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Artificial Muscles for Humanoid Robots
Bertrand Tondu
LESIA, Institut National de Sciences Appliquées de Toulouse
Campus Universitaire de Rangueil, 31077 Toulouse
France
1. The question of actuator choice for humanoid robots
It is important to recall that humanoid robot technology derives from the technology of
industrial robots. It is obvious that the developments of bipedal robots such as the
integration of robot-upper limbs to complex anthropomorphic structures have benefited
from progress in mechanical structures, sensors and actuators used in industrial robot-arms.
A direct link is sometimes made between the technology of redundant robot-arms and
humanoid robots as underlined in some technical documents of the Japanese AIST where it
clearly appears that the HRP2 humanoid robot upper limb is directly derived from the
Mitsubshi PA10 7R industrial robot-arm.
Due to its high number of degrees of freedom in comparison to industrial robots, a
humanoid robot requires great compactness of all actuator and sensor components. This is
why we believe that the harmonic drive technology associated with direct current electric
motor technology has played a non-negligible part in humanoid robot development. The
DC actuator offers the great advantage of being a straightforward technology, associated
with simple and well-known physical models, its integration into mobile robots benefits
from new developments in embedded batteries. However, its low maximum-torque-on-
mass and maximum-torque-on- volume ratios are a serious drawback for its use in direct
drive apparatuses. On the other hand, the ability of electric motors to generate very high
velocities in comparison with moderate jointed velocities needed by industrial robot-arms
and more by jointed anthropomorphic limbs, gives the possibility of using high ratio speed
reducers to amplify motor-torque. Moreover, the choice of a high ratio speed reducer offers
the advantage of masking inertial perturbations such as external torque perturbations. The
technical achievement of such ratios induces specific mechanical difficulties due to the
bulkiness of successive gears; harmonic drive technology – represented for example by
Harmonic Drive AG – resolves this problem in a very elegant manner: the harmonic drive
and the actuator fit together without excessive increase in mass and volume in comparison
with the actuator alone. It can be considered that most of today’s humanoid robots are
actuated by DC motors with harmonic drives (this actuation mode is mentioned, for
example, by Honda from its first paper about the P2 robot onwards (Hirai et al., 1998) and
then in the official ASIMO web site, as well as in papers concerning other Japanese and
European humanoid robots). But if this technology simplifies actuator mechanical
integration and leads to the use of simple joint linear control, despite the highly non-linear
character of robot dynamics, it is well-known that the use of a speed reducer multiplies the
Source: Humanoid Robots: Human-like Machines, Book edited by: Matthias Hackel
ISBN 978-3-902613-07-3, pp. 642, Itech, Vienna, Austria, June 2007
Open Access Database www.i-techonline.com
Humanoid Robots, Human-like Machines
90
joint stiffness by the its ratio squared. A high joint stiffness contributes to joint accuracy and
repeatability, but also induces a high danger level for users, which can be acceptable in the
case of industrial robot-arms separated from factory staff by special safety devices, but
becomes very problematical in the case of humanoid robots intended for working in public
environments. The need to find an actuation mode which associates power, accuracy and a
‘softness’ adapted to human presence, that is the question of actuator choice in humanoid
robotics. To address this problem we will first try to define the notion of artificial muscle in
paragraph 2, then deal with the question of artificial muscle actuators for humanoid robots
in paragraph 3, before analysing their integration within anthropomorphic limbs (paragraph
4) to finish with their control (paragraph 5).
2. Notion of artificial muscle
2.1 Performance criteria in the research of new actuators
A general theory of actuators does not exist; each actuator is defined according to the
physical theory on which its legitimacy is founded. A comparison of actuators can as a
consequence be delicate. This is why actuator designers have introduced a certain number
of performance criteria aimed at making such comparisons easier. In general, actuation can
be defined as a process of converting energy to mechanical forms, and an actuator as a
device that accomplishes this conversion. Power output per actuator mass, and per
volume, as actuator efficiency – defined as ‘the ratio of mechanical work output to energy
input during a complete cycle in cyclic operation ‘ (Huber et al., 1997) - are three
fundamental properties for characterizing actuators. However, artificial muscle technology
considers more specific performance criteria so as to accurately specify new actuator
technology in comparison with ‘natural muscular motor’ properties. The following
terminology, justified by the linear actuator character of the artificial muscle, generally
completes the power criteria – the definitions given in inverted commas are from (Madden
et al., 2004) :
•Stress : ‘typical force per cross-sectional area under which the actuator materials are
tested’; maximum stress corresponds to the maximum stress that can be generated in
specified functioning conditions; as will be seen later, it is important for a given
technology to specify the ‘actuator materials’ relating to stress: typical stresses of strips
or fibres of a given technology is not obligatorily similar to that of the artificial muscle
composed of a set of these strips or fibres;
•Strain : ‘displacement normalized by the original material length in the direction of
actuation’; maximum strain and maximum stress are according to Huber & others
‘basic characteristics of an actuator [since] for a given size of actuator they limit the
force and displacement’ (Huber et al., 1997, p. 2186); the terms contraction ratio and
maximum contraction ratio will also be used;
•Strain rate : ‘average change in strain per unit time during an actuator stroke’; the term
‘response time’ – in the sense given by control theory, will also be used to characterize
the speed of artificial muscle dynamic contraction;
•Cycle life : ‘number of useful strokes that the material is known to be able to undergo’;
this notion specifies the heavy-duty character of artificial muscle in given working
conditions; in practice this is an important notion since artificial muscles are essentially
made of ‘soft’ materials which can be weakened by shape changes imposed by the
actuation mode;
Artificial Muscles for Humanoid Robots 91
•Elastic modulus: ‘material stiffness multiplied by sample length and divided by cross-
sectional area’; this is a typical material science notion; when the artificial muscle is
considered as an actuator to be controlled, stiffness – and its inverse - compliance
notions can appear more appropriate.
It is important to note that this criteria list is not exhaustive; depending on author, other
performance criteria can be found: as an example, Huber et al consider two criteria not
listed above: actuator density (the ratio of mass to initial volume of an actuator) and strain
resolution (the smallest step increment of strain) (Huber et al., 1997). The first directly
concerns humanoid robotics: like skeletal muscles, artificial muscles are assumed to be
located in moving robot links; the second criterion can be interesting in a control
perspective to specify artificial muscle sensitivity.
Furthermore, we believe that the theoretical framework proposed by Hannaford and
Winters (Hannaford & Winters, 1990) for the analysis of actuator properties based on
Paynter’s terminology of generalized dynamic systems (Paynter, 1961) can be particularly
useful in our study: these authors propose characterizing any actuator by its two effort-flow
and effort-displacement characteristics, where ‘effort’ represents the output force or torque,
and ‘flow’ the linear velocity or angular velocity. For example, the DC motor is ideally
characterized by a linear effort-flow curve and a constant effort-displacement curve, as
illustrated in Figures 1.a and 1.b. Figures 1.c and 1.d give the typical characteristics of the
skeletal muscle by the association of ‘effort-flow’ characteristics corresponding to the so-
called tension-velocity curve with the ‘effort-displacement’ characteristics corresponding to
the so-called tension-length curve. We will return to this in the modelling of skeletal
muscle, but it is important to note the fundamental originality of skeletal muscle
characteristics: while most of the actuators have constant or pseudo-constant ‘effort-
displacement’ characteristics, this is not so for skeletal muscle. As a dynamic system in
Paynter’s sense, the ‘effort-displacement’ relationship defines passive element C (for
compliance or capacitance). Classical actuators generally have infinite compliance; a
dependence of force/torque on position can even appear as a drawback: it is up to the
actuator control and not the actuator itself to impose this dependence. Conversely, living
actuators aimed at a ‘relationship life’ have to combine the generation of the power
necessary for body mobility with a non-infinite compliance making for easy contact with the
environment – we will use later the term ‘natural’ compliance to characterize this
compliance peculiar to the skeletal actuator. Research on artificial muscles can be
understood as a new attempt to mimic the living so as to integrate it into a machine – the
humanoid robot – an original power-softness combination, yet glaringly absent in machine
technology.
2.2 The historical Kühn and Katchalsky notion of artificial muscle as a gel swelling
and deswelling under the effect of a chemical agent
The origin of the artificial muscle notion must be found in the first works of chemists on
certain materials whose swelling can be controlled in a reversible manner. At the end of the
1940s, Kühn & Katchalsky did indeed prove that an aqueous polymeric gel essentially
composed of polyacrylic acid ‘… is found to swell enormously on addition of alkali and to
contract rapidly when acid is added to the surrounding solution. Linear dilatations and
contractions of the order of 300 per cent were observed. This cycle of swelling and de-
swelling is reversible and can be repeated at will ‘ (Kühn et al., 1950, p.515). At that time the
Humanoid Robots, Human-like Machines
92
authors had designed a device transforming chemical energy into mechanical working in
the form of a 0.1 mm thick filament able to lift up a 360 mg load in some minutes when
swollen. Thus the original Kühn & Katchalsky experiment historically created the present
artificial muscle notion as a reversible contractile device. Katchalsky emphasized the
natural tendency of artificial muscles to generate an ‘equilibrium swelling’ brought
according to him about two opposing tendencies : first, ‘…the solution tendency of the
polymeric molecules and the osmotic pressure of the cations of the alkali bound by the gel’,
secondly ‘…the caoutchouc-type contraction tendency of the stretched polymer molecules’
(Katchalsky, 1949, p.V/8). More generally, we will go further and apply this natural
tendency to an equilibrium state of any artificial muscle type as an open-loop stability in
position. It is important to note, however, that this ability to pass from an equilibrium state
to another state would be nothing if it were not associated to a reversibility whose life cycle
is finally its measure. Note also that the life cycle of natural muscle is greater than 109
(Hunter & Lafontaine, 1992); no present-day artificial muscle is able to approach this value,
which is linked to the ability of living tissues to self-repair. Kühn & Katchalsky’s historical
studies were reconsidered in the 1980s within the framework of a renewed interest for
artificial muscles due to technological developments in robotics, and a demand for
implantable artificial biological organs. However, from a practical point of view, the Kühn
& Katchalsky actuator displays a major disadvantage: its excessively slow response time (in
the order of minutes). More generally, it will be seen throughout this chapter that the major
difficulty in the design of artificial muscles for robots consists of obtaining both quick
response time and high-power-stress to mass-and-power to volume, adapted to the
integration of artificial muscles to human-dimensions and mass anthropomorphic limbs.
