# Brain-inspired bodily self-perception model for robot rubber hand illusion

Yuxuan Zhao1, Enmeng Lu1, Yi Zeng1,2,3,4,5⋆

1Brain-inspired Cognitive Intelligence Lab, Institute of Automation,
Chinese Academy of Sciences, Beijing, China.
2State Key Laboratory of Multimodal Artificial Intelligence Systems,
Chinese Academy of Sciences, Beijing, China.
3Center for Excellence in Brain Science and Intelligence Technology,
Chinese Academy of Sciences, Shanghai, China.
4University of Chinese Academy of Sciences, Beijing, China.
5Center for Long-term Artificial Intelligence, Beijing, China.

To whom correspondence should be addressed; E-mail<EMAIL_ADDRESS>
> At the core of bodily self-consciousness is the perception of the ownership
> of one’s body. Recent efforts to gain a deeper understanding of the
> mechanisms behind the brain’s encoding of the self-body have led to various
> attempts to develop a unified theoretical framework to explain related
> behavioral and neurophysiological phenomena. A central question to be
> explained is how body illusions such as the rubber hand illusion actually
> occur. Despite the conceptual descriptions of the mechanisms of bodily self-
> consciousness and the possible relevant brain areas, the existing
> theoretical models still lack an explanation of the computational mechanisms
> by which the brain encodes the perception of one’s body and how our
> subjectively perceived body illusions can be generated by neural networks.
> Here we integrate the biological findings of bodily self-consciousness to
> propose a Brain-inspired bodily self-perception model, by which perceptions
> of bodily self can be autonomously constructed without any supervision
> signals. We successfully validated our computational model with six rubber
> hand illusion experiments and a disability experiment on platforms including
> a iCub humanoid robot and simulated environments. The experimental results
> show that our model can not only well replicate the behavioral and neural
> data of monkeys in biological experiments, but also reasonably explain the
> causes and results of the rubber hand illusion from the neuronal level due
> to advantages in biological interpretability, thus contributing to the
> revealing of the computational and neural mechanisms underlying the
> occurrence of the rubber hand illusion.

##  1 Introduction

At the core of bodily self-consciousness is the perception of the ownership of
one’s own body (?, ?). In recent years, in order to understand more deeply how
the brain encodes self body, some researchers have tried to establish a
unified theoretical framework to explain the behavioral and neurophysiological
phenomena in the coding of bodily self-consciousness from the perspectives of
Predictive coding and Bayesian causal inference. For these theoretical models,
a core problem that needs to be explained is how body illusions such as the
rubber hand illusion occur. The rubber hand illusion refers to the illusion
that occurs when the participant’s rubber hand and the invisible real hand are
presented with synchronized tactile and visual stimuli, in which the
participant will have the illusion that the rubber hand seems to become his or
her own hand (?).

Prediction coding method realizes body estimation by minimizing the errors
between perception and prediction (?). Hinz et al. (?) regard the rubber hand
illusion as a body estimation problem. They take humans and a multisensory
robotic that can perceive the proprioception, vision and tactile information
on its arm as participants, and verify their model through the traditional
rubber hand illusion experiment. The experiment shows that the proprioception
drifts are caused by prediction error fusion instead of hypothesis selection.

The Active inference models can be regarded as an extension of Predictive
coding approaches. Rood et al. (?) propose a deep active inference model for
studying the rubber hand illusion. They model the rubber hand illusion
experiment in a simulated environment. The results show that their model
produces similar perceptual and active patterns to that of human during the
experiment. Maselli et al. (?) propose an active inference model for arm
perception and control, which integrates the imperatives both in intentional
and conflict-resolution. The imperative of intentional is used to control the
achievement of external goals, and the imperative of conflict-resolution is to
avoid multisensory inconsistencies. The results reveal that intentional and
conflict-resolution imperatives are driven by different prediction errors.

Bayesian causal inference model is extensively used in the theoretical
modeling of multimodal integration, and has been repeatedly verified at the
behavioral and neuronal levels (?, ?). The Bayesian causal inference model can
well reproduce and explain a variety of rubber hand illusion experiments.
Samad et al. (?) adopted the Bayesian causal inference model of multisensory
perception, and test it through the rubber hand illusion on humans. The
results show that their model could reproduce the rubber hand illusion, and
suggest that the Bayesian causal inference dominates the perception of body
ownership. Fang et al. (?) present a nonhuman primate version experiment of a
rubber hand illusion. They conduct the experiment on human and monkey
participants. They adopted the Bayesian causal inference (BCI) model to
establish an objective and quantitative model for the body ownership of
macaques. With the BCI model, they investigate the computational and neural
mechanisms of body ownership in the macaque brain from monkey behavioral and
neural data, respectively. The results show that the BCI model can fit monkey
behavioral and neuronal data well, helping to reveal a cortical representation
of body ownership.

Although the above theoretical models describe the mechanism of bodily self-
consciousness and possible related brain areas from a conceptual perspective,
they still do not explain the computational mechanism of how the brain encodes
bodily self-consciousness and how the body illusion we subjectively perceive
is generated by neural networks.

Here we integrate the biological findings of bodily self-consciousness and
construct a Brain-inspired bodily self-perception model, which can achieve
association learning of proprioceptive and visual information and construct
the bodily self-perception model autonomously without any supervision signals.
In terms of experiments, this model can reproduce six rubber hand illusion
experiments simultaneously at behavioral and neuronal scales, and the
experimental results can well fit the behavioral and neural data of monkeys in
biological experiments. In terms of biological explainability, this model can
explain the causes and results of the rubber hand illusion reasonably from the
neuron scale, which is helpful to reveal the computational and neural
mechanism underlying the rubber hand illusion. In addition, the results of the
disability experiment indicate that the generation of rubber hand illusion is
the result of the joint action of primary multisensory integration area (e.g.,
TPJ) and high-level multisensory integration area (e.g., AI), and neither is
indispensable.

