IEEE TRANSACTIONS ON MECHATRONICS

1

Variable Ankle Stiffness Improves Balance Control:
Experiments on a Bipedal Exoskeleton
Barkan Ugurlu, Member, IEEE, Corinne Doppmann, Masashi Hamaya, Paolo Forni,
Tatsuya Teramae, Tomoyuki Noda, and Jun Morimoto, Member, IEEE

Abstract—This paper proposes a real-time balance control
technique that can be implemented to bipedal robots (exoskeletons, humanoids) whose ankle joints are powered via variablephysical stiffness actuators. To achieve active balancing, an
abstracted biped model, torsional spring-loaded flywheel, is utilized to capture approximated angular momentum and physicalstiffness, which are of importance in postural balancing. In
particular, this model enables us to describe the mathematical
relation between Zero Moment Point and physical stiffness. The
exploitation of variable physical stiffness leads to the following
contributions: i) Variable physical stiffness property is embodied
in a legged robot control task, for the first time in the literature
to the authors’ knowledge. ii) Through experimental studies
conducted with our bipedal exoskeleton, the advantages ofvariable physical stiffness strategy are demonstrated with respect
to the optimal constant stiffness strategy. The results indicate thatthe variable stiffness strategy provides more favorable resultsin terms of external disturbance dissipation, mechanical power
reduction, and ZMP/CoM position regulation.
Index Terms—balance control, exoskeleton, variable physicalstiffness, ankle stiffness, zero moment point, push recovery.

I. I NTRODUCTION

THE advent of the first active exoskeleton reported in [1]
led the way to several key developments in the field of
lower extremity life support systems. Applications vary fromrobot-aided physiotherapy [2] and power amplification [3] towalking support for paraplegics [4]–[6] and gait rehabilitation[7]. In [8], Dollar and Herr reviewed a great majority of thesedevices in terms of design, control, and implementation.
Orienting our research objective within this frame, wedeveloped a high-power, self-balancing, passively compliant
and wearable bipedal exoskeleton for robot-aided lower bodyrehabilitation applications. In particular, the ankle joints of ourrobot possess the variable physical stiffness feature, which, inturn, effectively allowed the synthesis of a novel balance control strategy to cope with unperceived external disturbances.
Therefore, this paper aims to disclose this aspect of our work;
The authors are with the Dept. of Brain Robot Interface, Computational
Neuroscience Laboratories, Advanced Telecommunications Research InstituteInternational (ATR), 619-0288, Kyoto, Japan. (e-mail: {hamaya, t-teramae,
t noda, xmorimo}@atr.jp)
B. Ugurlu is also with the Dept. of Mechanical Engineering, Ozyegin
University, 34794 Istanbul, Turkey. (e-mail: barkan.ugurlu@ozyegin.edu.tr)
C. Doppmann is also with the Dept. of Microengineering, École polytechnique fédérale de Lausanne (EPFL), Lausanne, Switzerland. (e-mail:corinnedoppmann@gmx.ch)
M. Hamaya is also with the Grad. School of Frontier Biosciences, Osaka
University, Osaka 565-0871, Japan.
P. Forni is also with the Dept. of Electrical Engineering, Imperial College
London, London SW7 2BT, U.K. (e-mail: paolo.forni91@gmail.com)

