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Journal ArticleDOI

Synergistic control of a multi-segments vertebral column robot based on tensegrity for postural balance

21 Jun 2018-Advanced Robotics (Taylor & Francis)-Vol. 32, Iss: 15, pp 850-864

TL;DR: A neuronal architecture to control a compliant robotic model of the human vertebral column for postural balance using a network of nonlinear Kuramoto oscillators coupled internally and externally to the structure and error-driven by a proportional derivative controller using an accelerometer for feedback.
Abstract: We present a neuronal architecture to control a compliant robotic model of the human vertebral column for postural balance. The robotic structure is designed using the principle of tensegrity that ...
Topics: Postural Balance (60%), Tensegrity (53%)

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Synergistic control of a multi-segments vertebral column
robot based on tensegrity for postural balance
Artem Melnyk, Alexandre Pitti
To cite this version:
Artem Melnyk, Alexandre Pitti. Synergistic control of a multi-segments vertebral column robot
based on tensegrity for postural balance. Advanced Robotics, Taylor & Francis, 2018, pp.1 - 15.
�10.1080/01691864.2018.1483209�. �hal-01822537�

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ADVANCED ROBOTICS
https://doi.org/10.1080/01691864.2018.1483209
Synergistic control of a multi-segments vertebral column robot based on
tensegrity for postural balance
Artem Melnyk
a
and Alexandre Pitti
b
a
Héphaïstos Project, Université Côte d Azur, INRIA, France;
b
Laboratoire E TIS, Université Paris Seine, Université de Cergy-Pontoise, CNRS UMR,
ENSEA, Cergy-Pontoise, France
ABSTRACT
We present a neuronal architecture to control a compliant robotic model of the human vertebral
column for postural balance. The robotic structure is designed using the principle of tensegrity that
ensures to be lightweight, auto-replicative with multi-degrees of freedom, flexible and also robust
to perturbations. We model the central pattern generators of the spinal cords with a network of
nonlinear Kuramoto oscillators coupled internally and externally to the structure and error-driven
by a proportional derivative (PD) controller using an accelerometer for feedback. This coupling
between the two controllers is original and we show it serves to generate controlled rhythmi-
cal patterns. We observe for certain coupling parameters some intervals of synchronization and
of resonance of the neural units to the tensile structure to permit smooth control and balance.
We show that the top-down PD control of the oscillators flexibly absorbs external shocks propor-
tionally to the perturbation and converges to steady state behaviors. We discuss then about our
neural architecture to model motor synergies for compliance control and also about tensegrity
structures for soft robotics. The 3D printed model is provided as well as a movie at the address
https://sites.google.com/site/embodiedai/current-research/tensegrityrobots.
ARTICLE HISTORY
Received 11 December 2017
Accepted 17 May 2018
KEYWORDS
Motor synergies; central
pattern generators;
tensegrity; vertebral column;
postural balance; phase
synchronization; soft
robotics; feedback
resonance; biological
robotics
1. Introduction
Animals musculoskeletal system is based on a com-
Q1
plex network of muscles, bones, nerves, tissues, and soft
bodies which are hard to replicate accurately in robots
[
1,2]. This dense architecture is however well ordered so
that the control done in the nervous system can realize
easily exible sensorimotor coordination at a very low
energy cost with the dynamical grouping of the muscles
known as motor synergies [
35]. Nonetheless, in order
to exploit fully the body structure, the nervous system
has to organize itself exibly and complementarily [
68].
For instance, the
well distribution of stress and strain
throughout the body warranties its ecological control so
that when we are exposed to a violent shock, we can still
stand or bend our knees or stien (or soften) our body
and joints w ith a small amount of control, just as a build-
ing would absorb an e ar thquake wave and balance itself,
or as a bridge would lean into the wind. In comparison,
current robots are still dicult to design and to control in
order to achieve robust postural balance under external
perturbations and dynamic motion.
In this paper, we propose to take inspiration of both
(1) the human musculoskeletal system of the dorsal spine
CONTACT Alexandre Pitti alexandre.pitti@u-cergy.fr Laboratoire ETIS, Université Paris Seine, Université de Cergy-Pontoise, CNRS UMR 8051, ENSEA,
Cergy-Pontoise, France
and (2) the neural architecture at the spinal cords level
to realize a multi-degrees of freedom vertebral column
robot [
912] and its neural controller in order to cope
with external perturbations. Our rst contribution is
on the one hand on t he design of an original neura l
controller composed of a
proportional derivative (PD)
controller and nonlinear oscillators in order to gener-
ate controlled rhythmical patterns and convergence to
steady state behaviors. Our second contribution is on the
other hand on the design of a novel vertebral column
robot constituted of connected auto-replicative tenseg-
rity elements [
13] mounted vertically as a multi-segment
inverted pendulum with soft lin ks. To our knowledge,
this coupling between a PD controller and nonlinear
oscillators to control synchronization as a minimization
process was never presented before.
We model the central pattern generators (CPGs) of the
spinal cords with a network of nonlinear Kuramoto oscil-
lators coupled internally and externally to the structure
and error-driven by a PD controller using an accelerom-
eter for feedback. We suggest that our proposed neural
controller, although simple, is similar to the role played by
the neuromodulators in the spinal cord that modulate the
© 2018 Taylor & Francis and The Robotics Society of Japan

