1

MIMo: A Multi-Modal Infant Model for Studying
Cognitive Development

arXiv:2312.04318v1 [cs.AI] 7 Dec 2023

Dominik Mattern, Pierre Schumacher, Francisco M. López, Marcel C. Raabe,
Markus R. Ernst, Arthur Aubret, Jochen Triesch

Abstract—Human intelligence and human consciousness
emerge gradually during the process of cognitive development.
Understanding this development is an essential aspect of understanding the human mind and may facilitate the construction of artificial minds with similar properties. Importantly,
human cognitive development relies on embodied interactions
with the physical and social environment, which is perceived via
complementary sensory modalities. These interactions allow the
developing mind to probe the causal structure of the world. This
is in stark contrast to common machine learning approaches, e.g.,
for large language models, which are merely passively “digesting”
large amounts of training data, but are not in control of their
sensory inputs. However, computational modeling of the kind
of self-determined embodied interactions that lead to human
intelligence and consciousness is a formidable challenge. Here
we present MIMo, an open-source multi-modal infant model for
studying early cognitive development through computer simulations. MIMo’s body is modeled after an 18-month-old child with
detailed five-fingered hands. MIMo perceives its surroundings via
binocular vision, a vestibular system, proprioception, and touch
perception through a full-body virtual skin, while two different
actuation models allow control of his body. We describe the design
and interfaces of MIMo and provide examples illustrating its use.
All code is available at https://github.com/trieschlab/MIMo.
Index Terms—cognitive development, developmental AI, infant
model, multimodal perception, physics simulation

I. I NTRODUCTION
A good measure of our understanding of a complex system
or process is our ability to rebuild it. In the context of human
cognitive development this translates to constructing models
of how the developing brain comes to control the developing
body in increasingly sophisticated ways. Human cognitive
development depends crucially on embodied interactions with
the physical and social environment, that is sensed through
our different sensory modalities. Faithful models of cognitive
development therefore need to reproduce these interactions and
how they give rise to sensory representations, motor skills,
conceptual structures, and a broad range of cognitive abilities.
D. Mattern is with the Department of Computer Science and Mathematics,
Goethe-University Frankfurt, Frankfurt am Main, Germany.
P. Schumacher is with the Max Planck Institute for Intelligent Systems,
Tübingen, Germany and the Hertie Institute for Clinical Brain Research,
Tübingen, Germany.
F.M. López, M. Raabe, M.R. Ernst, A. Aubret and J. Triesch are with the
Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany.
This research was supported by “The Adaptive Mind” and “The Third Wave
of Artificial Intelligence” funded by the Excellence Program of the Hessian
Ministry of Higher Education, Science, Research and Art. J. Triesch was
supported by the Johanna Quandt foundation. P. Schumacher was supported
by the International Max Planck Research School for Intelligent Systems
(IMPRS-IS).
This version of MIMo extends a previous version published at ICDL [1].

(a) Full body view

(b) Facial expressions

Fig. 1. MIMo, the multimodal infant model. (a) MIMo sitting in a room with
toys. (b) Six facial expressions of MIMo.

Importantly, these interactions are largely initiated and controlled by the developing child. For example, an infant controls
its visual, proprioceptive, and haptic inputs through its eye
and body movements. This ability to control and “experiment”
with different movements to observe their effects on sensory
inputs may be crucial for cognitive development, giving the
developing mind a means to probe the causal structure of
the world, rather than merely passively observing correlations
among sensed variables.
Importantly, such an active, self-controlled form of learning
is in stark contrast to a large body of work in Artificial
Intelligence (AI), including large language or vision models,
which learn certain aspects of the statistical structure of large
training datasets without having any control over their inputs.
Despite the impressive successes of such models, they may
ultimately be severely limited in their ability to understand
the causal mechanisms underlying their training data, which
will limit their ability to generalize in novel situations.
This should come as no surprise. Every scientist learns
that mere correlation is not sufficient evidence for inferring
causation. Therefore, scientists routinely exploit the ability to
manipulate a system under study using clever experimental
designs where they interfere with some variables and observe
the effects on others to distill the causal mechanisms at work.
Therefore, recreating the physical interaction with the environment must be a central aspect of rebuilding cognitive development and it may be equally essential for achieving human-

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like intelligence and consciousness in AIs. The idea that an
AI could learn like a developing child can be traced back
all the way to Turing [2]. However, serious “Developmental
Robotics” or “Developmental AI” efforts have become more
common and practical only in the last 20 years, for reviews
see [3]–[8].
There are two options for modeling the interaction of a
developing mind with its physical and social environment. The
first option is using humanoid robots. This is the approach
taken by the Developmental Robotics community. The main
advantage is the inherent realism: the system operates in the
real world governed by the actual laws of physics. However,
working with humanoid robots is expensive, time-consuming,
and suffers from the brittleness of today’s humanoid hardware.
All these factors negatively impact the reproducibility of the
research. Furthermore, the sensing abilities of today’s robots
are usually not comparable to those of actual humans. This
is particularly problematic for the sense of touch. The human
body is covered by a flexible skin containing various types
of mechanoreceptors, thermoreceptors, and nociceptors (pain
receptors). These allow us to sense touch, pressure, vibration,
temperature, and pain. Today, reproducing such a human-like
skin in humanoid robots is still out of reach.
The second option for modeling the interaction of the
developing mind with its physical and social environment is
to do it completely in silico. Many physics simulators or game
engines are available today that can approximate the physics
of such interactions [9]–[11], for review see [12]. Among
the disadvantages of such an approach are 1) inaccuracies
of such simulations due to inevitable approximations and
2) the high computational costs, especially when non-rigid
body parts and objects are considered. Nevertheless, the in
silico approach avoids all the problems of working with
humanoid robot hardware mentioned above. Furthermore, it
ensures perfect reproducibility. Lastly, if simulations can be
run (much) faster than real-time, this greatly facilitates the
simulation of developmental processes unfolding over long
periods of time (weeks, months, or even years).
To support such in silico research, we here present the
open source software platform MIMo, the Multi-Modal Infant
Model (Fig. 1). MIMo is intended to support two kinds
of research: 1) developing computational models of human
cognitive development and 2) building developmental AIs that
develop more human-like intelligence and consciousness by
similarly exploiting their ability to probe the causal structure
of the world through their actions.
We have decided to model the body of MIMo after an
average 18-month-old child. In total, MIMo has 82 degrees
of freedom of the body and 6 degrees of freedom of the eyes.
MIMo also features different facial expressions that can be
used for studies of social development. To simulate MIMo’s
interaction with the physical environment we use the MuJoCo
physics engine [13], because of its strength at simulating
contact physics with friction. Generally, we have aimed for
a balance between realism and computational efficiency in the
design of MIMo. To accelerate the simulation of physics and
touch sensation, MIMo’s body is composed of simple rigid
shape primitives such as a sphere for the head and capsules

for most other body parts. Presently, MIMo features four
sensory modalities: binocular vision, proprioception, full-body
touch sensation, and a vestibular system. We also plan to add
audition in the future.
The remainder of this article describes the detailed design
of MIMo and illustrates how to use it. In particular, we present
four scenarios where MIMo learns to 1) reach for an object,
2) stand up, 3) touch different locations on his body, and 4)
catch a falling ball with his five-fingered hand. These examples
are used to illustrate and benchmark potential uses of MIMo.
They are not intended as faithful models of how infants acquire
these behaviors.
This paper is an extended version of preliminary work previously published at the ICDL 2022 conference [1]. Compared
to the preliminary MIMo version we have added 1) fivefingered hands, 2) a new actuation model that more accurately
models the force-generating behaviour and compliance of real
muscles, 3) a detailed play room (see Fig. 2), in which MIMo
can interact, and 4) a new demo environment of learning
to catch a falling ball. A fifth contribution is that we have
improved computational efficiency and benchmarks have been
updated accordingly.
II. R ELATED W ORK
We focus on two major classes of software platforms for
simulating cognitive development during embodied interactions with the environment. The first kind is designed to
simulate a particular physical robot used in Developmental
Robotics research and intended to complement the work with
that physical robot. Examples are the iCub simulator [17] and
the simulator for the NICO robot [18] that has been implemented using the V-Rep robotics simulation environment [10].