There now follows a brief overview of present-day artificial muscle technologies.
(a) (b)
(c) (d)
Figure 1. Characterization of artificial and natural actuators based on ‘effort-flow’ and on
‘effort-displacement’ relations (inspired from (Hannaford & Winters, 1990), (a) and (b) Case
of the DC motor, (c) and (d) Case of the skeletal muscle (from (Winter, 1969))
Displacement
Torque
Velo cit y
T
o
r
q
u
e
Artificial Muscles for Humanoid Robots 93
2.3 The artificial muscle as any material structure exhibiting a reversible shape
change by a chemical or a physical agent
a. Contractile polymer gels
Aqueous solutions of polymeric acids considered by Kühn & Katchalsky are a particular
case of solvent-swollen crosslinked polymer gels that respond to changes in temperature,
pH, solvent, illumination, or other physical or chemical stimuli. The choice of pH or a
solvent as a stimulus applied to typically polyacrylamide (PAM), polyvinyl alcohol-
polyacrylic acid (PVA-PAA) or polyacrylonitrile (PAN) fibers or strips (all commercially
available) is particularly interesting due to the facility of producing the pH variation by
adding of acid or alkali solutions (typically through the control of the hydrogen ion by
means of chemical reactions with HCl and NaOH) or the facility of using cheap and readily
available solvent like acetone. Parallel to a better understanding of gels physics it has been
possible to develop micro sized gel fibers contracting in seconds and even tenths of seconds
and to increase both the force produced by gel fibers as resistance fibers (some of them can
support loads of about 100 N/cm2 approximatively equal to that of human muscle. M.
Suzuki, for example, has developed in the nineties a 12 cm length artificial muscle model by
PVA-PAA-PA1Am gel film of 50μm thickness able to raise a ball of 2 g from a lower
equilibrium position to an upper equilibrium position within 10 s (Suzuki, 1991). Although
in these conditions, the maximum power density obtained with gel fibres can indeed be
estimated as being close to that of skeletal muscle, it still appears difficult to apply this
technology to the actuation of human-sized robot limbs. However, later we will analyse the
interesting attempt made at the MIT in the 1990s to promote ‘pH muscle’
The relative slowness of the complete contraction-elongation cycle of ion sensitive gel fibre
is mainly due to the relative slowness of the ion sensitive mechanism itself. For this reason,
other stimulus modes were considered, in particular heat transfer since heat diffusion is
better than ion diffusion. Thermo-responsive polymer hydrogels are already used in drug
release, and the study of tensile properties of thermo-responsive gels have been clearly
established (Kim et al., 2005). In the field of artificial muscles, this stimulus mode seems,
however, to have been more studied in the case of fairly recent polymer types – in particular
liquid crystal polymers – assumed to respond quicker than gel fibres. In any case, for gels as
for other materials, thermal response always appears quicker in the heating than in the
cooling phase (we will not deal in this chapter with the promising technology of liquid
crystal polymers able to respond to a luminous flash in less than a second, but as noted by
De Gennes (De Gennes et al., 1997) which predicted their contractile possibilities and talked
of them as ‘semi-quick artificial muscles’, the return to low temperatures is slow).
b. Shape memory alloys
Another form of reversible thermal response can be generated by means of thermally
activated shape memory alloys based on the ‘shape memory effect’ discovered at the
beginning of the 1950s. Among available materials nickel-titanium alloys (NiTi or nitinol)
are particularly interesting for actuation use because of their low cost and electrical
resistivity which heats the material by passing an electrical current. Due to this Joule
heating, NiTi contraction and expansion cycles can occur based on transformations from
martensitic to austenitic phases. Typically a shape is ‘memorized’ at a high temperature
(600°) placing the nitinol in austenite phase. On decreasing the temperature, the material
reverts to the martensite phase. When an external stress is applied, and as the material is
reheated at a lower temperature the material, because of the instability of the martensite
Humanoid Robots, Human-like Machines
94
phase at these temperatures, returns to its well-defined high-temperature shape. In the
shape memory effect, the material exhibits residual strains that can be used to generate a
linear displacement. The possibility of developing NiTi fibres exhibiting both very high
strain rates (300%/s) and very high stress (200 MPa) (Hunter & Lafontaine, 1992) naturally
interested the designers of new robot actuators. Safak and Adam (Safak & Adams, 2002), for
example, developed a lobster robot actuated by antagonistic nitinol artificial muscle pairs.
Figure 2 shows an interesting application of nitinol to miniature humanoid robotics: the five
fingers of the miniature robot hand can react at 0.2 s constant times to grasp light objects
(Maeno & Hino, 2006). Besides the current need for small sizes to obtain quick responses,
the main drawback of nitinol-type artificial muscles is its limited maximum strain: about
5%, which is very far from the natural skeletal muscle’s 40 %. Moreover, the life cycle
becomes more limited as the strain increases.
Figure 2. Miniature robot-hand actuated by Nitinol shape memory alloy artificial muscles
controlled by heat transfer (from (Maeno & Hino, 2006))
The shape memory effect can be controlled not only by heat transfer, but also by means of
an electric field which offers the advantage of being an easier control parameter.
Ferromagnetic shape memory actuators have been largely studied and commercial versions
exist able to develop maximum strains of 10%, typical strain rates of 10 000%/s and typical
stresses of 1 Mpa to 9 MPa (Madden et al., 2004). However, the requirement of high
intensity magnets is a major drawback for human-sized robot-limbs. Finally, as for
thermally activated shape memory alloys, the difficulty of accurately controlling muscle
contraction is not a good point for applications to robotics. The same difficulty occurs with
recent conducting shape memory composites.
c. Electroactive polymers : From ionic polymer gels to ionic polymer-metal composites
It was demonstrated in the 1960s that the swelling/shrinking of ionic polymeric gels
generated by pH variation can also be obtained electrically. When an electric field is applied
to a strip of PAM, PAMPS or PAA-PVA, for example suspended in a surfactant solution, the
gel shows significant and quick bending towards the anode. According to Segalman and
others (Segalman et al., 1992) this is caused by the migration of unbound counter ions in the
gel, and the impingement of solvent ions at its surface which produce the strip bending.
The reversible phenomenon has been applied to the design of chemomechanical mobile
systems such as Shahinpoor’s swimming robot (Shahinpoor, 1992) or to polymer gel fingers
(Hirose et al., 1992). However, the application to linear actuators appears disappointing, as
recently reported by Choe and Kin who studied polyacrylonitrile linear actuators (Choe &
Kim, 2006): the tested fibre is a 10 mm long ‘single strand’ consisting of multiple filaments
Artificial Muscles for Humanoid Robots 95
(about 2000) whose diameter in the contracted state is about 0.5 mm, and 1.2 mm in the
elongated state; experimentally the fibre can produce a 0.1 N maximum force in both pH
activation and electric activation cases, but while this static tension is generated in fewer
than 10 s with a 1M HCl acid solution, it takes approximately 10 min for the same result
with a 5V electric field..
If the electrostatic approach of ionic polymer-gel based linear actuators is unsatisfactory, it
can be asked if more interesting results could be obtained using conductive polymers.
Efforts to develop conductive polymer artificial muscles can be viewed as the search for
associating polymer mechanical properties with the ease of electric field control. In general,
conductive polymers are electronically conducting organic materials featuring conjugated
structures, able to undergo dimensional changes in response to changes in the oxidation
state. Polyaniline, trans-polyacetylene and polypyrrole are three examples of such
employed structures. When, for example, a conducting polypyrole film is electrochemically
oxidized, positive charges are generated along the chains and hydrated counter ions from
the solution are forced to penetrate into the polymer in order to compensate for these
positive charges. This induces an opening of the polymer structure and an increase in its
volume. A reduction in polymer induces the reverse effect: positive charges are eliminated
due the injected electrons: the polymer recovers its neutral state and the film volume
decreases. This swelling-shrinking property can be applied to the design of artificial
muscles such as the bilayer structure, consisting of a conducting and flexible polypyrolle
layer adhering to an elastic and non-conducting film, proposed by Otero and Sansinena
(Otero & Sansinena, 1995), or the monolayer structure by assembling two different
polypyrroles (Ochoteco et al., 2006). The resulting actuator is a bending type reacting in an
aqeous solution under low intensity current variation. According to Madden & others a
maximum 12% strain and a maximum 12%/s strain rate can be expected (Madden et al,
2004), consequently quicker than electrically-activated ionic polymer gels; however,
conductive polymers suffer from the same major drawback as ionic polymer actuators: they
need to be contained in a solvant bath.