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2 A. MELNYK AND A. PITTI
gain of the sensory feedback on the alpha-motor neurons
activity to generate the desired synergy [
1416]; which
means select ing the most expected resonant modes rela-
tive to the perturbation. In line with [
8,17], we consider
postural coordination modes as emergent phenomena
giving rise to non-linearity properties such as phase tran-
sition, multistability and hysteresis [
18].
The paper is organized as follows. In Section 2, we
present rst our motivation for the design of a tensile
structure. In
Sec tion 3, we describe then its assembling
with replicated 3D printed elements, its motors and sen-
sors used in order to replicate the tendon-driven mecha-
nism and control of the human upper-body. We present
the neural oscillators used to model the so-called
CPGs
and the feedback-driven PD control used to model the
neuromodulators. Tested in passive and ac tive condi-
tions, the multi-DOF tensile structure shows a large spec-
trum of behaviors from very soft dynamics capable to
generate rhythmical oscillations to very rigid static pos-
tures capable to handle its own weight in every posture.
In
Sec tion 4, we propose four experiments to dis-
play the capabilities of our framework. In the rst s etup,
we dene the dynamics in open-loop control for var-
ious modes of coordination by varying the phase and
the duration of a pulse-width modulation (PWM) con-
trol and by analyzing the resonant frequencies of the
system and its rhythmical patterns. In the se cond exper-
iment, we analyze the system statically from a postural
viewpoint and study its robustness in the upward posi-
tion. In the third experiment, we propose to exploit error
feedback for closed-loop control of the structure using
CPGs [19]. Depending on the values of the internal and
external coupling parameters, we can synchronize non-
linear oscillators modeled with Kuramoto units to the
resonant modes of the structure and entrain it f reely
to specic directions. These privileged modes of syn-
chrony represent the natural motor synergies that are
possible to generate and control in the multi-segmented
structure [
20].
In the fourth experiment, we employ a top-down
mechanism, a PD controller, that controls the amplitude
level of the oscillators in order to absorb the external per-
turbations gradually on the vertebral structure so that it
can return b ack to its resting upward posture. Depending
on the strength of external perturbation, the controller
will set the oscill ators to a certain regime producing big
oscillations till recovery in order to absorb the shock.
In reverse, for tiny perturbations, the controller will set
the oscillators to a dierent regime that can dampen the
perturbations.
We discuss then the interest of our mechanical design
and of our neural network for controlling soft robots as
well as the links to human motor synergies.
2. State of art and motivation
One architectural design that explains well biomechani-
cal compliance is tensegrity structures [21,22]. Tensegrity
structures can be seen as physical networks of stress and
loads so that they have an inner stress and plasticity in
their struc ture that make them resilient, adaptive and
robust to some external loads. In comparison to most
robotic designs, they do not follow Newtons law for rig id
bodies as they have no j oints and no momentum or
torque since the motors are not on the axis of articulation.
Instead, they follow Hookes law for elastic bodies. These
features make them a promising paradigm for integrat-
ing structure and control design [
2325]. For instance,
we can easily formalize a tensegrity system as a network
of tension (muscles and soft tissues) and compression
(bones), or as a network of springs and masses [
26,27].
Therefore, they can be vie wed as complex dynami-
cal systems with many degrees of freedom [
10,28,29],
which is a property often seen in biological systems
[
3032].
The redundancy and nonlinearity within such dynam-
ical system might be considered at rst as an obstacle
to control, however, the symmetries of the overall struc-
ture and t he many resonant modes generated can serve to
decrease the dimensionality of the control problem. For
instance, one way to have an adaptive control is to exploit
phase synchronization of these modes
similar to coupled
chaotic maps [7,33].
In human control, this work is achieved by the
CPGs
at the spinal cord level, which are primitives that con-
trol the muscle grouping for general motion behaviors
[
14,34]. When we are standing upward, for instance,
groups of muscles are dynamically selected to contribute
to our stability depending on the error perturbation level
and the force direction [
35,36]. In robotics, such bio-
inspired control is still dicult to model when we design
a compliant body with many degrees of freedom and non-
linearities. In previous works, we have shown how we
can control such high degrees-of-freedom system with
chaotic controllers that sync dynamically to the resonant
frequencies of several robotic devices [
29,3739] and to
human p ar tners [40]. We b elie ve that this type of control
conveys some important features of the human musculo-
skeletal system control as done in the spinal cord by the
CPGs [34,41,42].
3. Material and methods
We present a tensegrity structure based on auto-
replicative elements, 3D printed and similar to the ones
proposed in [
13,43], see Figure 1( a, b) . This partic ul ar