Fig. 2. Top view of the play room environment. The room has a size of
4×4 m2 and is filled with furniture and toys. Furniture models are taken from
the 3D-FUTURE dataset [14] and toys from the Toys4K 3D Object dataset
[15]. Pictures taken from the Man-made category of the McGill Calibrated
Color Image Database [16] are placed on the walls. Additionally, the room
has a door and a window, which provides a view into a garden.

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Such platforms typically aim to faithfully reproduce the design
and behavior of the physical robot, permitting to substitute
work with the real robot through simulations. However, there
always remains a notorious gap between simulation and real
world. Furthermore, such simulation platforms also inherit any
shortcomings of the robot design relative to the human body
and human sensing capabilities. For example, if the robot
possesses only poor touch sensation, its simulated counterpart
will suffer from the same limitation.
The second kind of platform emulates human body and
sensing abilities directly and thus is not restricted by limitations of current robotics technology in general or that of
specific robots in particular. An early example is the seminal
work by Kuniyoshi and Sangawa [19]. More frequently, simulation models of specific aspects of sensorimotor development
have been proposed. These typically encompass only a small
subset of degrees of freedom and sensory modalities. An early
example is work on the development of grasping by Oztop and
colleagues [20]. A more recent example is the OpenEyeSim
simulator, which has been designed to support modeling the
development of active binocular vision [21] and is built using
the OpenSim software for simulating neuromusculoskeletal
systems [22]. While widely used in Reinforcement Learning
(RL) for locomotion tasks [23], standard humanoids introduced within the MuJoCo [24] or Bullet [11] platforms only
incorporate very limited haptic abilities and do not model
a child-like physical appearance. This may be too limiting,
because the structure and physiology of the body constrains
the kinds of interactions that are possible.
III. P HYSICAL D ESIGN
MIMo’s design is based on the MuJoCo humanoid, consisting of geometric primitives, primarily capsules. His overall
body dimensions and proportions were adapted from anthropometric measurements of 16–19 month old infants [25], treating
the unit of distance in MuJoCo as one meter. Body dimensions
for which no direct measurement is found in [25] where
induced from other measurements. For example, the length of
the lower arm is derived from the elbow-to-fingertip and hand
length measurements. We then made many small adjustments
to MIMo’s proportions to give him a more natural look, while
staying close to the experimental measurements. For example,
the upper arms appeared very thin compared to the torso and
had their circumferences increased by 0.4 cm, well within the
1.3 cm standard deviation reported by [25].
All joints are modeled as a series of one-axis hinges
and split into flexion/extension, abduction/adduction or internal/external rotation as appropriate for the joint. For the shoulders we merged the commonly used abduction and flexion
axes, instead using horizontal flexion, abduction and internal
rotation. This allows MIMo the same total range of motion
by combining horizontal flexion and abduction. Keeping both
axes would have allowed for an unrealistic, very large total
range of motion if both flexion and abduction were at their
limit, and MuJoCo’s joint limit functions were too simple to
prevent this in a satisfactory manner. We provide two different
versions of the hands for MIMo, a simple one with only

(a) Mitten hand

(b) Full hand

Fig. 3. Different versions of MIMo’s hands. (a) Simple “mitten” hand with
4 degree of freedom. (b) Five-fingered hand with 26 degrees of freedom.

a single finger and a fully articulated five-fingered version,
modified from [26], to enable experiments where dexterous
manipulation is required (see Fig. 3). In total the mitten hand
version has 44 degrees of freedom, while the full hand version
has 88. These consist of 30 in the body, 6 in the eyes and 8
and 26 degrees of freedom in the hands for the two versions,
respectively.
To produce range of motion and strength measurements, we
collected data from a large number of sources [27]–[38] and
then inferred missing values with the available data. For range
of motion we took values from the youngest age reported in the
various studies and assumed no change. For muscle strengths
we took data from [27] as a baseline. These authors consider
children aged 3–9 and we used values from the lower end of
this range for all joints reported. Joint strengths missing from
[27] were induced from other studies by assuming that the
relative strengths of joints stay constant, using the strengths
of the knee or elbow from [27] as reference values. Where
required we converted forces to torques using the appropriate
lever arms from MIMo based on the methodologies used in
the respective source.
Table I shows the range of motion and strengths for all
main joints. We treat extension, adduction and internal rotation
as positive and flexion, abduction and external rotation as
negative. Citations show the source of the data, while entries
without marked sources indicate best guesses based on the
other values. For the full hand model we kept the range of
motion from [26], with finger strengths for individual fingers
derived from [39]. For the mitten hand the strength was derived
from [27], with a range of motion that allows him to fully close
the hand.
MIMo can also change his facial expression. This is implemented by changing the texture of the head (see Fig. 1).
In addition to the neutral expression we provide six extra
textures, corresponding to the six basic emotions proposed by
[40] (enjoyment, sadness, surprise, disgust, anger, and fear).
These can be used to convey an internal emotional state, for

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TABLE I
J OINT RANGE OF MOTION AND STRENGTH FOR MIM O .
Joint
Neck flexion/ext.
Neck lateral flex.
Neck rotation

ROM [°]
-70 [27] to 80 [27]
-70 [32] to 70 [32]
-111 [32] to 111 [32]

Voluntary Torque [Nm]
-1.17 [31]∗ to 2.10 [31]∗
-1.17 to 1.17
-1.17 to 1.17

Trunk flexion/ext.
Trunk lateral flex.
Trunk rotation

-61 [30] to 34 [30]
-41 [30] to 41 [30]
-36 [30] to 36 [30]

-8.13 [30]∗ to 10.58 [30]∗
-7.25 [30]∗ to 7.25 [30]∗
-3.63 [30]∗ to 3.63 [30]∗

Shoulder horizontal
Shoulder flexion/ext.
Shoulder rotation

-118 [34] to 28 [34]
-183 [33] to 84 [33]
-99 [27] to 67 [27]

-1.8 [36]∗ to 1.8 [36]∗
-2.75 [35]∗ to 4 [35]∗
-1.6 [35]∗ to 2.5 [35]∗

Elbow flexion/ext.

-146 [27] to 5 [33]

-3.6 [27] to 3.0 [27]

Wrist palmar/dorsi
Wrist ulnar/radial
Wrist rotation

-92 [33] to 86 [33]
-53 [37] to 48 [37]
-90 [33] to 90 [33]

-1.24 [41] to 0.7 [28]∗
-0.83 [41] to 0.95 [41]
-0.7 to 0.7

Hip flexion/ext.
Hip ab-/adduction
Hip rotation

-133 [27] to 20 [29]
-51 [29] to 17 [29]
-32 [27] to 41 [27]

-8 [28]∗ to 8∗ [28]∗
-6.24 [28]∗ to 6.24 [27]
-2.66 [27] to 3.54 [27]

Knee flexion/ext.