The class of Ionic Polymer-Metal Composites (IPMC) can thus appear as a successful
attempt to maintain the ionic polymer contractile principle without the need for a solvant
bath. An IPMC is an ionic polymer in a composite form with a conductive metallic medium
such as platinium. The nafion developed by DuPont de Nemours & Co. is generally used as
a cation exchange thin membrane with metal electrode plated on both faces. Recently,
liquid nafion has been used to manufacture IPMC strips in various thicknesses (Kim &
Shahinpoor, 2002). Although they operate best in a humid environment, they can be
designed as self-contained encapsulated actuators to operate in various environments. As
theorized by Shahinpoor (Shahinpoor, 2002) an electric field induces a change in ion
concentration which attracts water molecules to one side of the polymer. Non-uniform
distribution of water produces a swelling on one side of the actuator, while the other side
contracts. The bending movement of the strips toward the anode is obtained at a low
voltage (typically 2V), and increases for higher voltages (typically up to 10 V) with a
reaction speed between μs and s. Because the IPMC does not produce linear actuation,
except in the case of fish-type mobile robots, its application to robotics is limited to gripping
mechanisms able to lift a few grams (Shahinpoor et al., 1998). The low stress generated by
IPMC - 10 to 30 MPa (Shahinpoor et al. 1998) - is another drawback of this type of artificial
muscle.
Humanoid Robots, Human-like Machines
96
d. Electroactive polymers : Dielectric elastomers
Dielectric elastomer actuator technology appeared in the middle of the 1990s. As will be
analysed in paragraph 3, this technology is considered as one of the most promising for
developing artificial muscles adapted to robot-limbs (Bar-Cohen, 2004). As in IPMC
technology, polymer shape change can be induced in dry environments, but at the expense
of higher stresses. A dielectric elastomer actuator can be considered as a compliant
capacitor inducing a stress when the capacitor is charged. According to Maxwell’s theory
applied to a constant volume elastomer, stress p and strains SX , SY , SZ of the dielectric
elastomer (assuming small, e.g. < 10%), respectively, in X, Y and Z directions, as illustrated
in Figures 3.a and 3.b, can be written as follows (Pelrine et al., 1998), (Pelrine et al., 2002) :
°
°
¯
°
°
®
=+++
−=
=
1)1)(1)(1(
)/(
)/(
22
0
2
0
ZYX
Z
SSS
YtVeeS
tVeep
(1)
where e0 is the permittivity of free space, e the polymer dielectric constant, V applied
voltage, t polymer thickness and Y elasticity modulus of the polymer-electrode composite
film. These three equations constitute a simplified model (limited by the assumption of
small strains) but which highlights the main parameters participating in the dimensioning of
the actuator: polymer dielectric constant e - e is equal to 1 for air – varies between 3 to 10
according to elastomer choice (Mathew et al., 2006) and electric field E = V/t whose value,
depending as it does on the elastomer, is an important factor in increasing actuation stress
by a factor of 10 to 100 compared to conventional electrostatic actuators. The simplicity and
relative efficiency of this model contrasts with the complexity of Flory’s model which
includes polymer gels swelling, in association with the difficulty of parametrizing the
conductive polymers. Performances of dielectric elastomers are particularly interesting in
comparison with other artificial muscle technologies as well as with natural muscle (Pelrine
et al., 2000) because they can associate high maximum strain, high maximum stress and low
response times: in the case of a silicone elastomer, a maximum strain of 32 % can be
generated with a maximum stress of 1.36 Mpa, and a time response of some msec.
Furthermore, their ability to be configured in many ways is particularly important for
robotics. The next paragraph analyses how linear actuators can be derived from this
technology. Two main disadvantages, however, have to be highlighted: firstly, dielectric
elastomers operate at relatively high voltages (100-4000 V), and secondly, due to their
capacity, electrical energy remains after actuation, which in practice requires energy
recovery circuits.
e. Elastomer inflatable structures
Physical elastomer properties are also at the origin of another large class of artificial muscles
that recent advances in chemo-mechanical actuators have pushed into the background.
They are not mentioned in numerous synthesis articles. We propose to call them ‘elastomer
inflatable structures’ because they are based on the unique property of elastomers to
support very large strains (up to 600%) without damage. Whereas the dielectric elastomer
operation principle is based on the generation of a compression stress, the operation
principle of elastomer inflatable structures is based on tensile stress. Thanks to a specific
guiding structure, which will be specified in paragraph 3, the stress generated inside the
Artificial Muscles for Humanoid Robots 97
elastomer inflatable structure is transformed into a linear force able to contract the artificial
muscle, as illustrated in Figures 3.c and 3.d.
(a) (c)
(b) (d)
Figure 3. Use of elastomer elasticity in artificial muscle designing, (a) and (b) operation
principles of dielectric elastomers (inspired from (Pelrine et al., 2000)): the elastomer film
placed between two compliant electrodes is compressed and expanded when an electric
field is applied, (c) and (d) operation principles of contractile inflatable structures: a guiding
structure is used to transform lateral stress generated by the pressure into a linear
contraction stress
2.4 The artificial muscle as a linear actuator mimicking natural skeletal muscle
behaviour: notion of skeletal artificial muscle
Until now the artificial muscle notion has been defined as a reversible contractile device,
independently in some ways from any model of the skeletal muscle. In the framework of
humanoid robots, based on a general anthropomorphism principle, the notion of artificial
muscle can be considered from a more physiological point of view, as a linear actuator
mimicking the natural skeletal muscle’s static and dynamic behaviour. According to this
approach, we suggest considering a fundamental abstract notion of artificial muscle inspired
from the macroscopic modelling of skeletal muscle: the derived ‘skeletal artificial muscle’
notion will be used as a reference biomimetic model independent of the technology
considered to achieve the abstract notion. According to the consideration developed by
Hannaford & Winter on the actuator notion, referred to in paragraph 1, the skeletal artificial
muscle notion can be specified by combining both tension-length and tension-velocity
Voltage on
V
compliant electrodes
(top and bottom sur faces)
elastomer film
Voltage off
pressure on
guiding structure (external braided
sheath, deformable structure included inside the tube,...)
elastomer tube
pressure off
Humanoid Robots, Human-like Machines
98
relationships, i.e. static and dynamic models of natural skeletal muscles. The resulting
artificial muscle model will be, as a consequence, a phenomenological model which puts
aside the microscopic phenomenon at the origin. It is well known that skeletal muscle
contraction is induced both by the recruitment of motor units and their firing rate (Ghez,
1991). In a phenomelogical muscle model, these factors are set together in the form of a
global variable which is traditionally called ‘neural activation’ and can be defined as a
normalized variable ubetween 0 and 1. In isometric conditions, i.e. at a constant length, the
typical skeletal muscle tension-length has already been illustrated in Figure 1.c. The static
behaviour of a skeletal muscle of initial length 0
l is characterized both by an active tension
corresponding to the contraction force produced when 0
ll ≤, and by a passive tension due
to the elasticity of muscle fibres beyond 0
l,. as is also well known. If we focus on active
tension, skeletal muscle behaves like a linear spring whose stiffness can be controlled by
neural activation. The following linear model, illustrated in Figure 4.a, results from these
considerations:
max
max
max 0and10,)1(
εε
ε
ε
≤≤≤≤−= uuFFstat (2)
where Fstat corresponds to the static tension,
ε
to the muscle contraction ratio – defined as
00 /)( lll −=
ε
where l is the current length of the muscle – max
Fthe maximum tension and
max
ε
the maximum contraction ratio. This linear model captures the main static property of
skeletal muscle : its ‘natural compliance’ C proportional to u which physically expresses the
existence of a restoring force r
F which brings back the muscle to its equilibrium position
when it is deviates of
δ
ε
; we get :
max
max
max
max
uF
C
uF
Fr
ε
δε
ε
+=
−=
(3)
In our opinion the ‘natural compliance’ factor – or its inverse, the stiffness – has a greater
importance than the ‘young modulus’ generally considered in artificial muscle technology,
as defined in paragraph 1: young modulus reflects material characteristics, while
compliance actuator characteristics.
Equation (2) is a purely static model; when applied to a dynamic contraction of the muscle,
this muscle tension model results in purely oscillating behaviour. In order to take into
account the natural damping of the natural muscle, it is consequently necessary to add a
supplementary term to the static tension model, we note ),,(
ε
ε
uFdamp and which can
depend on
ε
only if a pure viscous damping is assumed or on both u,
ε
and
ε
if the
damping is associated to more complex friction phenomena :
max
max
max 0and10,),,()1(
εεεε
ε
ε
≤≤≤≤−−= uuFuFF damp (4)
Artificial Muscles for Humanoid Robots 99
How to define this damping function? No simple direct model can be derived from skeletal
muscular physiology. However, Hill’s model provides a particularly powerful and elegant
indirect model . The Hill model is generally presented as the relationship between muscle
shortening velocity V and its corresponding tension, denoted for reasons to be explained
later, Hill
F, as follows :
bFFVaF HillHill )()( 0−=+ (5)
where F0 is the isometric contraction force at zero contraction ratio in given stimulation
conditions – according to our static : max0 uFF =–a is a constant having the dimensions of a
force and b a constant having the dimensions of a velocity. Ratio (a/F0) is typically between
0.2 and 0.3 which gives Hill’s equation curve a hyperbola shape , as illustrated in Figure 4.b.