the variable physical stiffness property is exploited in thelegged robot balancing task for the first time in the literature,to the authors’ knowledge.
This study chiefly focuses on the efficacy of the variablephysical stiffness modulation to address the legged robot
balance control task. The lower body exoskeleton used in our
experiments was considered as a bipedal robot without any
human user, so as to explicitly examine the sole contribution of
the controller. This is due to the fact that humans inadvertently
modulate their own muscle impedance characteristics when
the human-robot coupled system is perturbed, increasing thecomplexity of the evaluation. With this in mind, the stabilityof the human-robot coupled system will be investigated in a
future work.
The paper is organized as follows. The current section
continues with the discussion on the related works and thecontributions presented in this paper. The mechatronic hardware of our bipedal exoskeleton is presented in section II, witha special emphasis on its actuation principle. Variable physicalankle stiffness-based balance recovery control is disclosed in
section III with related numeric analyses. Experiment results
are discussed in section IV in which a comparison is provided.
The paper is concluded in section V by stating the end results
and addressing the future direction.
A. Related Works
Incorporation of compliance is of importance for almost
all multibody legged systems when considering dependability,
intrinsic stability, inherent safety, energy management, andenvironmental adaptability [9], [10]. In particular, softwarecontrolled active compliance schemes outperformed conventional feedback controllers in handling unperceived environmental conditions and external disturbances [6], [11]–[13].
While this strategy is useful in its own right, it may not
be considered inherently safe and energetically favorable due
to reflected inertia, high intrinsic impedance, and delays insensory response and control cycle. [10].
Actuators with elastic components are developed to introduce physical compliance for enhanced human-robotenvironment interaction capabilities [14], [15]. On one hand,
this actuation principle is effectively used in humanoids andexoskeletons, such as, in balance recovery [16], efficient
locomotion [17], and assistive control [18]. On the other hand,
physical stiffness characteristics of these actuators are often
nonadjustable; thus, enforcing the additional active compliance
control schemes to modulate the output impedance. ThisIEEE TRANSACTIONS ON MECHATRONICS

further requires modulations on the task-specific position or
torque inputs in a way so as to emulate the desired impedance
characteristics [6], [11], [12], causing inevitable deviations
from the position or torque references.
The central nervous system in legged creatures adaptively
controls the motion by means of muscle impedance regulation[19]. This allows them to stabilize their motion when subject
to disturbances [20], [21], even within the absence of neural
feedback [22]. In order to mimic such advanced behavior
in robotic systems, researchers developed VIAs (Variable
Impedance Actuator) to decouple the apparent output stiffness
and actuator torque [23]–[26]. On this matter, VIAs with electrical actuators often require complicated mechanical design,and their implementation to multi-DoF (Degrees of Freedom)
systems is an ongoing process due to their size and weight.
Akin to their biological counterparts, PAMs (Pneumatic
Artificial Muscle) possess superior characteristics as the main
power source. They have great power-to-weight ratios; candrive robot joints without any high-friction mechanical transmission gears. Their implementation to robotic systems israther simple in terms of mechanical design. More importantly,
they act as a simultaneous torque and stiffness generator whenantagonistically driven. While PAMs have some disadvantages
such as constant need of pressurized air, they were implemented to exoskeleton devices [27]–[29].
Despite the fact that VIAs become increasingly available[26], the variable physical stiffness feature has not beenthoroughly addressed in legged robot control, particularly, forreal-time balance control tasks. There are ongoing efforts inembedding VIAs to legged systems, e.g., [25]; however, acontrol algorithm that exploits the concept of variable physicalstiffness has not been proposed in the legged robotics literature.
Therefore, the main objective of this paper is to make acontribution in this direction.
B. Novelty
As discussed in [19]–[21], adaptive motion control isprovided by means of mechanical impedance regulation in
biological muscles. Especially, ankle stiffness modulation isobserved to be a key factor in human balancing [21], [30]–[32]. Motivated by the results in these studies, a real-timebalance control method is developed for our PAM-powered
bipedal exoskeleton which makes use of the variable physicalstiffness at the ankle joints to cope with unperceived external
disturbances.
To extract the mathematical relation between the dynamicbalance criterion ZMP (Zero Moment Point) and variablephysical stiffness, a torsional spring-loaded flywheel model
is constructed by appropriately combining the concepts introduced in [12] and [33] . In doing so, balance control task, i.e.,
ZMP regulation, can be interpreted in terms of ankle joint
stiffness modulation. In addition, the model is able to capture
the abstracted angular momentum, which is of importance inpostural balancing.
In developing the online balance controller, we offer twocontributions:i) Variable physical stiffness property is exploited for the
first time in the context of legged robot control, to the authors’

2

{B}

z
x
T  T T T

y

{1}
x

{1}

T

<<k1

T

y
x

{2}

[m 2 , I 2 ]

{2}

{2}

k2

y

{3}

[m 3 , I 3 ]

{3}

x
z

[m 1 , I 1 ]

{B}
{1}

T

{3}
z
x

(a)

k3

(b)

[m 4 , I 4 ](c)xFig. 1. a) Joint frames of XoR in the sagittal plane. b) The actual robot,
XoR, while being worn by an able-bodied. c) Multi-DoF representation of
XoR in the sagittal plane. Knee and ankle joints are passively compliant. The
arrow on the ankle joint indicates the stiffness variability.