-145 [27] to 4 [27]

-6.5 [27] to 10 [27]

Ankle plantar/dorsi
-63 [27] to 32 [27]
-3.78 [27] to 1.89 [27]
Ankle e-/inversion
-33 [38] to 31 [38]
-1.06 [38]∗ to 1.16 [38]∗
Ankle rotation
-20 to 30
-1.2 to 1.2
* Reported value scaled to be proportional to knee or elbow reference.

example for studies of social learning with multiple agents.
IV. ACTUATION M ODELS
We have implemented two actuation models incorporating
muscle-like properties and providing different trade-offs regarding accuracy and computational efficiency. In both models
we pursue a “big-picture” approach, grouping the various muscle groups acting on each joint into 1 actuator per movement
axis, with each model using a different internal mechanism
for torque generation.
A. Spring-Damper Model
In the first approach, each actuator is modeled as a combination of a motor with a spring-damper system. This approach
requires little run time, while providing reasonable accuracy.
The motor acts as the voluntary muscle force while the spring
acts to return the joint to its neutral position. The spring and
the damper loosely approximate viscoelastic characteristics of
real muscles. Note that the spring opposes any motion deviating from the equilibrium position. The joint strengths were set
as the maximum output torque of the motor. Damper strengths
were adjusted manually to ensure simulation stability. Spring
stiffness for most joints was set such that at maximum joint
deflection, net torque is reduced by 10
B. Muscle Model
The second approach implements a muscle-like model based
on [42], with adjusted parameters for MIMo. It is similar
to MuJoCo’s muscle actuators, while being more flexible

regarding muscle parameters. Compared to the spring-damper
model, this approach more accurately models the behavior of
real muscles, allowing in particular for adaptive compliance,
at the cost of increased run time (see Sec. IV-C, VII-B).
Each actuator is modeled as two opposing, independently
controllable muscles. The output torque of the whole actuator
is the sum of the torques of both muscles. We also retain 5
The torque of a single muscle depends on its current length l,
velocity l˙ and muscle activity a through:


τ = FL (l) FV (l,˙ vmax ) a(u, t) + FP (l) dfmax ,
(1)
where FL is the force-length curve, FV the force-velocity
curve and FP is a passive elastic force. The factor d accounts
for the moment arm. The muscle activity a is dependent on
time t and the control input u through
1
da
= (u − a),
(2)
dt
k
with time constant k = 10 ms. See [42] for more details.
We adjusted two of the parameters, fmax and vmax , for MIMo
specifically. The parameter fmax scales the normalized, unitless force-curves into the proper range, while vmax scales the
damping properties of the FV curve.
To determine appropriate fmax values we recreated the
experimental setups from previous studies measuring the joint
strengths (see Sec. III). A given joint is fixed in position and
maximum control input are applied. After a short time the
applied torque was measured and fmax adjusted so that the
applied torque matched the values from the literature.
As vmax measurements do not exist for most joints, we
produce an initial set of values for all joints that produce stable
behaviour and then scale them to the appropriate range by a
common factor derived from one of the few reference values
from the literature. To create the initial set, we use an iterative
approach. We set up a custom environment in which MIMo
is suspended in the air with gravity disabled. After setting
a starting vmax value, we take Bernoulli-distributed control
inputs of 0 or 1 (i.e. bang-bang-control) every two seconds
for 30 seconds. We determine the maximum achieved velocity
and use it as the new vmax . This process is repeated for some
number of episodes. To ensure convergence, we update vmax
using a learning rate α ∈ [0, 1], which is exponentially decayed
over multiple iterations. We also leverage symmetry of the
body by averaging between left and right versions of joints.
We then determine a scaling factor between our vmax value
and the one from [43], both for the knee joint, and apply this
factor to our values for all joints. We chose the knee joint for
this as we have a reference value for it, and because many
of the strength measurements were induced using the same
method of proportional scaling, also using the knee joint (see
Sec. III).
C. Muscle Compliance
A key property of muscular systems is adaptive compliance.
When a limb is perturbed from a stable position, the muscles
and tendons stretch elastically, altering the force response. It
has been shown that these properties support motion stabilization during certain tasks [44], [45]. The degree of compliance

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periments where high muscle fidelity is not critical.
D. Costs
We implement two versions of an action cost function c(u)
commonly used in reinforcement learning. Both use a measure
for the amount of effort required for the actuation, but the
second version cw (u) additionally considers the strength of
the actuators. These functions have the same general form for
both actuation models. For the spring-damper model we have:
P 2
u
(3)
c(u) = i i ,
n
P 2
i ui Ti
cw (u) = P
,
(4)
n i Ti
Fig. 4. These charts show MIMo’s shoulder position and actuator torque as
a ball is dropped onto his outstretched arm. The vertical line indicates the
moment of impact. For the motor in the spring-damper model, the actual
motor torque is constant, but net-actuation torque changes due to the springdamper as the joint is displaced, with the spring offering less resistance to
the motor and the damper acting to slow the motion.

can be adapted by the relative contraction levels of the muscle
pair.
In our spring-damper model, adaptive compliance is not
possible, as spring and damper properties are fixed parameters.
The muscle model features two independently controllable
muscles for each joint, instead of a single actuator. This allows
for the generation of the same movement with different cocontraction levels, naturally altering the level of compliance
and the response to perturbations. This effect is present in
humans, as seen in [46]. Here, two groups of people were
asked to catch falling balls while keeping their hands steady.
In the healthy group, pre-stiffening of the wrist and elbow
muscles was observed before impact, reducing deflection when
the ball hit their hand. In the second group, suffering of
cerebellar ataxia, the muscle activity did not increase until
after impact. This lead to a larger deviation in hand position.
To demonstrate this capability, we created a scenario where
MIMo holds his arm outstretched in a stable pose before
having a ball dropped on his arm. All joints except the shoulder
joint were locked in place. The shoulder joint was held in
position by the associated actuator. We measure shoulder
position and actuator torque as the arm deflects from the
impact and then returns to position. The control input to the
actuator was chosen to hold the arm stable before impact and
was constant during the whole simulation. We repeated this for
both actuation models. Control inputs were chosen manually.
We picked three sets of inputs with different activation levels
for the muscle model. There was only a single input for the
spring-damper motors that kept the arm steady.
The result is shown in Fig. 4. In the muscle model, higher
co-contraction levels lead to less deflection as the resisting
force increases more strongly after the impact. This adaptive
compliance is not possible using the spring-damper model.
Torque curves and overall response are quite similar between
the motor and the medium stiffness muscles, demonstrating
that the spring-damper model is reasonably accurate for ex-

where n is the number of motors in the scene and ui and Ti are
the control input and maximum torque of motor i, respectively.
For the muscle model we have
P
ai (ui )2
,
(5)
c(u) = i
P n
ai (ui )2 fmaxi
cw (u) = i P
,
(6)
n i fmaxi
where n is the number of muscles, ai is the activity of muscle
i and fmaxi is as described in Section IV-B.
Both actuation models expose any parameters or intermediate results for computing custom action penalties or metabolic
costs.
V. M ULTIMODAL SENSING
As with the actuation models, we pursue a big-picture
approach for our models of the sensory modalities. For
example, Golgi tendon organs measure the strain between
muscles and their tendons and thus measure the mechanical
load on the muscle, while muscle spindles measure muscle
contraction and velocity. All these receptors over a single joint
in essence measure the joint position, velocity and applied
torque over that joint. We do not model all these various
receptors themselves, instead computing the quantities directly.
Four different modalities are implemented: Proprioception,
vision, a vestibular system, and a full-body touch sensitive
skin. The first three have simple implementations and we list
the information they collect below. The touch-sensitive skin is
described in more detail.
MIMo’s proprioceptive system provides him with joint
positions and velocities, torques applied across each joint, and
limit sensors that activate as each joint approaches its range
of motion limits. In addition there are also quantities from the
actuation model, which depend on the specific implementation.
For example the muscle model provides the current muscle
activation for both muscles in each actuator.
Vision is implemented through two color cameras located
in his eyes. The range of motion is ±45° horizontally, -47°
to 33° vertically [47] and ±8° torsionally [48]. The cameras
render two RGB images with a 60º field of view, equivalent
to the central vision of humans [49].
The vestibular system, which provides our sense of balance,
is implemented as a combination gyroscope and accelerometer
located at the center of MIMo’s head.