##  2 Results

In this section, we first introduce the Brain-inspired bodily self-perception
model, then introduce the design of the experiment, and finally introduce the
Proprioceptive drift experiment result on the iCub humanoid robot, and the
results of Proprioceptive drift, Proprioception accuracy, Appearance
replacement, Asynchronous, Proprioception only, Vision only and Disability
experiments in the simulated environment.

###  2.1 Brain-inspired bodily self-perception model

We integrate the biological findings of bodily self-perception into a model to
construct a brain-inspired model for robot bodily self-perception, and the
architecture of the model is shown in Figure 1A.

(a) Brain-inspired Bodily Self-perception Model

(b) Neural network architecture of the model

Figure 1:  The architecture of the Brain-inspired Bodily Self-perception Model
and its neural network architecture. (a) Brain-inspired Bodily Self-perception
Model (including major functional brain areas, pathways, and their
interactions), and the arrow indicates the direction of information
transmission. M1, Primary motor cortex; S1, Primary somatosensory cortex; TPJ,
Temporo-parietal junction; V, Vision input; EBA, Extrastriate body area; AI,
Anterior insula. (b) The neural network architecture of the model. Brain areas
are shown in orange, neurons in brain areas are shown in circles, and the
connections between different brain areas are shown in black lines. The dotted
lines denote excitatory or inhibitory synapses which are depended on the
results of synaptic plasticity (such as $W_{S1-AI}andW_{EBA-AI}$ in bold), and
the solid lines indicate fixed synaptic weights (such as
$W_{M1-S1},W_{S1-TPJ},W_{TPJ-AI},W_{V-EBA},W_{EBA-TPJ}$ in italics).

We have derived and designed our computational model to include multiple
functional brain areas based on the current biological understanding of the
functions of various brain areas involved in bodily self-perception.
Specifically, the primary motor cortex (M1) is considered for encoding
motion’s strength and orientation, and controlling the motion execution (?,
?). In our computational model, the M1 is used to encode the orientation of
motion. The primary somatosensory cortex (S1) is considered for proprioception
to perceive limb position (?, ?). In our computational model, S1 receives
stimuli from M1 for the perception of arm movement orientation. The
extrastriate body area (EBA) is considered to be involved in the visual
perception of the human body and body parts (?), and in the rubber hand
illusion experiment, it is proved to be directly involved in the processing of
limb ownership (?). In our computational model, the EBA receives information
from Vision (V) and obtains finger orientation information. The temporo-
parietal junction (TPJ) integrates information from visual, auditory, and
somatosensory systems and is considered to play an important role in
multisensory bodily processing (?, ?), and has been reported be activated in
the rubber hand illusion experiment (?, ?). In our computational model, the
TPJ receives information from S1 and EBA, and performs primary multisensory
information integration. The anterior insula (AI) is considered to be a
primary region for processing interoceptive signals (?), multimodal sensory
processing (?, ?, ?), and it has also been reported to be activated in the
rubber hand illusion experiment (?, ?). In our computational model, the AI
receives information from S1, TPJ and EBA, performs high-level multisensory
information integration, and outputs the result.

Figure 1B shows the neural network architecture of the proposed model. This
model is a three-layer spiking neural network model with cross-layer
connections. The M1 area generates information about the robot’s motion
direction and the V area receives visual information about the robot. The AI
area outputs the robot’s behavior decision information according to the
highest firing rate of the neuron. Unsupervised learning of the bodily self-
perception model is realized through the motor and visual information, and
tested using the rubber hand illusion adapted from the macaque behavior
experiment (?). More details could be found in Materials and Methods section.

###  2.2 Experiments on the iCub robot

####  2.2.1 Experimental design

The overview of the robot experiment is shown in Figure 2.

Figure 2: Overview of the robot experiment. (a) Robot experiment settings. (b)
Starting position and target. (c) Overview of one trial in the task. (d)
Proprioceptive drift.

Figure 2A shows the scene settings of the experiment. The left panel shows the
equipment involved in the robot experiment, including an iCub humanoid robot,
a Surface Book 2 tablet with a camera in its back, a tablet stand, and a white
cardboard. The robot’s hand is placed in between the tablet and the white
cardboard. The tablet serves two functions: blocking the robot from seeing its
own hand directly; capturing images of the robot’s hand through the back
camera, rotating the image, and displaying the processed image in front of the
robot’s own eye-camera (the right eye-camera). The tablet stand is used to
support and hold the tablet in a desired position. The white cardboard blocks
sundries to make the background as clean as possible, thus reducing the
difficulty of image recognition and the possibility of incorporating other
intrusive visual cues. The settings of the equipment make sure that the robot
could only perceives its visual hand through the display of the tablet by its
own eye-camera. The right side panel shows, from top to bottom, a scene of the
robot experiment in the right rear view, the image displayed by the tablet and
the image perceived by the robot using its right eye-camera.

Figure 2B shows the Starting position and target during the robot experiment.
All points in the experiment are colored in red, and here we have marked the
initial positions as blue and black points for ease of illustration. The robot
first places its wrist on the blue dot below the image and places its finger
on the black dot. The red dots are the target that the robot needs to point to
during the experiment. These targets are distributed on a circular arc with
the blue dot as the circular dot (the position of the robot wrist) and the
distance between the blue dot and the black dot as the radius (the distance of
the robot’s wrist to its fingertip). With the point directly in front of the
circular dot as $0^{\circ}$, ranging from $-45^{\circ}$ to $45^{\circ}$, and
the interval is $15^{\circ}$. There are 9 target points in total.