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ADVANCED ROBOTICS 3
Colour online, B/W in print
Figure 1. Multi-joint vertebral column model based on auto-
replicative tensile elements for soft robotics. (a–c) Each element
forms a tetrahedron by its four edges, which ensures the whole
compliance and tension distribution in the three directions when
connected to other elements in line. (d) An Inertial Measure-
ment Unit (IMU) is placed at the end of the structure for position
control and acceleration feedback. We provide the design of the
replicative element freely at the address [44].
motif reproduces the very stable st ructure of the tetrahe-
dron (i.e. the pyramids) which can stand easily upward,
see Figure
1(c,d). When two structures are assembled as
two inverted pyramids, the coupled unit structure can
move in two directi ons and can support small sheer tor-
sions as well in the third direction, which is ideal for
modeling the humans rotational joints.
In comparison to other types of tensegrity motives,
this one has the advantage to require fewer structures and
few junctions part. Each element is connected to others
with springs, which confers to the design some visco-
elastic properties comparable to pre-stressed str uctures.
The tensile elements possess a stable conguration that
returns e ven after applying some external force pressure
(self-stabilisation). The whole structure has
10 elements
connected with spherical joints (ping-pong balls), which
models well the excentric rotations of bones articula-
tion. The vertebral column measures around 1-meter
height; and each element is occupying a volume of 11
centimeters cube. The system can be vie wed as a three-
dimensional version of
mass–spring dampers mounted
in series. The total weight of the robot vertebrae is under
800 g, counting the weight of the motors (25 g each) and
of each element (30 g), which is very light concerning
its size.
Conception. We display in Figure
2 the prototyping of
the tensegrity model w ith motors inserted and springs
attached. A better understanding of which part of the
robot each motor actuates is provided fur ther in the
Muscle-Tendon section Figure
3. To show the proper-
ties of compliance and postural stability of the structure,
we co-contract the motors and set its neutral postural
conguration respectively in the horizontal plane and in
upward tension, so that the structure has a maximum
momentum and tension on its morphology horizontally
and has to exploit its physics fully to stand vertically; see
resp. Figure
2(a–c). The balanced forces distribution of
each motor-driven cables on the whole structure makes
it stabilized in every position, even for the less energet-
ical ones as the horizontal plane or the vertical plane,
which are also dicult for humans who develop dier-
ent strategies to support their own postural balance [
18,
31,36,45].
Sensory
acquisition. To perceive the motion, an iner-
tial measurement unit (IMU) is placed at the top of the
vertebral column as
shown in Figure 1(d). This module
possesses one accelerometer and a g yroscope, which per-
mits to measure an angular velocity in rad/s and linear
acceleration in rad/s
2
. Since the Gyro drifts slowly from
its position and the accelerometer has high-frequency
parasites, we can combine the two information to get
rid of the slow variations of the gyroscope (
high-pass
lter) and the fast variations of the accelerometer (low-
pass lter). The equation of the complementary lter for
the Y angle is: θ
IMU
= 0.98x + Gy/dt) + 0.02xY
a
cc.
Where Y
a
cc is the angle of the accelerometer in degree
and Gy the variation of the gyroscope. We mount the
IMU at the extremity of the structure to have the maxi-
mum amplitude variation as the fee db ack signal. We plot
in Figure
1(d) the XY Z coordinate system in which the
x-axis is opposite to the gravitational eld and points
upward so that the IMU is aligned along the longitudinal
axis of the robot, the z-axis is perpendicular to gravity
and lies in the horizontal plane of the robot body and
the y-axis is aligned in accordance to both the
x- and z-
axis in order to form a right-hand three-axis coordinate
system. The rotations in roll φ, yaw ψ , and pitch θ rep-
resent changes in orientation about the x, z and y-axes
respectively, see Figure
1(d).
Muscle-tendon model. The structure is actuated by six
electrical micro-motors with a gear head and a shaft that
reel up a 10 cm tendon-like wire and assembled in oppo-
site sides, two by two, all over the structure and every two
segments to have some exibility (under-actuation).
Using the same the nomenclature proposed by
Geyer
and Herr
[46], we propose to model the system dynamics
as actuated
mass–spring–dampers connected in paral-
lel and in series. For instance, each tensile element is