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(a) Binocular vision

(b) Touch perception

Fig. 5. MIMo’s multimodal perception while holding a ball. (a) Anaglyph of
left and right eye views. (b) Visualization of touch sensors in the hand, with
those reporting a force colored red. The size of the circle corresponds to the
amount of force sensed.

A. Touch Perception
Human touch sensation is produced by a variety of receptors
responding towards specific aspects of touch, such as the
Slowly Adapting type 1 (SA1), which responds primarily to
direct pressure and coarse texture or the Rapidly Adapting
(RA) type for slip and fine texture [50]. As with the other
modalities, we model these types very simply, ignoring signal
travel times and condensing the various types of receptors into
a single generic “touch” sensor type that measures normal and
frictional forces at its location. Sensor points are spread evenly
on each individual body part, with the sensor density varying
between body parts based on the two-point discrimination
distances by [51]. Thus, the front and the back of the palm
have the same sensor density, but not the fingertips.
MuJoCo only performs rigid-body simulations in which all
contacts are treated as point contacts. Area contacts between
flat surfaces produce multiple contact points, for example at
the corners of the contact area. As soft-body physics is very
computationally expensive, we do not adjust these physics but
weakly simulate the deformation of the skin to these point
contacts, by distributing the point contact forces over nearby
sensor points according to a surface response function. Our
response function decreases sensed force linearly with distance
from the contact point and then normalizes over all sensor
points, such that the total sensed force remains identical to
the initial point contact force from MuJoCo. The distance
measure is the euclidean distance as geodesic approximations
were too computationally expensive. To avoid bleed-through
to the opposite side of thin bodies (such as the palm), we only
select nearby sensor points with a breadth-first-search on the
mesh of sensor points. While also expensive, the results of this
search can be cached and reused, leading to a only a small run
time penalty compared to using just the euclidean distance.
All of these aspects, from the sensor point density through
the response function can be easily adjusted or expanded.
VI. A PPLICATION P ROGRAMMING I NTERFACE
Our code is written in Python and built as an OpenAI
gym [52] environment to allow easy integration into existing
experimental setups and take advantage of the large amount
of documentation and third-party libraries that already exist,
such as the stable baselines library [53]. This environment is

intended as an abstract base class that will be subclassed and
adapted by other environments for specific experiments. These
subclasses would handle reward structure, sensor limits or any
additional constraints. Underdeveloped or limited sensors can
be implemented through their configurations, but for the most
part the user would implement any perceptual constraints. The
environment is set up to facilitate this in a straightforward
way. The configuration of the sensory modalities, such as
the density of the touch sensors or the field of view and
resolution of the visual system can be adjusted or disabled
easily during initialization without modifying the underlying
MuJoCo XMLs. Swapping between actuation models only
requires a single line change as well.
The action and observation spaces are generated automatically based on the configuration of the MuJoCo XMLs and the
sensor modules. Disabling touch perception also removes the
associated entry from the observation space. All of the sensory
modalities are programmed as separate modules and can be
readily attached to any MuJoCo-based gym environment.
Our simulation is time discrete with two different time
step types. The physics time step determines the temporal
resolution of the physics simulation and choosing a sufficiently
small one is important for simulation stability.
The second step type are control steps, during which observations are collected and the control algorithm is queried for
new motor commands. Control frequency is often an important
factor for RL algorithms. Control step size must be an integer
multiple of the physics step size.
VII. E XPERIMENTS
A. Illustrations of learning
While RL is a powerful framework to generate controllers,
its chaotic nature and requirements for large amounts of data
require a stable and efficient model. In the following, we
demonstrate that MIMo is well-suited for RL even while
including multimodal inputs. Note that badly designed models can negatively affect RL performance, even if they are
physically accurate in some regimes. We use four example
tasks: reaching for objects, standing up, self-body knowledge
and catching a falling ball. In these tasks, two different
state-of-the-art, widely used deep RL algorithms, Proximal
Policy Optimization (PPO) [54] and Soft Actor-Critic (SAC)
[23] are trained to optimize task-dependent reward functions
by controlling MiMo’s actuators. While both algorithms are
actor-critics, PPO is a widely-used on-policy approach closely
related to trust-region algorithms [55] and SAC is an off-policy
algorithm with a maximum-entropy formulation [56].
We use the default parameters of the Stable-Baselines3
library [53], consisting of linear networks with two hidden
layers of size 64 for PPO and size 256 for SAC, as well
as common improvements [57], [58] that are critical for
performance. Input and output layer sizes vary depending
on the observation and action spaces of the environments.
Performance is compared for PPO and SAC with 10 different seeds (Fig. 6). We do not claim that such extrinsically
motivated learning is how human infants learn these skills.
We merely use these examples to showcase MIMo learning
from multimodal input.

7

200
average reward

average reward

100

0

−100
PPO
SAC

0.0

0.1

0.2
0.3
million steps

0.4

150

100
PPO
SAC

50
0.5

0.0

0.5
1.0
million steps

(a) Reaching for objects

1.5

(b) Standing up

average reward

average reward

200

0

−250

100

0

PPO
SAC

PPO
SAC

−100
−500

0.0

0.5
million steps

1.0

(c) Self-body knowledge

0

1

2
million steps

3

4

(d) Catching objects

Fig. 6. Comparison of learning curves for PPO (red) and SAC (blue) in the four illustration environments, with 10 different seeds each. Snapshots show
typical postures of MIMo at the start (top) and end (bottom) of an episode. Videos are available at https://tinyurl.com/MIMo-playlist

a) Reaching for Objects: Reaching is a complex behavior that emerges in the first 6 months of age. Since it
requires hand-eye coordination, infants must combine vision,
proprioception, and touch to produce the desired motion [59].
A motor command is generated for the arm and hand muscles
to produce the reaching movement towards an object in their
visual field, with immediate haptic feedback about its success.
In our illustration, MIMo learns to reach for a ball. He is
standing in front of the target, which changes position randomly in each episode, always within reach of MIMo’s right
hand. He can only move his right shoulder, elbow, and hand
joints. His head and eyes are set to look directly at the ball, i.e.,
the initial visual search and object fixation is assumed. The
observation space only includes the proprioception sensory
modality. MIMo can use the joint angles of his head and
eyes to determine the position of the target. We introduce an
additional difficulty relative to the original version of the task
[1] by also sampling the initial condition of the right arm from
10 random positions. This ensures that MIMo effectively uses
his proprioception to reach the ball as fast as possible. The
reward function

