Instrumentation & Measurement Magazine 25-9 - 22

the simplest case, depends only on a subset of the hidden variables.
Although different neuron models can be adopted, in
the following applications the Izhikevich class I neuron is considered
[7]:
dV
dt




m 0.04 5 140mm
m

du
dt  
 a bV u
IfV V
m th

  c

V m
 u ud
(4)
where Vm is the membrane potential; u is the recovery variable;
Vth is the spike threshold; I is the input current and the parameters
are set to a=0.02, b=0.2, c=-65 and d=2. With these values,
the model implements a class I behavior, where the spiking frequency
is proportional to the amplitude of the input current.
The adopted synaptic model within the hidden layer
was introduced by Tsodyks and implements short-term
synaptic depression and short-term facilitation. For the
input and output layers, a typical impulse response firstorder
exponential time decaying function was adopted.
The input and hidden layer synaptic weights (Win
and Wres
,
respectively) are randomly initialized with a gaussian distribution,
whereas the output weights (i.e., Wout
method as:
W X X kI X y

out  
T

1
T
t
(5)
where X corresponds to the state matrix, which includes the
state of a selected subset of the lattice neurons for each input
pattern, k is a small constant gain introduced in presence of illconditioned
matrices, I is an identity matrix and yt
is the target
signal.
Although the internal lattice can be randomly generated
and does not need a learning mechanism, different strategies
were proposed to improve the model performance, based on
input-driven mechanisms such as an intrinsic plasticity rule
designed to maximize the transferred information and correlation-based
approaches such as the biologically inspired
spike-timing-dependent plasticity (STDP), to improve the
memorization performance if compared with static weights
solutions [8].
Applications
To demonstrate the applicability of LSMs to different
working scenarios, taking inspiration from the MB neural
structures, two cases of study are discussed. The first focuses
on the processing of proprioceptive information acquired at
the leg joints in a quadruped robot to estimate the ground reaction
forces generated by the legs during the stance phase.
The second application deals with the high-level task of a
sequence learning problem [4], showing how an insect-braininspired
architecture can be adopted for navigation control
in a roving robot.
22
) are subject
to learning. The supervised learning rule adopted to determine
Wout
is based on the Moore-Penrose pseudoinverse
V V uI
2   

(3)
Ground Reaction Force Estimation
In the robotic field, the use of robust and reliable distributed
sensors is fundamental and represents a still challenging task.
Legged robots are more and more adopted to explore complex
unstructured terrains. Under this perspective, efficient
and real-time locomotion controllers were already introduced
in the literature, among which the central pattern generator,
which though being in principle an open-loop strategy, allows
the system to efficiently account for sensory feedback. On the
other hand, an important issue still to be fully addressed is the
lack of efficient sensing devices and processing techniques to
adapt the locomotion in real-time, depending on the terrain
characteristics.
From this perspective, haptic feedback is a primary information
source for achieving reliable locomotion in legged
robots, especially on uneven terrains, where real-time gait
adaptation and attitude control are needed. To efficiently interact
with the terrain, haptic feedback is needed to estimate
the ground reaction forces (GRFs) acting on the individual
legs [9]. This is a critical aspect of legged locomotion since the
presence of repetitive impacts with the terrain can affect both
the safety and reliability of the sensing device, where multiple
false detections can occur, especially while working on uneven
terrains. To overcome this problem, reliable sensorless
techniques were proposed to estimate the ground-foot contact
information [10], [11].
The RC approach can be used in the form of LSM to design
an efficient robot state estimation method for mapping
local proprioceptive information acquired at the level of the
leg joints into exteroceptive information describing the legground
interaction. The robot adopted as a case study was a
simulated quadruped robot endowed with ground reaction
force sensory feedback, as fully described in [12].
The LSM was designed to receive as input the torque signals
acquired at the joint level (i.e., 12 revolute joints) and to
provide at the output the estimation of the GRF component
normal to the ground for each leg (i.e., 4 outputs). The best
network configuration, validated on different terrains including
flat, uphill and downhill with maximum slopes of ±15°,
is characterized by 18 lattice neurons (i.e., 14 excitatory and
4 inhibitory neurons) [7]. This network is considerably small
if compared with other implementations based on ESN networks,
where 100 reservoir neurons are considered [12].
The presence of unexpected faults in the sensory system
was also addressed. The network can reconstruct the missing
information from one or multiple joints from the data coming
from all of the others, also assessing the LSM capability to
work as a fading memory.
In Fig. 3 the comparisons between the estimated and actual
GRFs are considered for the front left leg. Even if the sensory
system of that leg is in fault, the degradation of the estimation
performance does not exceed 5.7% in terms of the correlation
coefficient; this guarantees a good performance in following
the stepping sequence.
The obtained results confirm that the LSM is a robust
state estimation network also in the presence of missing
IEEE Instrumentation & Measurement Magazine
December 2022
Instrumentation & Measurement Magazine 25-9

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