Figure 2C shows the overview of one trial in the task. (1) The robot puts its
hand in the starting position. (2) The point at the starting position
disappears, and the visual hand rotates at a random angle. Considering the
motion range and precision of the robot, the rotation angle ranges from
$-36^{\circ}$ to $36^{\circ}$, and the interval is $6^{\circ}$, including two
angles $-45^{\circ}$ and $45^{\circ}$. There are 15 rotation angles in total.
(3) The target is displayed. (4) Based on multisensory integration by vision
and proprioception, the robot makes behavioral decisions and points to the
target.

Figure 2D shows the measurement method of proprioceptive drift. The dark hand
is the visual hand, and the light hand is the veridical hand. The red target
point is the position of the hand estimated by the robot, while the veridical
hand is the position where the proprioceptive hand is located. Therefore, the
angle between the robot’s veridical hand and the target point is the
proprioceptive drift in the rubber hand illusion, that is, the angle between
the blue dotted line and the red solid line. The angle between the blue dotted
line and the orange dotted line is the disparity from the veridical hand to
the visual hand.

####  2.2.2 Experimental results

Before the rubber hand illusion experiment, the robot needs to construct the
bodily self-perception model through training. During training process, the
robot observes its veridical hand directly and trains through random movement.
The training process does not require any supervised signal. Figure 3A shows
the synaptic weights between S1 and AI, EBA and AI after training, in which
both of them have changed from excitatory connection to inhibitory connection.
It also shows that the intensity of inhibitory connection from vision (EBA-AI)
is higher than that from proprioception (S1-AI).

Figure 3B shows the behavioral results of the robot experiment. When the hand
rotation angle is small (small disparity angle), the proprioceptive drift is
small. With the increase of the disparity angle, the proprioceptive drift
increases, indicating that the robot mainly relies on visual information for
decision-making. When the hand rotation angle is medium (medium disparity
angle), the proprioceptive drift is medium. With the increase of the disparity
angle, the proprioceptive drift increases slowly or remains unchanged,
indicating that the robot mainly relies on proprioceptive information for
decision-making. When the hand rotation angle is large (large disparity
angle), the proprioceptive drift is zero. With the increase of the disparity
angle, the proprioception deviation does not change, indicating that the robot
completely relies on the proprioceptive information for decision-making.

Figure 3C shows the results of the behavior at a small disparity angle. The
disparity angle is $12^{\circ}$, the proprioceptive drift is $12^{\circ}$.
Figure 3D shows the results of the behavior at a medium disparity angle. The
disparity angle is $30^{\circ}$, the proprioceptive drift is $24^{\circ}$.
Figure 3E shows the results of the behavior at a large disparity angle. The
disparity angle is $45^{\circ}$, the proprioceptive drift is $0^{\circ}$.

(a) Weight changing (b) Behavioral result (c) Small disparity angle

(d) Medium disparity angle

(e) Large disparity angle

Figure 3: (a) Weight changing. (b) Behavioral result. The black dots represent
the results of behavioral experiments, and the black line represents the
curve-fitting results of the behavioral data (Multisensory integration). The
red line represents the proprioceptive drift that completely depends on the
visual information (Vision based). The blue line represents the proprioceptive
drift that completely depends on the proprioceptive information
(Proprioceptive based). The horizontal axis is the disparity degree between
the visual hand and the veridical hand, and the vertical axis is the degree of
proprioceptive drift. (c) Small disparity angle. (d) Medium disparity angle.
(e) Large disparity angle.

###  2.3 Experiments in simulated environment

####  2.3.1 Proprioceptive drift and Proprioception accuracy experiments

In the simulated environment, the rotation angle ranges from $-60^{\circ}$ to
$60^{\circ}$, and the interval is $3^{\circ}$. The result of the
proprioceptive drift experiment is shown in Figure 4A, which is similar to the
results of the rubber hand illusion behavior experiment in macaques and humans
(?). The behavior experiment results in (?) show that the proprioceptive
drifts increased for small levels of disparity, while it plateaus or even
decreases when the disparity exceeds $20^{\circ}$. In our experiment, the
proprioceptive drift increases rapidly when the disparity is less than
$21^{\circ}$, and became flatter when the disparity is greater than
$21^{\circ}$. The results show that when the disparity between the visual hand
and the robot’s veridical hand is small, the hand position perceived by the
robot will be closer to the position of the visual hand, while when the
disparity is large, the robot’s perception of the hand position is more
dependent on the hand position of proprioception.

A recent study has shown that the proprioception accuracy may influence the
proneness to the rubber hand illusion, but there are fewer relevant studies
(?). In our model, the accuracy of proprioception can be achieved by
controlling the standard deviation of the receptive field of the neuron model.
The larger the standard deviation, the wider the receptive field range, and
the lower the accuracy. On the contrary, the smaller the standard deviation,
the narrower the receptive field range, and the higher the accuracy.
Therefore, we test the effect of proprioception accuracy on rubber hand
illusion by controlling the standard deviation of the receptive field of the
neuron, and the result is shown in Figure 4B. It shows that when the
proprioception accuracy is high (that is, the standard deviation of the
receptive field is small), the robot can only produce illusions within a small
disparity range, and when the proprioception accuracy is low (that is, the
standard deviation of the receptive field is larger), the robot can produce
illusions within a large disparity range. That is, the experimental results of
the model prove that lower proprioception accuracy is more likely to induce
rubber hand illusion, while higher proprioception accuracy is more difficult
to induce. This conclusion is consistent with the recent studies (?, ?). It
should be noted that in order to make the experimental results more intuitive,
we unified the behavioral results of different proprioceptive accuracies into
a scale range.