100
if target reached,
r=
(7)
−∥pfingers − ptarget ∥ otherwise
is the negative distance between the positions of the fingers
and the target, with a sparse positive reward when contact is
detected. Each episode lasts 1000 time steps or until MIMo
successfully touches the ball. Results for this task are shown
in Fig. 6a.
b) Standing up: Infants learn to stand up by themselves
at around 10 months and start walking shortly after. This is a
gradual process that includes previous stages such as crawling

and maintaining balance. One particular stage is marked by the
emergence of pulling-to-stand, when infants who are unable
to stand without support grasp the edge of a solid surface
and pull themselves upwards, thus combining the strengths of
their arms and legs [60]. This behavior appears as early as 7
months of age and is a necessary milestone during independent
locomotion development.
To reproduce the pulling-to-stand behavior, we design an
environment where MIMo is placed sitting inside a crib. His
feet are fixed to the ground and his hands are fixed to the
crib’s rail guard, at a height of 45 cm. He can move the
joints in his arms, torso, and legs, with the aim of standing
up. The observation space includes the proprioception and
vestibular sensory modalities. The latter can be particularly
useful by providing information about vertical acceleration.
The extrinsic reward is given by
r = zhead − 0.01

X

u2i

(8)

i∈joints

where zhead is the head’s height measured from an initial
height of 20 cm, ui is the control input for joint j, and
the sum is taken over all active joints. This reward function
favors standing positions while penalizing states that require
excessive force. The parameters are set to balance the two
components. All episodes last 500 time steps. Results for this
task are shown in Fig. 6b.
c) Self-body Knowledge: Infants learn not only about the
world but also about themselves and their own bodies. In fact,
this begins as a tactile exploratory behavior before birth and
continues over the first few months of life [61]. Infants develop

8

a self-body knowledge that allows them to map the multimodal sensory inputs to the different parts of their bodies.
MIMo can learn this self-body knowledge by using his
touch perception. We design an environment where MIMo is
sitting with his legs crossed, such that his right arm can reach
all of his body parts. In each episode he is given a target
body part sampled uniformly at random from the geometric
primitives that make up his body. By only moving his right
arm, he is trained to activate the touch sensors on the target
body part. The observation space includes proprioception and
touch, as well as the target as a vector with one-hot encoding.
The reward function

r=




500
−∥ptouched − ptarget ∥

−1

if target touched,
if other part touched,
otherwise

(9)

is positive only if the target body part is touched. Otherwise, it
is either the negative distance to the target body part if another
touch signal is activated or a fixed negative value if there is no
touch signal. Each episode lasts 500 time steps or until MIMo
successfully touches the target. Results for this task are shown
in Fig. 6c.
d) Catching Objects: As they develop, infants learn to
rely on sensory feedback to adapt their actions in order to
achieve their goals. One example is catching a falling object,
where visual and haptic information gives a cue about when
and how to grasp. While newborns have an innate palmar grasp
reflex, they learn to predict the motion of objects to catch them
at around 8 months of age [62].
We illustrate this behavior in an experiment where MIMo
learns to grasp a ball that falls onto his hand. The ball’s size,
mass, and initial position are randomized in each episode.
Using the full hand model, MIMo’s body is fixed in a standing
position with his right arm stretched in front of him, such
that he can only move his right hand wrist and fingers. The
thumb is locked to the side. At each time step, his head and
eyes are automatically rotated to fixate on the falling ball.
His observation space includes proprioception, touch and the
size of the ball. MIMo needs to learn to integrate these pieces
of information to successfully grasp the ball. This experiment,
unlike the others, uses the muscle actuation model. The reward
function is given by

r=




−100
if ball falls beyond hand,
100
if ball is held for 1 second,

Nc − cw (a) otherwise

(10)

where Nc is the number of geometric primitives in contact
with the ball and cw (a) is the cost function for the actuators as
given by Equation 6. This cost function rewards grasping with
the fingers over using the wrist. Each episode lasts 800 time
steps, or until either the ball falls beyond the hand’s height or
MIMo has held onto the ball continuously for a full second.
Results for this task are shown in Fig. 6d.
Both SAC and PPO quickly converge to the optimal behavior for the simpler tasks, demonstrating that the parametrization of MIMo allows for stable motor control. The two harder

tasks, (b) and (d), require either full-body control or difficult
hand coordination across all fingers. In these scenarios, SAC
performs worse and we observe larger variance across seeds.
We conjecture that PPO benefits from its monotonic improvement guarantees and therefore achieves better learning stability
and lower variance across seeds.
B. Benchmarking MIMo
In this section we measure the simulation speed of MIMo. In
particular, we are interested in assessing under what conditions
we can achieve faster than real-time simulations.
Each benchmark runs for one hour of simulation time.
Environments have a maximum episode duration and are reset
when a goal is achieved or the time limit is reached. We
measure the real-time spent in each run, as well as in each
of the different components of the system: MuJoCo and the
sensory modalities. Physics steps last 5 ms for all benchmarks.
Unless stated otherwise we use the spring-damper actuation
model with the mitten hand version of MIMo. Results are
reported as real seconds required for each simulation second.
The test system is equipped with an AMD FX-8350, 16GB
RAM and a GTX 1070. The execution times are measured
using Python’s cProfile library.
In the first experiment we test performance with multiple
configurations for the different sensory modalities, focusing
on the vision and touch modules since they are most sensitive
to their configuration and consume the bulk of the processing
time. The environment consists of MIMo and two objects.
MIMo takes random actions continuously. Each episode has
a fixed length of 1 minute, with 60 episodes per benchmark.
The results can be seen in Fig. 7. The default configuration of
MIMo (vision resolution of 256 × 256 pixels) requires 0.69
real seconds for each simulation second, i.e., it is 1.44 times
faster than real time.
In the next benchmark we test the performance of our
demo environments. The number of episodes is no longer
fixed and individual episodes may be cut short if MIMo
achieves the goal of the environment. The reach, self-body, and
catch experiments perform two physics steps for every control
step, the default setting for MIMo environments. The stand-up
experiment uses one physics step per control step in order to
increase the stability of the simulation due to the additional
constraints between MIMo’s hands and the crib. We also test
the performance of the full hand version of MIMo. The configuration is the same as the first benchmark, but with the version
of MIMo replaced. Results for both benchmarks are plotted in
Fig. 8. The “Reach”, “Standup”, and “SelfBody” experiment
are all based on the default configuration with some modalities
disabled and joints locked in place. As a result, they perform
significantly faster. Interestingly, the physics simulation for
the stand-up environment takes longer than the baseline. This
slowdown comes from: 1. A slowdown in MuJoCo’s solver,
as MIMo’s joint positions are more constrained since both
his hands and feet are fixed in place. 2. The environment
configuration: MIMo’s initial position is slightly randomized
and the simulation allowed to settle for several physics steps
without any actions before each episode begins.

9

0.8
Realtime/Simtime

leads to a 23
Performance can be improved for specific experiments in
multiple ways. In addition to adjusting the configuration of
the modalities or the scene, the performance of the simulation
can be improved by reducing the frequency of control steps,
reducing the frequency of observation collection and thus the
time spent in the sensory modules.

Other
Vestibular
Proprioception
Vision
Touch
Physics
Init.

1.0

0.6
0.4

VIII. D ISCUSSION

0.2
0.0

V: 64² V: 64² V: 64² V: 64² V: 128 V: 256 V: 512
T: 0.25 T: 0.5 T: 1.0 T: 2.0 ² T: 1.0 ² T: 1.0 ² T: 1.0

Fig. 7. Results of the performance benchmarks. Each bar represents one
run consisting of 60 episodes of 1-minute length each. The labels indicate
the pixel resolution for the visual system (V) and a scalar multiplier for the
sensor density for the touch system (T) used. The 4 leftmost bars correspond
to configurations with increasing touch sensor density and constant visual
resolution, the 3 rightmost bars to increasing visual resolution and constant
touch sensor density. All configurations with visual resolutions lower than
512x512 pixels run significantly faster than real-time (dashed horizontal line).

