DM: Predicting the•• consequences of our own actions: the role of sensorimotor
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Two robots simulated a case in which virtual objects were held in one handand acted on by the other. Precise predictive grip-force modulation of therestraining hand was observed only when the force feedback gain between
the two robots was close to 1, just like with a real object. The results showthat predictive grip-force modulation requires not only self-generated movements but also a sensory consequence which is consistent with a specificcontext. That is, if the forward model’s prediction in Figure 2 is not good, thatcoordination scheme is not used. The authors proposed the conceptualmodel, which led to the basic idea of determining the responsibility of each
module by the goodness of the prediction of the forward model within thatmodule [62••].
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Multiplicity of internal models for dynamic and kinematic transformations wasinvestigated in order to determine whether multiple internal model can becomposed or decomposed when occasion calls. When subjects learned avisuomotor rotation and viscous curl field first, reaching errors were smaller
for a combination of these transformation than without prior experiences.
62. Wolpert DM, Kawato M: Multiple paired forward and inverse•• models for motor control. Neural Networks 1998, 11:1317-1329.
It was postulated that the best way to control learning and the contributionsof different motor primitives (controllers, or inverse models) is to use the prediction goodness of corresponding predictors (forward models). This basic
idea, strengthened by a responsibility predictor, provides an attractive
Bayesian framework to explain rich behaviors in complicated environments.
63. Haruno M, Wolpert D, Kawato M: Multiple paired forward-inverse•• models for human motor learning and control. In Advances in
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This describes mathematical and simulation studies examining the basic idea
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68. Wolpert DM, Ghahramani Z, Jordan MI: Perceptual distortion
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72. Todorov EV, Jordan MI: Smoothness maximization along a•predefined path accurately predicts the speed profiles of complex
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path of the hand in space, the velocity profile along that path will be the onethat minimizes jerk. This model explains the data better than the 2/3 power-law.
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point axis. These results suggest that the dynamic characteristics of the arm
are taken into account in the trajectory planning process.
74. Nakano E, Imamizu H, Osu R, Uno Y, Gomi H, Yoshioka T, Kawato M:•• Quantitative examinations of internal representations for arm
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77. Harris CM, Wolpert DM: Signal-dependent noise determines•• motor planning. Nature 1998, 394:780-784.
A unifying theory on trajectory formation of saccades and arm movements is
proposed. It is assumed that the neural control signals are corrupted bynoise, which increases with the size of the control signal. A simple principle
to minimize the variance of the final eye or hand position could thus reproduce known invariant trajectory characteristics, Fitts’ law, and the 2/3 powerlaw. The final position error is the time integral of the noise in the motor command, which is filtered by time-variant linearized dynamics of the motor plant.
In this interpretation, the minimum variance model could be viewed as a temporally weighted version of the minimum motor-command change model,
because the noise variance is related to the square of the motor command.
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80. Tamada T, Miyauchi S, Imamizu H, Yoshioka T, Kawato M: Cerebro•• cerebellar functional connectivity revealed by the laterality index
in tool-use learning. Neuroreport 1999, 10:325-331.
It is known that the anatomical connections between the cerebral cortex andthe cerebellar cortex are largely contralateral. Thus, if some area in the cerebral cortex is anatomically connected with some region in the cerebellar cortex, their bilateral activation patterns should be correlated. A new method toreveal cerebro-cerebellar functional connectivity was proposed while using
the laterality index. It has been suggested that a posterior–superior fissure of
the lateral cerebellum is involved in tool-use learning [42••]. Pars opecularisand pars triangularis were shown to be functionally connected with this partof the cerebellum. This is interesting because some theories advocate that
language evolution is an extension of human tool usage capability.