Let us recall that the Hill equation was established in a specific isotonic quick-release test
invented by Hill in his famous 1938 paper (Hill, 1938): during the almost constant speed
phase of the quick-release in ‘after-load’ mode, Hill
Fcorresponds to the load driven by the
muscle and captures the dynamic force produced by the muscle, including its damping
component. As a consequence, the quick-release test applied to any artificial muscle allows
an appreciation of its dynamic damping in comparison with that of skeletal muscle. Beyond
the purely biomimetic argument, we have recently tried to show the interest for an artificial
muscle to be in accordance with the Hill model in order to benefit from the natural load
variation adaptivity which seems to be an integral part of this dynamic model (Tondu &
Diaz, 2006).
(a) (b)
Figure 4. Physical model of skeletal artificial muscle based on both Force-Displacement and
Force-Velocity curves of the natural muscle: a linear static force-displacement whose slope
is proportional to the control variable is considered (a) with an additive damping term in
such a way that the artificial muscle can be dynamically in accordance with (b) the
fundamental Hill curve
Among all the technologies reported at the beginning of the paragraph, only the ones able to
be adapted to this restrictive notion of skeletal artificial muscle would really be suitable for
humanoid robotics. For example, the technology of certain conductive polymers essentially
b
F
FVaF
HillHill
)()(
0
−=+
3.0/2.0
0
≤≤
Fa
Maximum shortening velocity (V)
Force produced in quick-release
condition (or load) (F )
Hill
bFFVaF
HillHill
)()(
0
F
0
F
b/a
0
()
3.0/2.0
0
Fa
Contraction ratio ( )
ε
Static force (F)
uF
max
u’
u
ε
ma
x
δε
F
r
uu’
<
Humanoid Robots, Human-like Machines
100
leads to bending artificial muscle difficulty applicable to linear actuators. Let us now
analyse some attempts at artificial skeletal muscle.
3. Which artificial muscle technology for anthropomorphic limbs?
The three technologies that we present have all led to artificial muscles of skeletal muscle
size; they illustrate the present diversity of the stimulus mode: chemical for pH muscle,
electrical for roll actuator and fluidic for pneumatic muscles. It could be said that because
nobody is currently able to mimic the complex sequence of biomechanical microscopic
phenomena of natural skeletal muscle, the energy choice question of artificial muscle
remains open.
3.1 pH-sensitive muscles and Solvent-sensitive muscles
The possibility of preparing relatively easily gel contractile fibres from commercially
available polyacrylonitrile (PAN) or polyvinylalcohol (PVA) filaments led several
researchers in the 1980s and 1990s to develop skeletal artificial muscles on roughly the same
principle: a set of gel fibres is placed inside a rigid cell in which the circulation of two
solutions alternatively generating the swelling and shrinking of the gel fibres is made easy.
The resulting volume change can be used to pull and push a ‘tendon’. Figure 5 illustrates an
interesting prototype developed at MIT in the frame work of the Artificial Muscle Project by
Brock and others (Brock et al., 1994): acid and base are alternatively delivered to PAN gel
fibre bundles through an array of perforated Teflon tubes
(a)
(b)
Figure 5. Cylindrical polymer gel ‘pH muscle’ using PAN gel fibers, (a) Gel bundles cell
irrigated by perforated Teflon tubes connected to a common fluid manifold allowing
alternatively acid (HCl) and base (NaOH) circulation, (b) Arrangement of gel fiber bundles,
acid and base conduits in cross section (from (Brock et al., 1994))
Artificial Muscles for Humanoid Robots 101
The ‘pH muscle’ is used in antagonism with a spring and a modular pulley system: using a
simple bang-bang control a rotation from 0 to 70° is generated in approximatively 45
seconds with a maximum tension of 0.35 N. The confrontation of this experimental device
resulting from Caldwell’s experiments leads to a better understanding of the difficulty of
adapting this technology to powerful skeletal artificial muscles. The ‘solvent-sensitive
muscle’ cell imagined by Caldwell (Caldwell & Taylor, 1990), (Caldwell et al., 2000) is made
of parallel PAA/PVA strips inside a container where an acetone and 4 molar NaCl solution
can alternatively circulate. Originally (Caldwell & Taylor, 1990) 100 μm thick strips were
used, but more recently it was shown (Caldwell et al., 2000) that it was possible to optimize
the thickness choice so as to highly increase contraction velocity without losing in stress: a
50 μm thickness gives a 43 %/s strain per s – instead of 11%/s for 100 μm strips and close to
slow movements of the natural muscle – for a 30N/cm2. With a 43% maximum contraction
strain, the performances approach slow movements of the natural muscle. Ten strips are
used in Caldwell’s linear actuator, but the author highlights a major limit of this technology:
the difficulty of use on a large scale. Because strain rate and stress evolve inversely with
fibre thickness , it is necessary to constitute the artificial muscle of a great number of parallel
fibres to generate useful forces for robot arms, thus inducing a discouraging complexity. To
our knowledge, this interesting technology has not been considered for robot limb actuation.
These attempts, however, highlight a central point for the development of artificial skeletal
muscle: an mm2 size scale technology is not necessarily efficient for a cm2 size scale. The
central notion of artificial muscle stress as defined in paragraph 2 can finally appear
deceptive: in association with maximum strain and maximum strain rate it leads to making
believe that a certain number of technologies are perfectly adapted to mimicking the human
skeletal muscle, whereas their adaptation to a human size and weight robot has not been
proved.
3.2 Electroelastomer rolls
SRI International (MenloPark, California) which claims the discovery of electroelastomers
for new actuation has designed original linear actuators aimed at mimicking the shape and
behaviour of natural skeletal muscles. These cylindrical actuators called elastomer rolls or
simply rolls are composed of a central spring around which several layers of dielectric
elastomers are rolled, as defined earlier. The actuator is closed by two caps, used as the
electric poles between which the functioning high tension is placed. At rest, the central
spring is maintained at compression by its surroundings and when tension is applied the
compliant dielectric elastomers extend inducing actuator extension. Figure 11.a illustrates
this actuator technology: the presented skeletal artificial muscle is 65 mm long with 45 mm
active length, its highest strain is about 26% of active length for a 5 Hz response time, its
diameter is 1.2 cm; composed of 20 layers of acrylic films generating a maximum force of 15
N. For this prototype there results a maximum stress of about 0.4 MPa significantly lower to
the postulated value for dielectric elastomer artificial muscle technology (Pelrine et al., 2000)
– 1.36 Mpa as mentioned earlier - and also signficantly lower to that of natural skeletal
muscle. Although the roll appears to be really more powerful than ‘pH muscle’ it suffers
from the same drawback: the need to add layers – or fibres – in order to amplify its force,
consequently bringing about an increase of its section like a greater design complexity : 35
layers are necessary, for example, to increase the muscle maximum force from 15 N to 21 N
(Pei et al., 2003) . For this reason, roll technology remains difficult to apply to a direct
Humanoid Robots, Human-like Machines
102
actuation of a robot-arm as the beautiful picture of the ‘wrestling match between EAP
actuated robotic arms and human’ tends to prove (Figure 11.b) The roll actuators are too big
to be placed on the skeleton arm and have been removed to an appendant box.
Furthermore, unlike pH muscle (Caldwell et al., 1990) it has not been proved that roll
actuators accord with Hill’s model : as mentioned by Pei, ‘…the stiffness of the roll is the
sum of the central spring and the rolled polymer films’ and it can be asked if the central
restoring spring does not have a negative effect on the Hill-like damping behaviour which
polymers seem to favour.
3.3 Pneumatic muscles
The roll actuator uses rubber stress as a force generator; in a complementary way, it can be
said that rubber inflation-based actuators generate their contractile tension by means of the
exceptional possibilities of rubber strain. McKibben artificial muscle is the most impressive
example of this artificial muscle technological approach. After firstly analysing it , we will
briefly discuss recent competitive approaches.
a. The McKibben artificial muscle
Without trying to accurately specify its origin which seems to lose itself in the golden age of
rubber-industry derived technologies, McKibben muscle is a typical braided artificial
muscle technology whose name comes from the American nuclear physicist Joseph
L.McKibben who developed its prototype for bracing handicapped hands. As we have tried
to justify (Tondu & Lopez, 2000), pneumatic McKibben artificial muscle is like a tyre whose
braided sheath is free to open itself in order to allow the inflation of a pressurized inner
tube. McKibben muscle is indeed composed of an inner tube surrounded by a double helix
braid, characterized by its initial braid angle (α0) as illustrated in Figure 6.a. If we assume
that the inner tube integrally transmits its circumferential stress to the braided sheath, a
simplified model of the resulting contractile linear tension can be deduced from the
application of a virtual works theorem to an ideal cylinder the radius and length of which
evolve according to the braid opening (Tondu & Lopez, 1995). Let us note l0 as the cylinder
initial length – i.e. initial active muscle length – and r0 the cylinder initial radius – i.e. initial
active muscle radius. The following static tension/strain model results :
0
2
0
2
max
22
0sin1/bandtan3/a with 0],)1([)(
ααεεεπ
==≤≤−−= baPrFstat (6)
where Fstat is the generated static tension for a control pressure P in function of the
contraction ratio
ε
. This purely geometrical model does not take into account bound effects
as force lose due to material effects whose major one is friction braid fibre on braid fibre –
more accurate physical models can be found in (Chou & Hannaford, 1996), (Tondu & Lopez,
2000), (Colbrunn et al., 2001), (Davis et al., 2003)). It however captures three main characters
which found the static analogy between McKibben muscle and natural skeletal muscle :
1. Static tension is proportional to P which can so play the part of the neural activation u
(let us recall that static roll tension is proportional to the electric tension squared due to
the equation (1) model);
2. Static tension is proportional to initial muscle section )( 2
0
r
π
which is an important
property for scaling robot-limb actuators as already discussed in the case of the two
previous technologies;
Artificial Muscles for Humanoid Robots 103
3. Static tension continuously decreases when contraction ratio
ε
increases making the
actuator a true contractile actuator as opposed to roll actuator.