1.4

Realtime/Simtime

1.2
1.0
0.8

Other
Vestibular
Proprioception
Vision
Touch
Muscle
Physics
Init.

0.6
0.4
0.2
0.0

Reach

Standu

p

SelfBo
dy

Catch

Full Ha
n

d

Baselin

e

Fig. 8. Performance benchmarks for each of the demo environments and the
full hand version of MIMo. The benchmark of the default configuration, using
the mitten-hands, is also plotted for reference.

As to the full hand version, the performance of both
MuJoCo and the touch module is highly dependent on the
number of contacts in the simulation. Contacts between two
body parts of MIMo are particularly expensive as the force
distribution has to be computed for both bodies. This leads
to a significant slow-down for both MuJoCo and the touch
module due to contacts between MIMo’s fingers. The “Catch”
environment is based on the full hand version, with all joints,
except the right hand, locked into fixed positions, and touch
sensation only in the right arm and hand. This speeds up both
touch and physics performance. Muscle functions make up 3
The muscle actuation model adds a flat run-time cost of
0.8 ms per physics step for both versions of MIMo, which

In this work we have presented MIMo, the multimodal
infant model, an open-source research software platform for
1) building models of cognitive development in infants and
toddlers and 2) constructing AIs that can learn in a similar
self-directed fashion from interactions with their environment.
Compared to previous software platforms [11], [17]–[19], [24],
a key strength of MIMo is the combination of 1) state-of-theart physics simulation based on MuJoCo (https://mujoco.org)
with 2) a full-body touch-sensitive skin, and 3) a plausible
approximation of muscle-driven movement, while maintaining
the ability to run simulations faster than real-time on standard
hardware. We believe that these ingredients are essential for
advancing our understanding of the development of, e.g., early
self-models in infants, that pave the way toward full-fledged
adult-like forms of intelligence and consciousness.
In the past, computational models of cognitive development
have often been restricted to isolated cognitive phenomena.
Some examples are works on binocular vision [63], [64],
visual object and category learning [65]–[67], gaze following
[68], [69], learning to grasp objects [20], perservative reaching
[70], word learning [71]–[73], and countless others. While
such models have produced many important insights, they
often work with simplified sensory inputs and it is not clear
how to scale them to the rich multimodal sensory input
provided by our sense organs.
Recent approaches that train models with first-person video
and audio recordings of infants [74], [75] try to overcome this
limitation. Critically, however, the model still learns from just
passively observing these inputs recorded in this way, while
the actual infant actively generated this sensory input through
their own behavior. Therefore, as we have argued in the
Introduction, this first-person-recording approach is likely to
miss an essential aspect of cognitive development: the infant’s
ability to actively probe the causal structure of the world in
a targeted fashion. Capturing such more advanced forms of
learning in models necessitates modeling environments that
support embodied interaction with the physical environment.
We feel that the time is ripe to fully embrace such models
and we believe that it should be done without incurring the
burden and limited reproducability associated with working
with humanoid robots.
In the design of MIMo we faced a number of trade-offs
between realism and computational efficiency. The “right”
trade-off will always depend on the particular phenomenon
being investigated. The choices we made already permit
faster than real-time simulations on today’s standard hardware. However, this has resulted in various limitations. For
example, MIMo’s body is composed of simple rigid shape

10

primitives. Furthermore, MIMo is presently limited to just four
sensory modalities (binocular vision, proprioception, touch,
and a vestibular system). In the future, we plan to incorporate
nociception (pain perception), audition, and possibly olfaction.
Future work could also study the effects of a growing body
during development. All relevant aspects, such as MIMo’s
physical size and strength, can be adjusted even within
episodes. A model of the development of, say, a particular sensorimotor skill could be trained while parameters of MIMo’s
body slowly change.
We hope that MIMo will facilitate research into how cognition develops from embodied interactions with the physical
and social environment, whose rich structure is sensed through
multiple modalities. At the very least, it should make such
efforts easier and more reproducible. Furthermore, we hope
that MIMo will enable a more cumulative and collaborative
approach to such research, where models of the development
of higher-level cognitive functions are built on top of previously published models of the development of precursor skills.
After all, human development is often a cumulative process,
where new representations, skills, and competences are built
on top of already existing ones in an open-ended fashion.
R EFERENCES
[1] D. Mattern, F. M. López, M. R. Ernst, A. Aubret, and J. Triesch, “Mimo:
A multi-modal infant model for studying cognitive development in humans and ais,” in 2022 IEEE International Conference on Development
and Learning (ICDL). IEEE, 2022, pp. 23–29.
[2] A. M. Turing, “Computing machinery and intelligence,” Mind, vol. 59,
no. 236, pp. 433–460, 1950.
[3] M. Asada, K. F. MacDorman, H. Ishiguro, and Y. Kuniyoshi, “Cognitive
developmental robotics as a new paradigm for the design of humanoid
robots,” Robotics and Autonomous Systems, vol. 37, no. 2, pp. 185–193,
2001, Humanoid Robots.
[4] M. Lungarella, G. Metta, R. Pfeifer, and G. Sandini, “Developmental
robotics: a survey,” Connection Science, vol. 15, no. 4, pp. 151–190,
2003.
[5] J. Schmidhuber, “Developmental robotics, optimal artificial curiosity,
creativity, music, and the fine arts,” Connection Science, vol. 18, no. 2,
pp. 173–187, 2006.
[6] M. Asada, K. Hosoda, Y. Kuniyoshi, H. Ishiguro, T. Inui, Y. Yoshikawa,
M. Ogino et al., “Cognitive developmental robotics: A survey,” IEEE
Transactions on Autonomous Mental Development, vol. 1, no. 1, pp.
12–34, 2009.
[7] A. Cangelosi and M. Schlesinger, “From babies to robots: The contribution of developmental robotics to developmental psychology,” Child
Development Perspectives, vol. 12, no. 3, pp. 183–188, 2018.
[8] K. Doya and T. Taniguchi, “Toward evolutionary and developmental
intelligence,” Current Opinion in Behavioral Sciences, vol. 29, pp. 91–
96, 2019, artificial Intelligence.
[9] C. Gan, J. Schwartz, S. Alter, D. Mrowca, M. Schrimpf, J. Traer, J. D.
Freitas et al., “ThreeDWorld: A platform for interactive multi-modal
physical simulation,” in Thirty-fifth Conference on Neural Information
Processing Systems Datasets and Benchmarks Track (Round 1), 2021.
[Online]. Available: https://openreview.net/forum?id=db1InWAwW2T
[10] E. Rohmer, S. P. N. Singh, and M. Freese, “V-rep: A versatile and
scalable robot simulation framework,” in 2013 IEEE/RSJ International
Conference on Intelligent Robots and Systems, 2013, pp. 1321–1326.
[11] E. Coumans and Y. Bai, “Pybullet, a python module for physics
simulation for games, robotics and machine learning,” 2016.
[12] J. Collins, S. Chand, A. Vanderkop, and D. Howard, “A review of physics
simulators for robotic applications,” IEEE Access, vol. 9, pp. 51 416–
51 431, 2021.
[13] E. Todorov, T. Erez, and Y. Tassa, “Mujoco: A physics engine for
model-based control,” in 2012 IEEE/RSJ International Conference on
Intelligent Robots and Systems, 2012, pp. 5026–5033.
[14] H. Fu, R. Jia, L. Gao, M. Gong, B. Zhao, S. Maybank, and D. Tao,
“3d-future: 3d furniture shape with texture,” International Journal of
Computer Vision, pp. 1–25, 2021.