(a) Proprioceptive drift experimental result (b) Proprioception accuracy
experimental result

Figure 4: (a) Proprioceptive drift experiment result. (b) Proprioception
accuracy experiment result.

In the proprioceptive drift experiment, the robot’s behavior is influenced by
the dynamic change of the neurons’ firing rate in the model. In our model,
multisensory integration takes place in two areas: TPJ and AI. TPJ is the low-
level area of multisensory integration, which realizes the initial integration
of proprioceptive information and visual information. The synaptic weights of
$W_{S1-TPJ}$ and $W_{EBA-TPJ}$ are the same, but since the perception of
visual information is caused by movement, TPJ is more affected by visual
information during multisensory integration. AI is a high-level area of
multisensory integration. It integrates the proprioceptive information from
S1, the visual information from EBA, and the initial proprioceptive-visual
integration information from TPJ to achieve the final integration of
multisensory information, and the integration result affects the behavior of
the robot. After training, $W_{S1-AI}$ and $W_{EBA-AI}$ change from the
initial excitatory connections to inhibitory connections. The inhibitory
strength of $W_{EBA-AI}$ is greater than that of $W_{S1-AI}$, which means that
AI has a strong inhibitory effect on visual information during multisensory
integration (Figure 3A).

The firing rate of the TPJ and AI in the proprioceptive drift experiment
(Multisensory integration - Visual dominance) is shown in Figure 5. When the
visual disparity is small, the receptive field overlap of proprioceptive
information and visual information is huge, so the TPJ area presents a single
peak, visual-information-dominated multisensory integration result. The
results of multisensory integration when the proprioceptive perception is
$0^{\circ}$, and the visual disparity is $12^{\circ}$ are shown in Figure 5A
and Figure 5C. Figure 5C shows the dynamic changes of the six neurons with the
highest firing rate in TPJ. The firing rate from high to low is
$12^{\circ},9^{\circ},15^{\circ},6^{\circ},18^{\circ},3^{\circ}$, and the
initial integration result in TPJ is $12^{\circ}$. The AI area presents
multisensory integration results of bimodal peaks (as shown in Figure 5B and
Figure 5D). The anterior peak is mainly inhibited by neurons near the
proprioceptive perception $0^{\circ}$ and the visual perception $12^{\circ}$.
The firing rate from high to low is
$18^{\circ},15^{\circ},12^{\circ},9^{\circ},6^{\circ},3^{\circ}$, and the
result of anterior peak integration is $18^{\circ}$. In the posterior peak,
the inhibition intensity decreases with the disappearance of the
proprioceptive and visual stimulation, and the firing rate is
$12^{\circ},9^{\circ},15^{\circ},6^{\circ},18^{\circ},3^{\circ}$ from high to
low. The firing rate of neurons in the posterior peak is higher than that in
the anterior peak, and the final integration result in AI is $12^{\circ}$.

(a) Firing rate of the neurons in TPJ (b) Firing rate of the neurons in AI (c)
Local amplification of the neurons in TPJ (d) Local amplification of the
neurons in AI

Figure 5: The firing rate of the neurons in TPJ and AI in the proprioceptive
drift experiment (Multisensory integration - Visual dominance). The
proprioceptive perception is $0^{\circ}$, the visual disparity is
$12^{\circ}$. The proprioception drift is $12^{\circ}$ after multisensory
integration. (a and b) The firing rate of the neurons in TPJ and AI. (c and d)
The results of local amplification near the maximum peak firing rates of the
neurons in TPJ and AI. Here the six neurons with the highest firing rates are
selected and the dynamic changes of these neurons are plotted.

The firing rate of the TPJ and AI in the proprioceptive drift experiment
(Multisensory integration - Proprioception dominance) is shown in Figure 6.
When the visual disparity is moderate, the information integration in TPJ
mainly occurs at the location where the proprioceptive information and visual
information receptive fields overlap. The TPJ area presents multi-peak,
proprioceptive-information-dominated multisensory integration result. The
results of multisensory integration when the proprioceptive perception is
$0^{\circ}$, and the visual disparity is $39^{\circ}$ are shown in Figure 6A
and Figure 6C. Figure 6C shows the dynamic changes of the six neurons with the
highest firing rate in TPJ. The firing rate from high to low is
$24^{\circ},27^{\circ},21^{\circ},18^{\circ},30^{\circ},33^{\circ}$, and the
initial integration result in TPJ is $24^{\circ}$. The AI area presents multi-
peak multisensory integration results (as shown in Figure 6B and Figure 6D).
Figure 6B shows the dynamic changes of all neurons. Figure 6D shows the
dynamic changes of the six neurons with the highest firing rate in AI. The
firing rate from high to low is
$24^{\circ},27^{\circ},21^{\circ},18^{\circ},30^{\circ},0^{\circ}$. The final
integration result in AI is $24^{\circ}$.

(a) Firing rate of the neurons in TPJ (b) Firing rate of the neurons in AI (c)
Local amplification of the neurons in TPJ (d) Local amplification of the
neurons in AI

Figure 6: The firing rate of the neurons in TPJ and AI in the proprioceptive
drift experiment (Multisensory integration - Proprioception dominance). The
proprioceptive perception is $0^{\circ}$, the visual disparity is
$39^{\circ}$. The proprioception drift is $24^{\circ}$ after multisensory
integration. (a and b) The firing rate of the neurons in TPJ and AI. (c and d)
The results of local amplification near the maximum peak firing rates of the
neurons in TPJ and AI. Here the six neurons with the highest firing rates are
selected and the dynamic changes of these neurons are plotted.