(a)
(b) (c)
Figure 6. Pneumatic artificial muscle based on the use of a structure guiding the inflation of
a elastomer chamber, (a) external structure case: operation principle of the McKibben muscle
(see text), (b) internal structure case: longitudinal fibres included in a silicone tube (from
(Saga et al., 2005) , see also (Nakamura et al., 2003)) – this type of muscle is as ‘old’ as
McKibben muscle (Matsushita, 1968) -(c) Typical membrane case : pleated muscle (from
(Daerden & Lefeber, 2001)) (see text)
The static tension-contraction ratio curve parametrized in P offers a large linear range in a
similar way as natural muscle (see Figures 1.c and 7.a). If the maximum contraction ratio,
typically between 25% and 35% depending on the pressure, is relatively high in comparison
with other artificial muscle technologies, it is still below the typical 40% maximum ratio of
skeletal muscle (which even reaches 50% due to passive tension of skeletal muscle in vivo).
Furthermore, if the fibre-on fibre-friction acting during muscle functioning necessarily
induces a problematical dry and kinetic friction (which we discuss later) we also consider
that kinetic friction caused by specific textile braided sheaths - like in rayon – can be
responsible for a very good accordance of the dynamic McKibben muscle with Hill’s model
(Tondu & Diaz, 2006). Figure 7.b illustrates the tension-velocity curve obtained in quick-
release conditions, at a constant 2 bar pressure, for a McKibben muscle characterized by
initial length l0=335 mm, initial radius r0=10 mm, and of initial braid angle
α
0=23°.
Finally, McKibben artificial muscle appears to have a close analogy with natural skeletal
macroscopic static and dynamic behaviour. However, its purely mechanical principle
implies an increase in artificial muscle volume while skeletal muscle works at constant
volume: McKibben muscle volume typically doubles between its zero-contraction and full-
contraction states. The maximum contraction ratio is less than the skeletal muscle 40%
typical value, and which cannot be increased by its own passive tension, is a second
Double-helix braided shell
Inner tube
Humanoid Robots, Human-like Machines
104
limitation for a perfect use of McKibben muscle in the actuation of anthropomorphic robot-
limbs. Non-constant volume behaviour – which in fact is a characteristic of all fluidic
muscles – induces another problem: fluid consumption of the artificial muscle, which
implies a specific energy autonomy difficulty for its application to mobile humanoid robots.
It is, however, possible in the case of an anthropomorphic musculature based on an
antagonistic principle (see next paragraph) to imagine a recovering of consumed air from
one elongated muscle to one contracted muscle but this is technologically delicate to put
into work. This is the true paradox of McKibben artificial muscle which we will discuss at
paragraph end: a unique phenomenological behaviour in analogy with skeletal muscle
associated to a traditional and costly energy power source.
(a) (b)
Figure 7. Characteristics of a typical pneumatic McKibben muscle (of initial length l0=335
mm, initial radius r0=10 mm and initial braid angle
α
0=23°), (a) Tension-Displacement
curves at constant pressure 1, 2 and 3 bar, (b) Tension-Velocity curve at constant 2 bar
pressure
b. Alternatives to McKibben muscle
McKibben muscle is one of the most known and used pneumatic artificial muscles in
Robotics due to its ease of construction and its oblong shape which mimics the natural
spindle shape of skeletal muscle, but a large number of other pneumatic muscles have also
been developed. It is not easy to classify them; we propose to distinguish three main kinds
of pneumatic artificial muscles according to the type of guiding structure of the elastomer
inflatable chamber, as illustrated in Figure 6: firstly, the guiding structure is external to the
inner tube, as in the case of McKibben muscle; secondly, the guiding structure is included
inside the inner tube as considered when longitudinal fibres are embedded in the elastomer
(Figure 6.b) and, thirdly, the elastomer chamber is specifically designed to inflate and
contract (Figure 6.c). The first type is the easiest to elaborate while the third is the most
sophisticated. ‘Pleated muscles’ developed at Brussels Vrije’s University appear at the
moment to be one of the most interesting examples of the third type applied to humanoid
robotics. It was developed in opposition to McKibben muscle technology. If indeed we
ignore the energy problem of pneumatic muscles to focus on the control problem it can be
asked if the non-linear character of the actuator is not a too-difficult obstacle to surmount for
stable and accurate control. In particular, in the case of an external guiding structure, a
friction force generally appears inside the guiding ‘mechanical structure’ during muscle
contraction as between the fibres of a McKibben braided sheath. Due to dry friction, a
hysteresis phenomenon results, as illustrated in Figure 7.a for the muscle alone, and in
Figure 15.b for the actuator made of two antagonistic muscles. Hysteresis is an undesirable
M
u
s
c
l
e
ma
x
i
mum
shortening velocity (cm/s)
Load (kg)
Hill model : (F +15)V=(55- )11.5
Hill
F
Hill
00.05 0.1 0.15 0.2 0.25 0.3
0
20
40
60
80
100
Contraction ratio (%)
Static force (dN)
3 bar
2 bar
1 bar
Artificial Muscles for Humanoid Robots 105
non-linear effect; as will be analysed in the next paragraph; it is not, in our opinion, the
major drawback to a robust control of anthropomorphic limbs actuated by artificial muscles.
However, an artificial muscle without hysteresis is obviously a progress in the field; this is
the case for the ‘pleated muscle’ which in the absence of any external braid rubbing against
it, avoids the phenomenon. The ‘pleated muscle’ is a ‘cylindrical membrane of high stiffness
and high flexibility [folded] along its cylindrical axis like accordion bellows’ (Daerden &
Lefeber, 2001). When pressurized, inflation happens by unfolding and the artificial muscle
shortens and bulges. As illustrated in Figure 12.a, static force characteristics – except for
hysteresis – is globally similar to that of McKibben muscle, with a maximum contraction less
dependent on pressure. The counterpart of braided sheath elimination is, however, a more
complex geometrical shape of the artificial muscle (whereas the McKibben muscle globally
keeps a cylindrical shape), pleated muscle offers a contracted complex ‘flower’-like shape).
What results, firstly, is an increase in the maximum muscle section which, at the same
generated stress, can really be higher than that of McKibben muscle and which induces
mechanical integration difficulties (see next paragraph). Secondly, muscle shape geometrical
complexity implies a more complex mathematical model of muscle inflation. The three
fundamental properties exhibited by McKibben muscle also appear present in pleated
muscle technology, but in comparison to McKibben muscle no simplified corresponding
model can be deduced. The following static model is indeed proposed (Daerden & Lefeber,
2001) :
),/,( 00
2
0arlfPlFstat
ε
= (7)
where 0
lis the initial active length,
ε
the contraction ratio, 0
r the initial muscle radius, a is a
parameter depending on the Young modulus of the membrane elastomer and f is a
dimensionless force function for which no closed form seems easy to exhibit (Daerden &
Lefeber, 2001). Furthermore, the concordance of the force-velocity curve with Hill’s model
has not yet been established. Lastly, it is important to note that ‘pleated’ artificial muscle can
have a more limited lifespan than external guiding structure muscles due to the stress
imposed to the membrane. As mentioned by Verrelst, the first generation pleated pneumatic
artificial muscle has a limited lifespan due to the overlap used to make a cylindrical pleated
membrane. The proposed second generation has a 400 000 cycle life but induces a complex
mathematical model (Verrelst et al., 2006).
In conclusion, the current field of available artificial muscles for humanoid robots is
paradoxical: on the one hand, electroactive polymer-based roll actuators, although very
promising, do not yet have sufficient power-to-volume to be embedded in robot-limbs and
to actuate them; on the other hand, purely mechanical pneumatic artificial muscles appear
to be at present the most biomimetic of muscles, although their energy mode is
questionable. This paradoxical situation can, however, be settled in the following manner:
even if given up in the future in favour of EAP-based muscles or other bio-inspired artificial
muscles, fluidic artificial muscles, in our opinion, tackle the difficult question of mechanical
integration and control of anthropomorphic limbs actuated by biomimetic artificial muscles,
as considered in the two next paragraphs.
Humanoid Robots, Human-like Machines
106
4. Specific design of anthropomorphic limbs actuated with skeletal artificial
muscles
4.1 Antagonistic muscle revolute actuator
Skeletal artificial muscle applied to the actuation of anthropomorphic limbs is not aimed at
acting alone. However, to mimic the complex organisation of human musculature, as
explored by Washington’s Biorobotics Laboratory in the upper limb case (Figure 8), appears
at present to be an insurmountable task for the humanoid robot specialist. On the contrary,
a basic muscular organization seems to be necessary for adapting linear skeletal artificial
muscle to the revolute joint structure of anthropomorphic limbs: the revolute actuator made
of two antagonistic artificial muscles illustrated in Figure 9. The two antagonistic muscles
are assumed to be attached by means of a non-extensible pulley-chain system, where R
denotes the pulley radius. We assume two identical artificial muscles of initial l0 active
length. In the general case, we will note, respectively, agonistic muscle control by u1 and
antagonistic muscle control by u2 , and the resulting actuator angle by
θ
.