[15] S. Stojanov, A. Thai, and J. M. Rehg, “Using shape to categorize:
Low-shot learning with an explicit shape bias,” in Proceedings of the
IEEE/CVF Conference on Computer Vision and Pattern Recognition
(CVPR), June 2021, pp. 1798–1808.
[16] A. Olmos and F. A. A. Kingdom, “Mcgill calibrated colour image
database,” http://tabby.vision.mcgill.ca.
[17] V. Tikhanoff, A. Cangelosi, P. Fitzpatrick, G. Metta, L. Natale, and
F. Nori, “An open-source simulator for cognitive robotics research:
The prototype of the iCub humanoid robot simulator,” in Proceedings
of the 8th Workshop on Performance Metrics for Intelligent Systems,
ser. PerMIS ’08. New York, NY, USA: Association for Computing
Machinery, 2008, p. 57–61.
[18] M. Kerzel, E. Strahl, S. Magg, N. Navarro-Guerrero, S. Heinrich,
and S. Wermter, “Nico — neuro-inspired companion: A developmental
humanoid robot platform for multimodal interaction,” in 2017 26th IEEE
International Symposium on Robot and Human Interactive Communication (RO-MAN), 2017, pp. 113–120.
[19] Y. Kuniyoshi and S. Sangawa, “Early motor development from partially ordered neural-body dynamics: experiments with a cortico-spinalmusculo-skeletal model,” Biological Cybernetics, vol. 95, no. 6, pp. 589–
605, 2006.
[20] E. Oztop, N. S. Bradley, and M. A. Arbib, “Infant grasp learning: a
computational model,” Experimental brain research, vol. 158, no. 4, pp.
480–503, 2004.
[21] A. Priamikov, M. Fronius, B. Shi, and J. Triesch, “Openeyesim: a
biomechanical model for simulation of closed-loop visual perception,”
Journal of Vision, vol. 16, no. 15, pp. 25–25, 12 2016.
[22] S. L. Delp, F. C. Anderson, A. S. Arnold, P. Loan, A. Habib, C. T.
John, E. Guendelman et al., “Opensim: Open-source software to create
and analyze dynamic simulations of movement,” IEEE Transactions on
Biomedical Engineering, vol. 54, no. 11, pp. 1940–1950, 2007.
[23] T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine, “Soft actor-critic: Offpolicy maximum entropy deep reinforcement learning with a stochastic
actor,” in Proceedings of the 35th International Conference on Machine
Learning, ser. Proceedings of Machine Learning Research, J. Dy and
A. Krause, Eds., vol. 80. PMLR, 10–15 Jul 2018, pp. 1861–1870.
[24] Y. Tassa, T. Erez, and E. Todorov, “Synthesis and stabilization of
complex behaviors through online trajectory optimization,” in 2012
IEEE/RSJ International Conference on Intelligent Robots and Systems,
2012, pp. 4906–4913.
[25] S. Ressler, “Anthrokids-anthropometric data of children,” National
Institute of Standards and Technology, 1977. [Online]. Available:
https://math.nist.gov/∼SRessler/anthrokids/
[26] V. Kumar, “Manipulators and manipulation in high dimensional spaces,”
Ph.D. dissertation, University of Washington, Seattle, 2016. [Online].
Available: https://digital.lib.washington.edu/researchworks/handle/1773/
38104
[27] M. J. McKay, J. N. Baldwin, P. Ferreira, M. Simic, N. Vanicek, J. Burns,
. N. P. Consortium et al., “Normative reference values for strength and
flexibility of 1,000 children and adults,” Neurology, vol. 88, no. 1, pp.
36–43, 2017.
[28] M. N. Eek, A.-K. Kroksmark, and E. Beckung, “Isometric muscle torque
in children 5 to 15 years of age: Normative data,” Archives of Physical
Medicine and Rehabilitation, vol. 87, no. 8, pp. 1091–1099, 2006.
[29] W. N. Sankar, C. T. Laird, and K. D. Baldwin, “Hip range of motion in
children: what is the norm?” Journal of Pediatric Orthopaedics, vol. 32,
no. 4, pp. 399–405, 2012.
[30] T. Gomez, G. Beach, C. Cooke, W. Hrudey, and P. Goyert, “Normative
database for trunk range of motion, strength, velocity, and endurance
with the isostation b-200 lumbar dynamometer,” Spine, vol. 16, no. 1,
p. 15—21, January 1991.
[31] A. Jordan, J. Mehlsen, P. M. Bülow, K. Østergaard, and B. DanneskioldSamsøe, “Maximal isometric strength of the cervical musculature in 100
healthy volunteers,” Spine, vol. 24, no. 13, p. 1343, 1999.
[32] A. M. Öhman and E. R. Beckung, “Reference values for range of motion
and muscle function of the neck in infants,” Pediatric Physical Therapy,
vol. 20, no. 1, pp. 53–58, 2008.
[33] H. Watanabe, K. Ogata, T. Amano, and T. Okabe, “The range of joint
motions of the extremities in healthy japanese people–the difference
according to the age (author’s transl),” Nihon Seikeigeka Gakkai Zasshi,
vol. 53, no. 3, pp. 275–261, 1979.
[34] I. Günal, N. Köse, O. Erdogan, E. Göktürk, and S. Seber, “Normal
range of motion of the joints of the upper extremity in male subjects,
with special reference to side,” Journal of Bone & Joint Surgery, vol. 78,
no. 9, p. 1401, 1996.