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4 A. MELNYK AND A. PITTI
Colour online, B/W in print
a) b) c)
d) e)
Figure 2. Robustness in co-contraction in horizontal and upward postural configuration. Static postures demand to set the contraction
of all the motors to specific lengths. In these situations, the motors act as rigid tendons and loads are distributed overall the structure.
Maximal efforts are delivered on the structure when set at the horizontal in (a), in the vertical plane with different directions in (b), and
upward at the vertical in (c).
Colour online, B/W in print
Figure 3. Muscle model in co-contraction within the structure. Motors are mounted with springs in parallel and in series on the structure,
Q22
which ensures the tensegrity system to be always pre-tensed. The motors pairs M1/M2 and M3/M4 are mounted in the opposite direction
for co-contraction.
formed with an act ive contractive element (CE) together
with
elastic series (ES) springs constituting one muscle-
tendon unit (MTU), see Figure
3(a). Each spring has
an optimum length l
opt
in which the global system
is in a static conguration. if the CE stretches an ES
spring beyond its optimum length (l
ES
> l
opt
), a parallel
elasticity (PE) spring engages in the opposite direction
so that its length becomes l
PE
< l
opt
. Conversely, as each
tensile unit possesses two actuators mounted in oppo-
sition, the opposite PE prevents the ES of abrupt slack.
We can now put in equation the systems behavior using
these elements depending on the action of CE. Knowing