Figure 8. Anthroform Biorobotic Arm project of Washington’s BioRobotics Laboratory
(Hannaford et al., 1995) composed of pneumatic McKibben artificial muscles mimicking the
shoulder musculature attached to human bones (to our knowledge, no control of the arm
has been developed)
Artificial Muscles for Humanoid Robots 107
(a) (b)
Figure 9. Operation principle of the antagonistic muscle actuator, (a) Initial state, (b) Current
state (see text)
If we limit our model to the use of the artificial muscles in purely active tension – i.e.
without any form of passive tension – it is necessary to assume that in its rest angular
position
θ
=0, both muscles are equally contracted of 0
ε
with a same control 0
uallowing the
0
ε
initial contraction. In the current position
θ
the agonist and antagonist contraction ratios
are respectively given by - let us number ‘1’ the agonistic muscle and ‘2’ the antagonistic
muscle :
)/(and)/( 002001 lRlR
θ
ε
ε
θ
ε
ε
−=+= (8)
The actuator torque T can be written as follows :
)( 21 FFRT −= (9)
where 1
F is the agonistic force and 2
Fis the antagonistic force. The application of the
fundamental model of equation (4) leads to the following expression :
)],,(),,(R[and/,)/1(with
(10)),,,()()(
222111max0max
2
2max0max1
21212211
εεεεεεε
θθθ
uFuFTlFRKRFK
uuTuuKuuKT
dampdampdamp
damp
−==−=
−+−−=
Let us consider the static component of the actuation torque :
θ
)()( 212211 uuKuuKTstat +−−= (11)
This general expression of the static torque – which is similar to the simplified Hogan’s
model of the biceps/triceps system (Hogan, 1984) – leads to highlight three fundamental
properties of the artificial muscle antagonistic actuator in analogy with the fundamental
biceps-triceps natural muscular system :
1.The actuator is stable in open-loop both in position and stiffness.
It is possible to define the following equilibrium position
θ
equ corresponding to a null static
torque :
)].(/[)]([ 212211 uuKuuK
equ +−=
θ
(12)
ε=0
ε
axis
θ
T
Humanoid Robots, Human-like Machines
108
In this equilibrium position, the stiffness actuator S defined as follows :
)( 212 uuKS += (13)
can be changed by multiplying the u1 and u2 inputs by a same factor, although the
conditions 1
1≤u and 1
2≤uare verified.
2. The actuator is both a torque and a stiffness generator.
The previous property is the consequence of the fact that the actuator can be considered as a
double input-output system whose (u1,u2) are the inputs and (Tstat,S) are the outputs
defined as follows :
»
¼
º
«
¬
ª
»
¼
º
«
¬
ª
−−
++
=
»
¼
º
«
¬
ª
⇔
»
¼
º
«
¬
ª
»
¼
º
«
¬
ª−−−
=
»
¼
º
«
¬
ª
S
T
KKK
KKK
KK
u
u
u
u
KK
KKKK
S
Tstatstat
2
1
212
212
21
2
1
2
1
22
2121
θ
θθθ
(14)
We will use this double nature of the antagonistic artificial muscle actuator in next control
paragraph.
3. The maximum actuator torque decreases continuously from an actuator angle limit to
the other one.
Let us assume that each actuator muscle can fully contract of its
ε
max maximum contraction
ratio. If the two muscles are identical, the two actuator angle limits can be defined as
follows:
]/)(,/)([],[ 00max00maxmaxmin RlRl
ε
ε
ε
ε
θ
θ
−+−−= (15)
For every actuator angle
θ
belonging to this range, we get the following expression of the
maximum torque, corresponding to a maximum control of the agonistic muscle (u1=1) and a
null control of the antagonistic muscle (u2=0) :
θθ
21max )( KKT −= (16)
The maximum torque decreases in consequence from
θ
min to
θ
max with the 2
K− slope. In
comparison with classical actuators, the presence of the restoring torque term ‘
θ
)( 212 uuK +− ’
gives to the biomimetic actuator a natural compliance which can be actively controlled
independently from the actuator position. However, a drawback results that is analysed in
next paragraph: angular position actuator torque dependence induces a specific sensitivity
of the actuator on gravity.
4.2 Gravity test with artificial muscle actuator
The first request for any actuation mode of a robot-limb is its ability to move each link all
along the desired joint range. As for humans, the most important resistance of humanoid
robot links is gravity. We consider that testing the ability of an artificial muscle actuator
embedded on the kinematic chain to directly drive joints of a human size (in volume and
weight) robot-limb could be a more rigorous test than the ‘arm wrestling contest’ organized
by NASA (see the rules for the wrestling match between EAP actuated robotic arms and
human on the website http://armwrestling.com/rulesandregulations.html) to test EAP-roll
actuator performances, illustrated in Figure 11.b. In particular this ‘gravity test’ is made
Artificial Muscles for Humanoid Robots 109
difficult by the specific nature of the artificial muscle actuator highlighted in the previous
paragraph. Let us consider the case of a single actuator driving a link as illustrated in Figure
10.a: the two antagonistic muscles represent, for example, the biceps-triceps system
actuating the arm placed in a vertical position, the considered joint the elbow flexion-
extension and the link the set forearm + hand. Let us further consider a total joint range of
180° imposing the actuator zero-position when the moving link is at the horizontal position.
If the positive direction corresponds to the flexion movement, gravity torque is always
resistive and can be written as follows : cos
θ
mglTgravity −= , as illustrated in Figure 10.a. The
maximum available actuator torque is given by equation (16) and subsequently the total
torque can be deduced as simulated in Figure 10.b. It appears that in the [-90°,+90°] joint
range, the total torque becomes minimum, and it is clear that if this minimum is negative, a
special point results where the total torque becomes null and as a consequence, the actuator
is no longer able to lift the link. In a more general manner, the gravity test appears as a
quasi-static test which consists of checking that the total static joint torque keeps strictly
positive on the considered actuator joint range. It is interesting to note that a load in hand
can easily put the test in difficulty. The two shoulder movements in flexion-extension and
abduction-adduction are particularly concerned by this test: the situation is analogous to
the one illustrated in Figure 10 but now the link to lift represents the whole upper limb with
a possible load in hand. Consequently, the actuation of a robot shoulder by artificial
muscles can necessitate very strong muscles, notably if the flexion-extension and abduction-
adduction movements are, respectively, performed by only one pair of antagonistic muscles.
For example, the robot shoulder of our 7R anthropomorphic of the same size as a human
upper limb - but of double weight – illustrated in Figure 13.b is actuated by McKibben
pneumatic muscles able to develop more than 500 dN under a 5 bar pressure. Generally,
this difficulty in actuating a human-like shoulder by artificial muscles reveals the need for
future humanoid robots to mimic not only the antagonistic muscle principle, but also
natural muscular system redundancy, as attempted in Figure 8.
(a) (b)
Figure 10. Effect of gravity on the antagonist artificial muscle actuator (a) Double joint angle
dependence of the actuator when submitted to gravity, (b) Simulation of total torque
highlighting a possible joint position beyond which the actuator is no longer able to lift the
arm
maximum
gravity effect
minimum actuator torque-
null gravity effect
+90°
-90°
maximum actuator torque-
null gravity effect
mg
l
-90° +90°
T =-mglcos
gravi
θ
T=K-K
max 1 2 r
θ
T=T-T
total max gravi
Actuator angle
Torques
Humanoid Robots, Human-like Machines
110
4.3 Integrating artificial muscles to anthropomorphic kinematic structures
The integration of artificial muscle into a humanoid robot whose limbs, size and weight are
those of a medium sized human being induces specific constraints in actuator joint range,
actuator power-to-volume, actuator power-to-mass, and robot energy range. If we leave the
latter constraint which depends on the development of embedded batteries, the first three
are direct consequences of artificial muscle technology applied on a human-scale robot.
Power-to-mass is generally not a difficulty due to the low mass density of polymer-type
materials, but generating both actuator ‘joint range’ and ‘power-to-volume’ similar to
skeletal muscle ones is a major challenge because of the difficulty in designing compact
artificial muscle working at a constant volume as a skeletal muscle does. As already
mentioned, EAP-roll actuators cannot yet fully satisfy these constraints. Pneumatic muscles
are at present the most able ones within sight of these two criteria. This is the reason why all
current anthropomorphic limbs actuated by artificial muscles use pneumatic ones, but it is
important to emphasize that, even in the case of this technology choice, the integration of
artificial muscle actuator to anthropomorphic robot-limbs is made difficult by their limited
biomimetic behaviour :
•the global cylindrical shape of the McKibben pneumatic muscle helps its integration in
spite of its volume increase, but its relatively limited maximum contraction is a real
drawback for the actuation of large joint movements: in particular, flexion/extension
and abduction/adduction human shoulder movements are particularly difficult to
mimic with artificial muscles, without using excessively long artificial muscles; our 7R
robot prototype, illustrated in Figure 13.b, has shoulder joint ranges equal to [0,+180°]
in abduction-adduction and to [0,+100°] in flexion-extension thanks to transmission
gears amplifying the actuator angular motion at a 1.5 ratio in order to limit shoulder
width to about 35 cm (Tondu et al., 2005). In the case of the Shadow Robot illustrated in
Figure 13.a, it can be noted that the shoulder muscles are placed vertically in the robot
waist, which is not adapted to humanoid architecture;
•the pleated muscles offer the advantage of high maximum contraction ratios weakly
dependent on the control pressure, but its bulkiness when the muscle is contracted
prevents the putting into parallel of two antagonistic muscles: as illustrated in Figure
12.b, the two pleated muscles have to be shifted in order to allow the antagonistic
muscle actuator to get working which reduces the actuator range. Lucy robot (Verrelst
et al. 2005), illustrated in Figure 12.c, is a successful application of pleated muscle
actuation, but it can be asked if it is as well adapted to actuation by upper limbs
necessitating larger joint ranges.