(a) Firing rate of the neurons in TPJ (b) Firing rate of the neurons in AI (c)
Local amplification of the neurons in TPJ (d) Local amplification of the
neurons in AI

Figure 7: The firing rate of the TPJ and AI in the proprioceptive drift
experiment (Multisensory integration - Proprioception based). The
proprioceptive perception is $0^{\circ}$, and the visual disparity is
$60^{\circ}$. The proprioception drift is $0^{\circ}$ after multisensory
integration. (a and b) The firing rate of the neurons in TPJ and AI. (c and d)
The results of local amplification near the maximum peak firing rates of the
neurons in TPJ and AI. Here the six neurons with the highest firing rates are
selected and the dynamic changes of these neurons are plotted.

The firing rate of the TPJ and AI in the proprioceptive drift experiment
(Multisensory integration - Proprioception based) is shown in Figure 7. When
the visual disparity is large, the overlapping area of proprioceptive neurons
and visual neurons’ receptive fields is small, and the integration of TPJ is
weak. Therefore, the TPJ presents completely doublet peak results, with the
anterior peak dominated by proprioceptive information and the posterior peak
dominated by visual information. The results of multisensory integration when
the proprioceptive perception is $0^{\circ}$, and the visual disparity is
$60^{\circ}$ are shown in Figure 7A and Figure 7C. Figure 7C shows the dynamic
changes of the six neurons with the highest firing rate in TPJ. It shows that
the anterior peak presents the integration result dependent on proprioception
information, and the firing rate from high to low is
$0^{\circ},3^{\circ},6^{\circ}$. The posterior peak presents the integration
result dependent on visual information, and the firing rate from high to low
is $60^{\circ},57^{\circ},54^{\circ}$. The firing rates of the six neurons are
$60^{\circ},0^{\circ},57^{\circ},3^{\circ},54^{\circ},6^{\circ}$ from high to
low, and the initial integration result in TPJ is $60^{\circ}$. The AI area
presents doublet peak multisensory integration results (as shown in Figure 7B
and Figure 7D). Since the inhibition weight of visual connections ($W_{EBA-
AI}$) in the AI area is greater than that of proprioception ($W_{S1-AI}$), the
anterior peak that relies on proprioception is used as the final output. The
firing rate from high to low is
$0^{\circ},3^{\circ},6^{\circ},60^{\circ},57^{\circ},54^{\circ}$. The final
integration result in AI is $0^{\circ}$.

####  2.3.2 Appearance replacement and Asynchronous experiments

The result of the appearance replacement experiment is shown in Figure 8A,
which is similar to the results of the prior knowledge of body representation
behavior experiment (that is, replacing the visual hand in the rubber hand
illusion with a wooden block) in macaques and humans (?). The experimental
result in (?) shows that the proprioceptive drifts in the wood condition is
significantly reduced than that in the visual hand condition. In our
experiment, in the case of high similarity (that is, the hand in the robot’s
field of vision is similar to its own hand), the proprioceptive drift of the
robot is significantly smaller than that of the own visual hand. In addition,
the range of visual disparity that can induce the robot’s rubber hand illusion
is narrower. When the disparity exceeded $21^{\circ}$, the robot’s
proprioceptive drift is $0^{\circ}$, and the rubber hand illusion disappears.
In the case of dissimilarity (that is, the hand in the robot’s field of vision
is completely different from its own hand), the robot’s proprioceptive drift
is $0^{\circ}$, indicating that the robot does not consider the hand in the
field of view as its own. At the neuronal scale, the response of neurons in
EBA area to a similar hand is lower than that of their own hand, which leads
to the weak contribution of visual information for multisensory integration,
with TPJ and AI relying more on proprioceptive information for integration;
the neurons in the EBA area respond much less to dissimilar hands than their
own hand, further weakening the contribution of visual information for
multisensory integration in the TPJ and AI areas.

The studies in (?, ?) show that the majority of participants would not
experience the rubber hand illusion if the asynchrony is greater than 500 or
300 ms. Here we test the effect of synchrony on the rubber hand illusion. The
result of the asynchronous experiment is shown in Figure 8B. When the delay
time is 100 ms, the proprioceptive drift of the robot is smaller than that of
the own visual hand. When the delay time is 500 ms, the robot’s proprioceptive
drift is $0^{\circ}$, indicating that the robot does not think that the hand
in the field of view is its own. At the neuronal scale, the delayed
presentation of visual information will weaken the contribution of visual
information to multisensory integration, and a large delay will result in the
inability to integrate proprioceptive information and visual information
within the effective firing time window of neurons.

(a) Appearance replacement experiment result (b) Asynchronous experiment
result

Figure 8: The results of appearance replacement experiment and asynchronous
experiment.

####  2.3.3 Proprioception only and Vision only experiments

When there is only proprioception information, that is, when the robot only
moves its own hand and no hand is observed in the field of vision, the AI
neuron is fired, indicating that the robot thinks that the moving hand belongs
to itself. When there is only visual information, that is, the robot’s own
hand does not move, but the hand movement can be seen in the field of vision,
the neuron in AI is not fired, indicating that the robot does not think that
the moving hand belongs to itself. At the neuronal scale, the main reason for
this result is that the inhibition intensity of visual information in AI is
stronger than that of proprioceptive information.

####  2.3.4 Disability experiment

We explore the effects of TPJ disability and AI disability on the rubber hand
illusion by setting synaptic weights between different brain areas. Take the
Proprioception accuracy experiment as an example.