11

[35] R. E. Hughes, M. E. Johnson, S. W. O’Driscoll, and K.-N. An, “Agerelated changes in normal isometric shoulder strength,” The American
Journal of Sports Medicine, vol. 27, no. 5, pp. 651–657, 1999.
[36] M. Katoh, “Test-retest reliability of isometric shoulder muscle strength
measurement with a handheld dynamometer and belt,” Journal of
Physical Therapy Science, vol. 27, no. 6, pp. 1719–1722, 2015.
[37] S. N. Da Paz, A. Stalder, S. Berger, and K. Ziebarth, “Range of motion
of the upper extremity in a healthy pediatric population: introduction to
normative data,” European Journal of Pediatric Surgery, vol. 26, no. 05,
pp. 454–461, 2016.
[38] S.-K. Bok, T. H. Lee, and S. S. Lee, “The effects of changes of ankle
strength and range of motion according to aging on balance,” Annals of
Rehabilitation Medicine, vol. 37, no. 1, pp. 10–16, 2013.
[39] T. Ohtsuki, “Decrease in grip strength induced by simultaneous bilateral
exertion with reference to finger strength,” Ergonomics, vol. 24, no. 1,
pp. 37–48, 1981.
[40] P. Ekman, “An argument for basic emotions,” Cognition and Emotion,
vol. 6, no. 3-4, pp. 169–200, 1992.
[41] J. M. Vanswearingen, “Measuring wrist muscle strength,” Journal of
Orthopaedic & Sports Physical Therapy, vol. 4, no. 4, pp. 217–228,
1983.
[42] I. Wochner, P. Schumacher, G. Martius, D. Büchler, S. Schmitt,
and D. Haeufle, “Learning with muscles: Benefits for data-efficiency
and robustness in anthropomorphic tasks,” in 6th Annual Conference
on Robot Learning, 2022. [Online]. Available: https://openreview.net/
forum?id=Xo3eOibXCQ8
[43] L. A. Frey-Law, A. Laake, K. G. Avin, J. Heitsman, T. Marler, and
K. Abdel-Malek, “Knee and elbow 3d strength surfaces: peak torqueangle-velocity relationships,” Journal of applied biomechanics, vol. 28,
no. 6, pp. 726–737, 2012.
[44] A. Mo, F. Izzi, D. F. B. Haeufle, and A. Badri-Spröwitz, “Effective
viscous damping enables morphological computation in legged
locomotion,” Frontiers in Robotics and AI, vol. 7, 2020. [Online].
Available: https://www.frontiersin.org/articles/10.3389/frobt.2020.00110
[45] F. Izzi, A. Mo, S. Schmitt, A. Badri-Spröwitz, and D. F. B. Haeufle,
“Muscle prestimulation tunes velocity preflex in simulated perturbed
hopping,” Scientific Reports, vol. 13, no. 1, p. 4559, Mar 2023.
[Online]. Available: https://doi.org/10.1038/s41598-023-31179-6
[46] C. E. Lang and A. J. Bastian, “Cerebellar subjects show impaired adaptation of anticipatory emg during catching,” Journal of neurophysiology,
vol. 82, no. 5, pp. 2108–2119, 1999.
[47] W. J. Lee, J. H. Kim, Y. U. Shin, S. Hwang, and H. W. Lim, “Differences
in eye movement range based on age and gaze direction,” Eye, vol. 33,
no. 7, pp. 1145–1151, 2019.
[48] A. L. Rosenbaum and A. P. Santiago, Clinical strabismus management:
principles and surgical techniques. W.B. Saunders, 1999.
[49] H. Strasburger, I. Rentschler, and M. Jüttner, “Peripheral vision and
pattern recognition: A review,” Journal of Vision, vol. 11, no. 5, pp.
13–13, 12 2011.
[50] K. O. Johnson and S. S. Hsiao, “Neural mechanisms of tactual form
and texture perception,” Annual Review of Neuroscience, vol. 15, no. 1,
pp. 227–250, 1992.
[51] F. Mancini, A. Bauleo, J. Cole, F. Lui, C. A. Porro, P. Haggard, and
G. D. Iannetti, “Whole-body mapping of spatial acuity for pain and
touch,” Annals of Neurology, vol. 75, no. 6, pp. 917–924, 2014.
[52] G. Brockman, V. Cheung, L. Pettersson, J. Schneider, J. Schulman, J. Tang, and W. Zaremba, “OpenAI Gym,” arXiv preprint
arXiv:1606.01540, 2016.
[53] A. Raffin, A. Hill, A. Gleave, A. Kanervisto, M. Ernestus, and N. Dormann, “Stable-baselines3: Reliable reinforcement learning implementations,” Journal of Machine Learning Research, vol. 22, no. 268, pp. 1–8,
2021.
[54] J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal policy optimization algorithms,” arXiv preprint arXiv:1707.06347,
2017.
[55] J. Schulman, S. Levine, P. Abbeel, M. Jordan, and P. Moritz, “Trust
region policy optimization,” in Proceedings of the 32nd International
Conference on Machine Learning, ser. Proceedings of Machine
Learning Research, F. Bach and D. Blei, Eds., vol. 37. Lille,
France: PMLR, 07–09 Jul 2015, pp. 1889–1897. [Online]. Available:
https://proceedings.mlr.press/v37/schulman15.html
[56] S. Han and Y. Sung, “A max-min entropy framework for reinforcement
learning,” Advances in Neural Information Processing Systems, vol. 34,
pp. 25 732–25 745, 2021.
[57] L. Engstrom, A. Ilyas, S. Santurkar, D. Tsipras, F. Janoos, L. Rudolph,
and A. Madry, “Implementation matters in deep rl: A case study on ppo

and trpo,” in International Conference on Learning Representations,
2020. [Online]. Available: https://openreview.net/forum?id=r1etN1rtPB
[58] T. Haarnoja, A. Zhou, K. Hartikainen, G. Tucker, S. Ha, J. Tan,
V. Kumar et al., “Soft actor-critic algorithms and applications,” CoRR,
vol. abs/1812.05905, 2018. [Online]. Available: http://arxiv.org/abs/
1812.05905
[59] D. Corbetta, R. F. Wiener, S. L. Thurman, and E. G. McMahon, “The
embodied origins of infant reaching: Implications for the emergence of
eye-hand coordination,” Kinesiology Review, vol. 7, no. 1, pp. 10–17,
2018.
[60] O. Atun-Einy, S. E. Berger, and A. Scher, “Pulling to stand: Common
trajectories and individual differences in development,” Developmental
Psychobiology, vol. 54, no. 2, pp. 187–198, 2012.
[61] L. Jacquey, J. Fagard, K. O’Regan, and R. Esseily, “Development of
body know-how during the baby’s first year of life,” Enfance, vol. 2,
no. 2, pp. 175–192, 2020.
[62] P. van Hof, J. van der Kamp, and G. J. Savelsbergh, “The relation between infants’ perception of catchableness and the control of catching.”
Developmental Psychology, vol. 44, no. 1, pp. 182–194, 2008.
[63] M. Dominguez and R. A. Jacobs, “Developmental constraints aid the
acquisition of binocular disparity sensitivities,” Neural Computation,
vol. 15, no. 1, pp. 161–182, 2003.
[64] S. Eckmann, L. Klimmasch, B. E. Shi, and J. Triesch, “Active efficient
coding explains the development of binocular vision and its failure in
amblyopia,” Proceedings of the National Academy of Sciences, vol. 117,
no. 11, pp. 6156–6162, 2020.
[65] D. Mareschal, R. M. French, and P. C. Quinn, “A connectionist account
of asymmetric category learning in early infancy.” Developmental psychology, vol. 36, no. 5, p. 635, 2000.
[66] F. Schneider, X. Xu, M. R. Ernst, Z. Yu, and J. Triesch, “Contrastive
learning through time,” in SVRHM 2021 Workshop@ NeurIPS, 2021.
[67] A. Aubret, C. Teulièr, and J. Triesch, “Toddler-inspired embodied
vision for learning object representations,” in 2022 IEEE International
Conference on Development and Learning (ICDL). IEEE, 2022, pp.
81–87.
[68] Y. Nagai, K. Hosoda, A. Morita, and M. Asada, “A constructive model
for the development of joint attention,” Connection Science, vol. 15,
no. 4, pp. 211–229, 2003.
[69] J. Triesch, C. Teuscher, G. O. Deák, and E. Carlson, “Gaze following:
why (not) learn it?” Developmental science, vol. 9, no. 2, pp. 125–147,
2006.
[70] E. Thelen, G. Schöner, C. Scheier, and L. B. Smith, “The dynamics of
embodiment: A field theory of infant perseverative reaching,” Behavioral
and brain sciences, vol. 24, no. 1, pp. 1–34, 2001.
[71] D. K. Roy and A. P. Pentland, “Learning words from sights and sounds:
A computational model,” Cognitive science, vol. 26, no. 1, pp. 113–146,
2002.
[72] C. Yu and D. H. Ballard, “A unified model of early word learning:
Integrating statistical and social cues,” Neurocomputing, vol. 70, no. 1315, pp. 2149–2165, 2007.
[73] F. Xu and J. B. Tenenbaum, “Word learning as bayesian inference.”
Psychological review, vol. 114, no. 2, p. 245, 2007.
[74] S. Bambach, D. Crandall, L. Smith, and C. Yu, “Toddler-inspired visual
object learning,” Advances in neural information processing systems,
vol. 31, 2018.
[75] E. Orhan, V. Gupta, and B. M. Lake, “Self-supervised learning through
the eyes of a child,” Advances in Neural Information Processing Systems,
vol. 33, pp. 9960–9971, 2020.