Analysis of these two points emphasizes the difficulty of actuating anthropomorphic robot-
limbs by artificial muscles: the global ‘optimal’ character of the human muscular-skeletal
system makes all attempts at mimicking the system difficult if one analogical term is
missing.
Artificial Muscles for Humanoid Robots 111
(a) (b)
Figure 11. Roll actuator composed of rolled dielectric elastomers (a) – from (Pei et al., 2003) –
and application of this technology to the actuation of an anthropomorphic arm in the
framework of the NASA’s ‘armwrestling contest’ – from NASA web site (see the three big
roll actuators inside the purple box in (b))
(a)
(b)
(c)
Figure 12. Pleated artificial muscle applied to biped robots, (a) Static characteristics of the
pleated artificial muscle, (b) Corresponding antagonist actuator showing the difficulty to
place simultaneously the two inflated muscles into antagonism, (c) Lucy biped robot
moving in a vertical plane (from Lucy web site)
Humanoid Robots, Human-like Machines
112
(a) (b)
Figure 13. Two examples of anthropomorphic robot-arm design actuated by pneumatic
McKibben muscles: (a) shadow robot-arm equipped with shadow hand showing artificial
shoulder musculature placed in the robot’s ‘waist’ (from Shadow Robot Group web site), (b)
7R anthropomorphic robot-arm prototype built in the laboratory with 30 cm horizontal
shoulder muscles developing a maximum force exceeding 500 dN
5. Control of anthropomorphic limbs actuated by skeletal artificial muscles
5.1 Non-linearities of robot joints actuated by artificial muscle actuators
The use of flexible materials such as the recourse to original stimulus modes (pH, solvent,
heat, etc.) are complexity factors of the physical models of any artificial muscle actuator.
What results is a non-linear character generally more manifest than for other robotic
actuators. In particular, it is well known that the more nonlinear the plant the more
imprecise its physical or identified model on which its control can be based. Using Slotine &
Li’ terminology (Slotine & Li, 1991) the artificial muscle actuator is more concerned than
others by ‘structured (or parametric) uncertainties’ as by ‘unstructured uncertainties (or
unmodelled dynamics)’. Furthermore, in the case of robot-limbs actuated by artificial
muscles, the specific actuator non-linearities enter into combination with dynamic robot
nonlinearities due to the direct drive character of robot joints. We emphasized in the
previous paragraph the part played by gravitational forces but, as for any direct drive robot,
jointed limbs actuated by artificial muscles have also to support dynamic perturbations due
to inertial variations, or to velocity effects. Even if it is considered that a humanoid robot
does not have to support the accelerations and velocities generated by the joints of high
performance industrial robot-arms it is clear that the mimicking of certain sporting or daily-
life gestures can induce torque perturbations due to the inertial, centrifugal or Coriolis terms
of classical robot-limb dynamics. It seems important to us, however, to emphasize the
following point: repeatability of the accuracy of the end-effector of a humanoid robot limb
(hand, finger, foot, head, etc) can be defined in analogy with human gestures: they are,
consequently, closer to the mm scale than to the 1/10 mm as required for a great number of
tasks performed by industrial robot-arms. It can be roughly considered that an acceptable
accuracy value for antagonistic artificial muscle actuators of a humanoid robot performing
tasks at ‘human accuracy’ – the accuracy of drawing a line with a pencil - is about one or a
bit less than one degree. From this point of view, the artificial muscle actuator can finally
Artificial Muscles for Humanoid Robots 113
appear more adapted to humanoid robots mimicking human gestures than ultra-accurate,
but non naturally compliant electric motors. This is true provided there is the possibility of
being able to design a control mode of the artificial muscle as effective as the one resulting
from the complex and badly known human movement learning principles. In the next
paragraph we analyse some current or envisaged control modes of artificial muscle robot
actuators: all results mentioned were obtained on pneumatic artificial muscles which as
already emphasized, seem the only ones to have been actually tested on human-scale robot-
limbs.
5.2. Single-variable position control
The antagonistic artificial muscle has been previously defined as a multiple input-multiple
output (MIMO) system. Since the first target of the actuator control is a control position, it
can be asked if it is possible to simplify the actuator functioning in order to consider it as a
single input-single output (SISO) system whose output is reduced to the angular position. A
simple way of doing this, initiated in our opinion by Bridgestone (Bridgestone, 1987),
consists of a symmetrical control of agonist and antagonist muscles in the form of a ‘Δu’
input control added to the initial ‘u0’ to control the agonist when antagonist control of ‘Δu’
decreases , as follows :
uuuuuu Δ−=Δ+= and 0201 (17)
The new torque expression results :
),,(22 021
θθ
uTuKuKT damp Δ−−Δ= (18)
The relationship between input Δu and equilibrium position θequ is now
uuKK
equ Δ= )/( 021
θ
and actuator stiffness is now constant : 02
2uKS=. The artificial muscle
actuator can now be considered as a revolute actuator to which a linear or non-linear control
approach can be applied. Furthermore, its open-loop position stability gives an original
opportunity for facilitating joint control: it is indeed possible to identify the angular joint
and to use the identification result as a feedforward term. We have demonstrated the
advantage of this approach in controlling a 2R-SCARA-type robot actuated by four similar
pneumatic McKibben muscles (Tondu & Lopez, 2000). In the framework of humanoid
robotics, this kinematic architecture corresponds to a arm-forearm set performing horizontal
shoulder and/or elbow flexion-extension movements – without the consequent gravity
effect. In this case, a second-order linear model of the form :
)()/()( 21
2pUapapbp Δ++=
θ
(19)
appears to be very satisfactory to identify the step response. Physically, according to the
torque model of equation (18), and assuming that the joint drives a constant inertia (forearm
inertia or in the case of the shoulder joint, maximum forearm + arm inertia), the term ‘a2 ‘
can be interpreted as a specific actuator stiffness and ‘a1’ as a linear viscous term
approaching complex actuator damping. A typical linear controller illustrated in Figure 14.a
results where the identified model is used as a feedforward term in association with a PID
linear feedback, for example.
Humanoid Robots, Human-like Machines
114
(a) (b)
Figure 14. General scheme of position control of a robot-limb actuated by artificial muscle
actuators, (a) control based on identified linear joint models, (b) control based on a robot
dynamic model associated to a physical actuator model
However, as mentioned in paragraph 5.1, the artificial muscle actuator control has to face
both actuator and robot non-linearities. A Simple linear control – even helped by the
feedforward term – can appear not to be robust enough. Non-linear approaches are thus
necessary to address the control problem of anthropomorphic limbs actuated by artificial
muscles. Sliding mode control is one of these: it is particularly interesting because it
integrates identified actuator models and/or robot dynamics. As emphasized by Slotine
sliding control is one of the main approaches in robust control to deal with model
uncertainties (Slotine & Li, 1991). Let us note
θ
θ
−= d
e and
θθ
−= d
e; if we limit our
analysis to second order models, the sliding surface is the line defined by the equation :
CeeS += (20)
where C is the sliding line slope. Let us assume for example that the robot joint behaves like
a second order linear model in the form of equation (19). The sliding condition 0=S
leads to
the following expression of the perfect control u
ˆ:
])([
1
ˆ1221 eaCCaaa
b
uddd
−+−++=
θθθ
(21)
Completed by a discontinuous component v chosen for example according to Harashima
(Harashima et al., 1985) with
α
,
β
and
γ
parameters as :
)sgn(][ Seev
γβα
++= (22)
the final actuator control is :
vuu ˆ+=Δ (23)
d
d
d
q
q
q
q
q
Identified
linear joint
models
Artificial
muscle
actuators
and
Robot
d
d
d
q
q
q
Linear feedback with
or without sliding mode
u
u
forward
+
+
_
q
_
+
+
sliding mode
d
d
d
q
q
q
q
q
Robot
dynamic
model
Actuator
model
Artificial
muscle
actuators
and
Robot
d
d
d
q
q
q
Linear feedback with
or without sliding mode
u
u
forward
T
forward
+
+
_
_
+
+
sliding mode
q
Artificial Muscles for Humanoid Robots 115
(a) (b)
(c) (d)
Figure 15. Experimental control of a 2R robot actuated by pneumatic McKibben muscles
mimicking horizontal shoulder/elbow movements, (a) Photography of the robot, (b) Static
characterics of the actuator, (c) and (d) Experimental tracking of a straight-line path
according to a trapezoidal velocity profile with a sliding mode control (see text)
In comparison with the previous linear control, the feedforward model is now completed
both by a continuous linear feedback component, and also by a discontinuous component
aimed at giving robustness to the control, while sliding condition 0<SS is checked (see
(Asada & Slotine, 1986) and (Slotine & Li, 1991) for theoretical analysis and application to
robotics). Physically the controller’s ‘robustness’ is preserved while the identified
parameters of the model are kept to a limited range – typically 20%. This simple approach
can be very adapted to robot limbs actuated by artificial muscles as emphasized in
experiments performed in our laboratory on the arm-forearm prototype mimicking
shoulder-elbow horizontal flexion-extension movements: the tracking of a straight-line at
0.1 m/s shows a mean path deviation of 2.5 mm with a maximum error of 8 mm (Figure
15.c) - occurring during acceleration/deceleration phases - and dynamic joint accuracy of
+/- 0.5° for joint 2 and +/- 1.5° for joint 1 (see details in (Tondu & Lopez, 2000)). Note
finally that sliding mode control has also to be applied to control ‘pH muscle’ (Brock. et al.,
1994) or shape memory alloy actuator (Grant & Hayward, 1997).