In the TPJ disability experiment, we set $W_{S1-TPJ}$ and $W_{EBA-TPJ}$ as 0.
Multisensory information is integrated by the AI only, and the TPJ no longer
integrated any information. After training and testing, the experimental
result of TPJ disability with different proprioception accuracy is shown in
Figure 9A. This result indicates that when TPJ is completely disabled,
multisensory information integration by AI alone cannot induce the rubber hand
illusion. In addition, we simulate the impact of varying extents of TPJ
disability on the rubber hand illusion by setting different synaptic weights.
The experimental results show that when the extent of TPJ disability is low
(e.g., the values of $W_{S1-TPJ}$ and $W_{EBA-TPJ}$ are large), TPJ is still
able to integrate multisensory information, and the robot can be induced
rubber hand illusion. But the proprioceptive drift is smaller, and the range
of visual disparity that can induce the robot’s rubber hand illusion is
narrower. As the extent of disability increases (i.e. the values of
$W_{S1-TPJ}$ and $W_{EBA-TPJ}$ decrease), the rubber hand illusion becomes
more difficult to be induced. The experimental results are consistent with the
behavioral experiment results that use the Transcranial Magnetic Stimulation
over TPJ to reduce the extent of rubber hand illusion (?).

(a) TPJ disability (b) AI disability

Figure 9: The result of disability experiment

In the AI disability experiment, we set $W_{S1-AI}$, $W_{TPJ-AI}$ and $W_{EBA-
AI}$ as 0. Multisensory information is integrated by the TPJ, and the AI no
longer integrated any information. After training and testing, the
experimental result of AI disability with different proprioception accuracy is
shown in Figure 9B. As seen in Figure 9B, although the robot is induced with
the rubber hand illusion at partial visual deflection angles, the AI
disability robot mainly relies on vision for decision-making at most visual
deflection angles. That is, AI disability cannot effectively induce the rubber
hand illusion.

The results of the disability experiment indicate that the generation of
rubber hand illusion is the result of the joint action of primary multisensory
integration area (e.g., TPJ) and high-level multisensory integration area
(e.g., AI), and neither is indispensable.

###  2.4 Comparison with other models

Computational models of self-body representation, especially those that can
reproduce and explain the rubber hand illusion, are less studied. Researchers
have proposed theoretical models of body representation mainly from the
perspectives of Predictive coding and Bayesian causal inference (?). Table 1
shows the comparison results with other models.

The core idea of the Predictive coding approaches (?, ?) is to refine the body
estimation through the minimization of the errors between perception and
prediction. The Active inference models (?, ?) can be regarded as an extension
of Predictive coding approaches. These methods can well reproduce and explain
the proprioceptive drift experiment, and have been verified in human, robot
and simulated environment. However, these studies did not involve various
experiments of the rubber hand illusion, nor could they explain the specific
computational mechanism of individual neurons and population neurons.

Bayesian causal inference model is extensively used in theoretical modeling of
multimodal integration, and has been repeatedly verified at the behavioral and
neuronal levels. The Bayesian causal inference model can well reproduce and
explain a variety of rubber hand illusion experiments (?, ?). However, in the
experiment of rubber hand illusion, most of the Bayesian causal inference
models have problems similar to the Predictive coding approaches, such as the
explanatory scale remains at the behavioral scale, and also does not explain
how the rubber hand illusion is generated from the neuron scale. In addition,
there are also some studies on neural network modeling, although they mainly
focus on multimodal integration and do not involve rubber hand illusion
experiments (?).

Compared with these models, we build a Brain-inspired bodily self-perception
model from the perspective of brain-inspired computing. Our model can not only
reproduce as many as six experiments of the rubber hand illusion, but also
reasonably explain the rubber hand illusion from the neuron scale at the same
time, which is helpful to reveal the computational and neural mechanism of the
rubber hand illusion. And the computational model of Disability experiment
demonstrates that the rubber hand illusion cannot be induced without TPJ,
which performs primary multisensory integration, and AI, which performs high-
level multisensory integration.

Table 1: Comparison with other models. $O$ represents that the model could
reproduce the correlation feature, and $-$ represents that it is not
mentioned.

Experiment |  (?) |  (?) |  (?) |  (?) |  (?) |  (?) | Our model
---|---|---|---|---|---|---|---
Proprioceptive drift | O | O | O | O | O | O | O
Proprioception accuracy | - | - | - | - | - | - | O
Appearance replacement | - | - | - | - | - | O | O
Asynchronous | - | - | O | - | O | - | O
Proprioception only | - | - | - | - | O | - | O
Vision only | - | - | - | - | O | - | O
Disability | - | - | - | - | - | - | O
Model | PC | PC | Deep AIF | AIF | BCI | BCI | Brain-Self
Participant | H, R | R | S | H | H | M, H | R, S

  * •

Model: PC, Predictive coding; AIF, Active inference model; BCI, Bayesian
causal inference model; Brain-Self, Brain-inspired Bodily Self-perception
Model.

  * •

Participant: H, Human; R, Robot; S, simulated environment; M, Monkey.

##  3 Discussion

In this study, we integrate the biological findings of bodily self-
consciousness and construct a Brain-inspired bodily self-perception model,
which could construct the bodily self-perception autonomously without any
supervision signals. It can reproduce six rubber hand illusion experiments,
and reasonably explain the causes and results of rubber hand illusion from the
neuron scale. Compared with other models, our model explains the computational
mechanism that the brain encodes bodily self-consciousness and how the body
illusion we subjectively perceive is generated by neural networks. Especially,
the experimental results of this model can well fit the behavioral and neural
data of monkeys in biological experiments. This model is helpful to reveal the
computational and neural mechanism of the rubber hand illusion.

