• cerebellum
• controller
• head stabilization
• humanoid robot
• model
• reflex
• simulation
• testing

Head stabilization is fundamental for many animals survival. Its posture and the way it
compensates the movements of the other part of the body as the torso, especially during
everyday basic movements like walking or running, are crucial to give a stable reference
frame for the two essential perceptual systems for detection of self-motion relative to space:
the visual and vestibular systems.
Vision is the most useful sensor for many animals to provide information about the
surrounding environment and is an important function for protection from enemies.
The vestibular informations operate to create an inertial guidance system determining
the spatial orientation in order to coordinate movements and balance.
Another advantage of head stabilization during movements and locomotion is in
maintaining gaze stability and preserving visual acuity.
The head/trunk coordination helps the interpretation of the inputs from the sensors, as
the visual and vestibular receptors are stimulated as soon as the head moves, in order to
maintain equilibrium while standing or walking.
In vestibular injured patients however, this compensation was not observed. This
brought to understand the role of the vestibular information for the head stabilization and
the existence of the vestibulocollic reflex (VCR), a reflex loop wich stabilize the head in the
inertial space.
This works is based on the analysis and the study of the existent models of this
mechanism, both the biological ones and the robotic ones and presents a new bio-inspired
controller for the iCub robot head based on above-mentioned study.
In particular, the Recurrent Architecture was employed wich is inspired by the recurrent
connection found in the cerebellum and so it is a good candidate to simulate the role of the
cerebellum and its plasticity in the learning process. The structure is as an adaptive filter.
In the cerebellar modelisation, the inputs of the system (Figure 1) (represented by the
vector y) are carried by MossyFibers (MF), which converge in the Granule Cells (GC). Each
GC receives input from several MFs and from recurrent connections (not shown) and its
output is distributed along a Parallel Fiber (PF). Attached to the bundle of PFs there are
Purkinje Cells (PC). Each PC receives input from all the PFs and receives an additional input
from a Climbing Fiber (CF). This additional input is assumed to act as a teaching signal
ii
Figure 1: Schematic diagram of the organization of the cerebellar microcircuit (taken from
Porril et al.2004)
for the weights wij of the PC-PF synapse. If we see the model as an adaptive filter, GC are
modelled as filters with transfer function Gi and PC perform a weighted sum of signals pi
carried by Parallel Fibers. The learning algorithm used in this approach is the decorrelation
control, implemented in the cerebellum block. The sensory error here is due to a incorrect
motor response: when there is no more correlation between the two cerebellar input (sensory
error and efferent motor copy) the learning stops because is no more possible reducing the
sensory error.
In decorrelation control, mossy-fibre inputs are predictor variables, to be decorrelated
from the target determined by the CF signal, processing of the MF input y(t) by the granule
cell layer is meant as analysis by a bank of linear filters Gi so that the PFs carry signals
pi(t) = Giy(t). PC output is modelled as z(t) = ∑ wi ∗ pi(t) of these PF inputs, so the PC
implements a linear filter C = ∑ wi ∗ Gi
. The CF input is interpreted as a training signal
e(t), which adapts synaptic weights using learning rule δwi = −β ∗ e ∗ pi
.
Using this architecture in the cerebellar block in Figure 2 was possible to create a
controller for the head of humanoid robot iCub really biologically inspired. Like the human
head with its vestibular system, iCub head own an Inertial Measurement Unit (IMU) wich
is able to sense the linear acceleration and the angular velocities around the three axes.
Using the iCub kinematics and dynamics and the cerebellar architecture described above
was possible to implement in Matlab Simulink the controller. This model has as input the
angular velocities of the head, more precisely the difference between a reference velocity and
the one estimated by the cerebellum. The Inverse Jacobian transforms the command from
the operative space to the joint space and it goes as input to the robot. The error used as
a teaching signal is the velocity measured by the inertial sensor. The reference velocity vr
is an estimation of the torso velocity obtained by the difference between the angular pitch
velocity of the head and the one misured by the inertial sensor.
iii
Figure 2: Block diagram of the model.
The validation of the model has been tested on a single axis of rotation, in this case the
pitch. It was done giving as a disturb for the system single sinusoids at different frequencies
and also a sum of sinusoid. The range of frequency used is between 0.1 and 1 Hz that is
the oscillatory range of frequency distinctive of the locomotion with a time sampling of 100
Hz. In the figure 3 we can see in red the error decreasing fo both the single sinusoid and
the sum and the head velocity compensates the torso. In this range the system converges.
The convergence time is a parameter we used to verify the quality of the system. It represent
the time needed to the system to reach a stabile condition. In this case it increase when the
frequency of the disturbs increase, but, at a given frequency, it results more or less the same
for al the weights. Head pitch velocity compensates the torso pitch velocity, as happen in
human body trough the VCR action.
a)
b)
Figure 3: Head and torso angular velocities and error for a single sinusoid input at 1 Hz a
and for a sum of sinusoids b).
The system was trained with a sum of sinusoid for 100 s. The coefficients of the weights
obtained after the training (figure 4) were used to set the coefficient of a new session.
Simulating the system with a single sinusoid at 0.5 Hz in input, we can notice that system is
stabilised faster and reach easily the convergence. (Figure 5)
iv
Figure 4: The evolution of the weights during the training set
In conclusion, a bionspired controller, working in velocity, has been implemented and
tested and we demonstrate it is able to stabilize the head when an external disturb occour.
A future work could be the validation of the model for all the three axes of rotation.
a) b)
Figure 5: Head and torso angular velocities and error for a single sinusoid input at 0.5 Hz
before a) and after the training b)