However, this approach has two limits: firstly, a moderate load at upper limb can induce
large variations of inertial parameters; secondly, as previously emphasized, gravity has a
large effect on the control: Figure 16 illustrates the identified linear model of the elbow joint
-2 -1.5 -1 -0.5 00.5 11.5 2
-3
-2
-1
0
1
2
3
D
P PRESSURE (BAR)
JOINT 1 POSITION (
R
D)
Humanoid Robots, Human-like Machines
116
of our 7R anthropomorphic arm moving on a vertical plane in response to pressure steps. A
second order can be postulated as a first approximation, but a better result is obtained if this
second order model is completed by a pure delay of 6 to 8 ms – thus leading to a third linear
model approximation. Furthermore, the dynamic parameters now vary around their mean
values of +/- 40% while their variation was limited to about +/- 15% in the case of non-
gravity perturbed horizontal movements. Linear identified third order models have also be
considered in the case of the antagonistic Rubbertuators – McKibben type muscles –
actuated the Vanderbilt university’s ISAC robot (Thongchai et al., 2001). These authors have
proposed to use the joint identified model in the framework of a fuzzy controller using both
linear quadratic regulator (LQR) and sliding mode techniques. Because a fuzzy controller
has already appeared to us difficult to tune on the 2R robot of Figure 15.a (Tondu & Lopez,
2000), due to the actuator/robot system dynamics complexity, we are not sure that a fuzzy
approach will be relevant to highly anthropomorphic robot limbs actuated with artificial
muscles.
(a) (b)
Figure 16. Identification of the elbow joint of our 7R anthropomorphic robot-arm actuated
by McKibben artificial muscle actuators, (a) Close-up on the elbow joint, (b) Open loop
identification – model is in dotted line - in response to pressure differential steps
Consequently, it seems necessary so as to effectively control humanoid robots actuated by
artificial muscles, to take into account both an actuator model and a robot dynamic model.
In this framework, neural network control can constitute alternative bio-mimetic approaches
(Hesselroth et al., 1994), (Van der Smagt et al., 1996), (Tian et al., 2004), (Thanh & Ahn, 2006)
but their practical use in the programming of a large range of robot tasks is yet to be
established. Adaptive methods can also be considered – see, for example, (Caldwell et al.
1995) - but to be effective they need a reference dynamic model and faced with the dynamic
problem complexity, it seems necessary to add the knowledge of a complete dynamic robot
model to the control scheme. Following the classic ‘inverse torque method’ a complete
robot dynamic model is substituted to the linear identified joint model, but it is then
necessary to associate it with a physical actuator model as emphasized in the control block
scheme of Figure 14.b. This is a major drawback of the method when we are aware of the
complexity of any artificial muscle physical model. Sliding mode control can always be
applied to this dynamic model-based approach as developed by Cai and Dai (Cai & Dai,
2003) on the simulation of a vertical two-link manipulator using a 4 parameter McKibben
muscle model (Cai & Yamaura, 1998). A dynamic limb model in association with an
00.5 11.5
0
20
40
60
80
100
120
Time (s)
E
lbow position (deg)
0.5 bar
1 bar
1.5 bar
2 bar
2.5 bar
3 bar
Artificial Muscles for Humanoid Robots 117
antagonistic pleated muscle actuator model is also used to simulate the Lucy robot dynamic
control (Verrelst et al., 2005).
Control results based on this complete dynamic approach are still awaited to appreciate the
possibilities of controlling humanoid robots actuated by artificial muscles. In this
framework, it is clear that the simpler the actuator model, the easier is its control.
5.3. Multiple-variable position-compliance control
The linear or non-linear feedback component of the previous considered approaches
introduces a ‘servo-stiffness’ which modifies the natural stiffness of the actuator. But if the
feedback term stiffness is not too high – in particular by limiting proportional and integral
components – the resulting global stiffness can be yet adapted to the achievement of tasks
involving a contact of the robot with its environment as illustrated in Figure 17 : our 7R
robot-arm prototype performs a straight-line against a solid wall fitted with a soft painting
roller. A constant contact all along the trajectory is achieved by programming the end-
effector tool slightly beyond the contact surface. This experiment proves that the SISO
control of the artificial muscle actuator can also be adapted to contact.
Figure17. Example of a task involving a permanent contact with the environment performed
by our 7R anthropomorphic robot-arm actuated by pneumatic McKibben muscle actuators
However, the stiffness can be badly adapted to the task of producing, for example, Cartesian
restoring force-torques varying in an inadequate manner with the imposed surface. By
means of force-torque sensors the well-known hybrid position-force control approach can be
naturally applied to robot-limbs actuated by artificial muscles. A more specific approach
can, however, be highlighted: to use the MIMO nature of the artificial muscle actuator to
control both position and stiffness in decoupling inputs ‘u1‘ and ‘u2‘. The general MIMO
scheme of Figure 18.a can be viewed as a generalization of Figure 14.b’s SISO scheme, in
which a actuator model in the form of the equation (14) model is introduced. The desired
stiffness can now be imposed in accordance with Cartesian task requirements. Interesting
preliminary results have been reported by Tonietti and Bicchi (Tonietti & Bicchi, 2002) based
on a 2 d.o.f. robot-arm actuated by pneumatic McKibben muscles – Chou & Hannaford’
McKibben muscle model was used - in which a time-varying stiffness was programmed. It is
also possible to control the stiffness by estimating the real one assumed to be proportional to
the sum of ‘u1 + u2’ by means of muscle activation sensors –pressure sensors, for example, in
the use of pneumatic muscles as made in the ambitious German Bielefeld University
Humanoid Robots, Human-like Machines
118
anthropomorphic grasping robot, without actually having resort to actuator and robot
models. The association of this last basic scheme with the Figure 18.a scheme leads to a
general approach of controlling both position and compliance in taking into account both
robot dynamic model and actuator model for a global controller robustness.
(a)
Mixing
position/
stiffness
controller
Artificial
muscle
actuators
and
Robot
u
_
+
u
1
2
S
d
+
real stiffne ss estimated
from a measure of ‘u +u ’
12
q
d
_
q
(b)
Fig. 18. General schemes of position-compliance control of a robot-limb actuated by artificial
muscle actuators : actuator compliance is imposed in the form of a desired stiffness (a) or
controlled from a real stiffness estimation based on a measure of the actuator inputs sum (b)
As in the case of single position control approach, further experiments in hybrid
position/stiffness control applied to anthropomorphic robot-limbs are necessary to prove
the feasibility of this compliance-based approach. This is in opposition to the current and
weakly biomimetic approach of controlling humanoid robot-limbs by means of wrist 6 axis
force-torque sensors.
6. Conclusion
The functioning of natural skeletal muscle is based on microscopic phenomena that no
technology is at present able to reproduce. The notion of artificial muscle is as a
consequence mainly founded on a macroscopic model of the skeletal muscle. The
mimicking of both tension-length and tension-velocity characteristics is aimed at giving
future humanoid robots touch ability which is so fundamental in the ‘relational life’ of
human beings. No definitive technology has as yet emerged in the design of artificial
muscle. It is, however, interesting to note that the most promising ones are based on the use
of polymers whose physical properties (responses to chemical or physical agents, elasticity,
etc.) mimic some dynamic properties of animal tissues. In particular pH, temperature or
electric field are now currently used to produce and control the shape changes of polymer
fibres or polymer-based composite materials. These results are generally obtained on a
small scale – typically a mm2-section scale – and the application of these technologies to
macroscopic skeletal muscle scales – typically a cm2-section scale – generally induces a
performance loose in power-to-volume and power-to-mass. Today the integration of
artificial muscles to anthropomorphic limbs on a human-scale in volume and mass,
necessitates power-to-mass and power-to-volume very close to human skeletal muscle..
Pneumatic artificial muscles, in the form of McKibben artificial muscles or alternative types
such as pleated artificial muscles, are at present able to mimic these natural muscle dynamic
properties. As a consequence, we consider that their use is interesting to test control
d
d
d
q
q
q
q
q
Robot
dynamic
model
Actuator
model
Artificial
muscle
actuators
and
Robot
d
d
d
q
q
q
Linear, robust or
adaptive control
u
T
T
forward
+
+
_
_
+
+
q
u
1
2
S
d
Artificial Muscles for Humanoid Robots 119
approaches aimed at giving artificial muscle actuators speed, accuracy, robustness and
compliance similar to human limb movements, while awaiting a more biomimetic
technology able to supersede the dangerous DC motor/harmonic drive combination as a
typical humanoid robot actuation mode.
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