In the biological experiment of rubber hand, Fang et al. (?) recorded the
firing rate of neurons in the premotor cortex of 2 monkeys in the behavior
task. They defined two types of neurons: integration neurons and segregation
neurons. If a neuron’s firing rate under the visual-proprioceptive congruent
task is greater than that under the proprioception-only task, it indicates
that the neuron prefers to integrate visual and proprioception information,
which they define as ‘integration neuron’; Conversely, if a neuron’s firing
rate under proprioception-only task is greater than that under visual-
proprioceptive congruent task, it means that the neuron prefers only
proprioception information, which they define as ‘segregation neuron’. By
analyzing the firing rates of neurons under different tasks, they found that
the firing rates of integration neurons decreased with increasing visual
disparity during the target-holding period, and the firing rates of
segregation neurons increased with increasing visual disparity during the
preparation period.

In our computational model, neurons in the TPJ and AI areas exhibit similar
properties. Figure 10 shows the dynamic changes of neuronal firing rates in
TPJ and AI areas in different tasks. In order to make the comparison of
results more intuitive and significant, the results of visual-proprioceptive
congruent (VP) condition, proprioception-only (P) condition and part of
visual-proprioceptive conflict (VPC) conditions are selected for display. The
VPC conditions includes the results when proprioception is $0^{\circ}$ and
visual deflection is $30^{\circ},33^{\circ},36^{\circ},39^{\circ},42^{\circ}$,
respectively. Clearly, neurons in the TPJ area consistently exhibit
integration properties. With the increase of visual disparity, the integration
intensity of neurons in TPJ becomes weaker and the firing rate of neurons
becomes lower. Neurons in the AI region exhibit the properties of separation
and integration at different stages. In the early stage (such as about 200ms),
the neurons in the AI area exhibit separation properties, and the firing rate
of neurons increases with the increase of visual disparity. In the later stage
(such as about 400ms), the neurons in the AI area exhibit integration
properties, and the firing rate of neurons decreases with the increase of
visual disparity.

The reason for the integration effect in TPJ is that when the visual disparity
is small, the receptive field overlap of proprioceptive information and visual
information is huge, so the integration effect is strong and the firing rate
of neurons is high; when the visual disparity is huge, the receptive field
overlap of proprioceptive information and visual information is small, so the
integration effect is weak and the firing rate of neurons is low.

AI is a high-level area of multisensory integration that receives excitatory
stimulus (proprioc-eption-visual integration information) from TPJ, and
inhibitory stimulus from S1 (proprioception information) and EBA (visual
information) simultaneously. In the separation stage, the firing rate of
neurons is highest in the proprioception-only task and the lowest in the
visual-proprioceptive congruent task, and in the visual-proprioceptive
conflict task, the firing rates of the neurons increased with the increase of
visual disparity. The reason is that when the proprioceptive stimulation
disappears, the firing rate of neurons in S1 decreases; when the visual
stimulation appears, the firing rate of neurons in EBA increases, and the
inhibitory effect of information from EBA on information from TPJ in AI
increases. In the proprioception-only task, the firing rate of neurons in AI
is highest due to the absence of inhibition from EBA. In the visual-
proprioceptive congruent task, the receptive field of proprioceptive
information and visual information overlap completely, the inhibitory effect
of EBA on TPJ was strongest in AI, so the firing rate of neurons in AI is the
lowest. In the visual-proprioceptive conflict task, the information
integration in TPJ mainly occurs at the location where the proprioceptive
information and visual information receptive fields overlap. With the increase
of visual disparity, the inhibition of EBA on the integration information in
TPJ decreases, leading to the increase of the firing rate of neurons in AI. In
the integration stage, the proprioceptive and visual stimulation disappears,
and their firing rates decrease. Due to the cumulative effect, the firing rate
of neurons in TPJ continues to increase, and the inhibition of S1 and EBA in
AI on TPJ decreases, highlighting the integration effect of TPJ.

(a) Firing rate of the TPJ (b) Firing rate of the AI

Figure 10: The dynamic changes of neuronal firing rates in TPJ and AI areas in
different tasks.

##  4 Materials and Methods

The brain-inspired bodily self-perception model is shown in Figure 1.

The neurons representing angles in M1 and V are described by Equation 1.
$S_{j}(t)$ represents stimulus j at time $t$, and Vj(t) represents the firing
rate of the neuron. The intensity of the stimulus is related to the receptive
field of the neuron. Equation 2 describes the receptive field of the
$\theta_{j}$. When the stimulation angle is $J$, the stimulation intensity of
neuron representing $J$ is the largest, and the stimulation intensity of other
neurons decreases successively. The firing rate of the neuron will increase
when the stimulus is present and will decay when the stimulus has ended. $C$
is the parameter that controls the rate of increase and decrease. We set
$C=0.04$ in M1, V, S1 and EBA areas, $C=0.01$ in TPJ area, and $C=0.15$ in AI
area. The firing rate of the neuron and the receptive fields of different
neurons are shown as Figure 11.

$\Delta V_{j}(t)=-C\times(V_{j}(t)-S_{j}(t))$ (1)

$s=e^{(\theta-\theta_{J})/2\delta^{2}}$ (2)

(a) Firing rate of the neuron (b) Receptive fields of different neurons

Figure 11: The characteristic behaviors of neurons. (a) The firing rate of the
neuron that represents $0^{\circ}$ when receiving $0^{\circ}$ stimulation, the
stimulation is presented at 0 ms and ends at 100 ms.(b) Receptive fields of
different neurons.