Figures (3)
Citations
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Hajun Lee1, Yeonwoo Jang1, Jun Kyu Choe1, Suwoo Lee1  +4 moreInstitutions (1)
26 Aug 2020
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Auke Jan Ijspeert1Institutions (1)
TL;DR: Research carried out on locomotor central pattern generators (CPGs), i.e. neural circuits capable of producing coordinated patterns of high-dimensional rhythmic output signals while receiving only simple, low-dimensional, input signals, is reviewed.
Abstract: The problem of controlling locomotion is an area in which neuroscience and robotics can fruitfully interact. In this article, I will review research carried out on locomotor central pattern generators (CPGs), i.e. neural circuits capable of producing coordinated patterns of high-dimensional rhythmic output signals while receiving only simple, low-dimensional, input signals. The review will first cover neurobiological observations concerning locomotor CPGs and their numerical modelling, with a special focus on vertebrates. It will then cover how CPG models implemented as neural networks or systems of coupled oscillators can be used in robotics for controlling the locomotion of articulated robots. The review also presents how robots can be used as scientific tools to obtain a better understanding of the functioning of biological CPGs. Finally, various methods for designing CPGs to control specific modes of locomotion will be briefly reviewed. In this process, I will discuss different types of CPG models, the pros and cons of using CPGs with robots, and the pros and cons of using robots as scientific tools. Open research topics both in biology and in robotics will also be discussed.

1,543 citations


Journal ArticleDOI
Emanuel Todorov1Institutions (1)
TL;DR: This work has redefined optimality in terms of feedback control laws, and focused on the mechanisms that generate behavior online, allowing researchers to fit previously unrelated concepts and observations into what may become a unified theoretical framework for interpreting motor function.
Abstract: The sensorimotor system is a product of evolution, development, learning and adaptation-which work on different time scales to improve behavioral performance. Consequently, many theories of motor function are based on 'optimal performance': they quantify task goals as cost functions, and apply the sophisticated tools of optimal control theory to obtain detailed behavioral predictions. The resulting models, although not without limitations, have explained more empirical phenomena than any other class. Traditional emphasis has been on optimizing desired movement trajectories while ignoring sensory feedback. Recent work has redefined optimality in terms of feedback control laws, and focused on the mechanisms that generate behavior online. This approach has allowed researchers to fit previously unrelated concepts and observations into what may become a unified theoretical framework for interpreting motor function. At the heart of the framework is the relationship between high-level goals, and the real-time sensorimotor control strategies most suitable for accomplishing those goals.

1,513 citations


Book
01 Jan 2003
Abstract: 'SYNC' IS A STORY OF A DAZZLING KIND OF ORDER IN THE UNIVERSE, THE HARMONY THAT COMES FROM CYCLES IN SYNC. THE TENDENCY TO SYCHRONIZE IS ONE OF THE MOST FAR- REACHING DRIVES IN ALL OF NATURE. IT EXTENDS FROM PEOPLE TO PLANETS, FROM ANIMALS TO ATOMS. IN 'SYNC' PROFESSOR STEVEN STROGATZ CONSIDERS A RANGE OF APPLICATIONS - HUMAN SLEEP AND CIRCADIAN RHYTHMS, MENSTRUAL SYNCHRONY, INSECT OUTBREAKS, SUPERCONDUCTORS, LASERS, SECRET CODES, HEART ARRHYTHMIAS AND FADS - CONNECTING ALL TRHOUGH AN EXPLORATION OF THE SAME MATHEMATICAL THEME: SELF- ORGANISATION, OR THE SPONTANEOUS EMERGENCE OF ORDER OUT OF CHAOS. FOCUSED ENOUGH TO PRESENT A COHERENT WORLD UNTO THEMSELVES, STROGATZ'S CHOSEN TOPICS TOUCH ON SEVERAL OF THE HOTTEST DIRECTIONS IN CONTEMPORARY SCIENCE.

1,377 citations


Journal ArticleDOI
Eve Marder1, Ronald L. CalabreseInstitutions (1)
TL;DR: Cellular, circuit, and computational analyses of the mechanisms underlying the generation of rhythmic movements in both invertebrate and vertebrate nervous systems are discussed.
Abstract: Rhythmic movements are produced by central pattern-generating networks whose output is shaped by sensory and neuromodulatory inputs to allow the animal to adapt its movements to changing needs. This review discusses cellular, circuit, and computational analyses of the mechanisms underlying the generation of rhythmic movements in both invertebrate and vertebrate nervous systems. Attention is paid to exploring the mechanisms by which synaptic and cellular processes interact to play specific roles in shaping motor patterns and, consequently, movement.

1,213 citations


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