Neurons in other areas are described by Equation 3. The $V_{i}$ is the firing
rate of the postsynaptic neuron, $V_{j}$ is the firing rate of the presynaptic
neuron, and the $W_{ij}$ is the synaptic weight between the presynaptic neuron
$j$ and the postsynaptic neuron $i$. Specifically, the neurons in each brain
area in the computational model are described as shown in Equation 4.

$\begin{split}&V_{i}(t+1)=V_{i}(t)+\Delta V_{i}(t)\\\ &\Delta
V_{i}(t)=-C\times(V_{i}(t)-tanh(W_{ij}\times V_{j}(t)))\\\ \end{split}$ (3)

$\begin{split}&V_{S1}(t+1)=V_{S1}(t)+\Delta V_{S1}(t)\\\ &\Delta
V_{S1}(t)=-C\times(V_{S1}(t)-tanh(W_{M1-S1}\times V_{M1}(t)))\\\
&V_{EBA}(t+1)=V_{EBA}(t)+\Delta V_{EBA}(t)\\\ &\Delta
V_{EBA}(t)=-C\times(V_{EBA}(t)-tanh(W_{V-EBA}\times V_{V}(t)))\\\
&V_{TPJ}(t+1)=V_{TPJ}(t)+\Delta V_{TPJ}(t)\\\ &\Delta
V_{TPJ}(t)=-C\times(V_{TPJ}(t)-tanh(W_{S1-TPJ}\times V_{S1}(t)+W_{EBA-
TPJ}\times V_{EBA}(t)))\\\ &V_{AI}(t+1)=V_{AI}(t)+\Delta V_{AI}(t)\\\ &\Delta
V_{AI}(t)=-C\times(V_{AI}(t)-tanh(W_{S1-AI}\times V_{S1}(t)+W_{TPJ-AI}\times
V_{TPJ}(t)+W_{EBA-AI}\times V_{EBA}(t)))\\\ \end{split}$ (4)

The synaptic plasticity in this model is defined as shown in Equation 5.
$W_{ij}$ in this model represents the synaptic weight between the postsynaptic
neuron $i$ and the presynaptic neuron population $j$.

$W_{ij}(T+1)=W_{ij}(T)+\Delta W_{ij}(T+1)\times W_{inhibit}(T+1)$ (5)

where

$\Delta W_{ij}(T+1)=\int_{T}^{T+1}\Delta w_{ij}(t)dt$

The $\Delta w_{ij}(t)$ is calculated using Equation 6.

$\Delta w_{ij}(t)=\alpha V_{i}(t)V_{j}(t)+\beta
V^{\prime}_{i}(t)V_{j}(t)+\gamma V_{i}(t)V^{\prime}_{j}(t)$ (6)

where

$\alpha=\int_{-\infty}^{+\infty}f(u)du,\beta=\int_{-\infty}^{0}uf(u)du,\gamma=-\int_{0}^{+\infty}uf(u)du$

$f(u)$ is the STDP function reported in (?, ?, ?). According to our previous
research in (?), we set the parameters of $\alpha=-0.0035$, $\beta=0.35$,
$\gamma=-0.55$ in this model.

$W_{inhibit}$ is the lateral inhibitory synaptic weight used to control the
location of synaptic weight update, which is described by the Equation 7. $fs$
is the firing state of the postsynaptic neuron, and $fn$ is the number of
firings of the postsynaptic neuron. If the firing rate of the postsynaptic
neuron is greater than the threshold, the firing state of the neuron is 1,
otherwise it is 0. We set the threshold as 0.7 in this model.

$W_{inhibit}(T+1)=tanh(W_{inhibit}(T)-\frac{2\times\arccos fs}{\pi}\times
e^{fn}-1)+1$ (7)

where

$fs=\left\\{\begin{matrix}1&V_{i}>threshold\\\ 0&V_{i}\leq
threshold\end{matrix}\right.$

The details of visual processing such as motion perception and appearance
learning are shown in our previous work (?, ?).

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## Acknowledgments

Funding: This study was supported by the Key Research Program of Frontier
Sciences, CAS (Grant No. ZDBS-LY-JSC013), the Strategic Priority Research
Program of the Chinese Academy of Sciences (Grant No. XDB32070100), the
Beijing Municipal Commission of Science and Technology (Grant No.
Z181100001518006).

Author contributions:  Conceptualization, Y.Zh. and Y.Ze.; Methodology, Y.Zh.;
Software, Y.Zh. and E.L.; Validation, Y.Zh. and E.L.; Formal Analysis, Y.Zh.;
Investigation, Y.Zh.; Writing - Original Draft, Y.Zh., E.L. and Y.Ze.;
Visualization, Y.Zh.; Supervision, Y.Ze.; Project Administration, Y.Ze.;
Funding Acquisition, Y.Ze.

Competing interests:  All authors declare that there is no conflict of
interest.

## Supplementary materials

Movie: Rubber hand illusion experiment on the iCub robot (Multisensory
integration - Visual dominance, Proprioception dominance, Proprioception
based)

Description:

_Part I_ : Experiment on the iCub robot (Multisensory integration - Visual
dominance): When the hand rotation angle is small (small disparity angle), the
proprioceptive drift is small. The robot mainly relies on visual information
for decision-making.

_Part II_ : Experiment on the iCub robot (Multisensory integration -
Proprioception dominance): When the hand rotation angle is medium (medium
disparity angle), the proprioceptive drift is medium. The robot mainly relies
on proprioceptive information for decision-making.

_Part III_ : Experiment on the iCub robot (Multisensory integration -
Proprioception based): When the hand rotation angle is large (large disparity
angle), the proprioceptive drift is zero. The robot completely relies on the
proprioceptive information for decision-making.

Movie Address: https://youtu.be/G941vAfaJ-Q