1

2

3

Fig. 2. The PAM-powered exoskeleton robot exhibits its position control
functionality by performing self-balanced squatting motion with a dummymannequin inside [34].

knowledge. Software-controlled actively compliant robots [6],[7], [11], [12], and legged systems with nonadjustable physicalstiffness [16]–[18] demonstrated favorable locomotion control
performances; yet, the utilization of variable physical stiffness
has not been investigated in the related literature. This paper
offers the first implementation of variable physical stiffness,with a special emphasis on its efficacy for the real-time balance
control of a bipedal system.
ii) The proposed balancing strategy is compared to optimal
constant stiffness strategy [16] by conducting experiments onan actual bipedal exoskeleton robot. Results are compared interms of external disturbance dissipation response, ZMP/CoM(Center of Mass) position regulation, mechanical power reduction, and air mass consumption.
II. A S OFT B IPEDAL E XOSKELETON : X O R
In order to conduct research on robot-aided rehabilitation,
sensorimotor learning and neurophysiology, a soft bipedal
exoskeleton, named XoR, was developed at the BRI - Computational Neuroscience Laboratories of ATR, [29]. Each XoRleg has 3 active DoFs that actuate hip, knee, and ankle
joints through flexion/extension. This configuration allows therobot to demonstrate self-balancing and bipedal squatting withno support, nor tethering mechanism; though its motion isIEEE TRANSACTIONS ON MECHATRONICS

3

TABLE IM ECHANICAL S PECIFICATIONS OF X O R
Hip - Knee length:
Knee - Ankle length:
Ankle - sole length:
Total Weight

Disturbance

39 [cm]38 [cm]14 [cm]22.2 [kg]

α=α0
kf

m
constrained in the sagittal plane. Fig. 1 shows the physicalsystem and its joint frames. Fig. 2 displays three snapshotsfrom the self-balanced squatting experiments with a dummymannequin. Mechanical specifications of the robot are concisely listed in Table I.
The current version of XoR was chiefly constructed to
conduct tasks in the sagittal plane, such as, sit-down andstand-up rehabilitation [2], squatting and active self-balancing.
Therefore, this work primarily focuses on planar motions,in which the legs are moved in a synchronized manner. As
a consequence, ankle joints are required to output greater
torque while hip joints demand the minimum amount of torqueoutput, since no stepping motion is involved in the target tasks.
With this in mind, knee and ankle joints are powered
via PAM actuators, due to their high power-to-weight ratio
and physical compliance [26]. Ankle joints are driven via
two antagonistically coupled PAMs (Festo MAS-10) throughflexion/extension, while knee joints are powered via single
PAM units (Festo MAS-40) through flexion. Hip joints are
actuated via low power motors (Maxon, EC-4 pole). The robot
also has hip extensors; however, they are disabled in thisstudy. This hybrid actuation strategy is implemented to comply
with the dimensional and weight requirements, in addition toaddressing physical compliance and high torque output at theknee and ankle joints.
Ankle joints, powered via antagonistic PAM couples, enables us to control the position (q3 ) and the physical stiffness(k3 ) in a simultaneous fashion. The details regarding the simultaneous position and variable stiffness control is provided in[34]. Knee joints allow the reliable position control; however,its stiffness (k2 ) change depending on the joint state. Utilizing
the forward stiffness model and knee torque measurement, we
can estimate the changes in k2 [34]. Hip joints, actuated via
low power motors, only enable the position (q1 ) control. The
stiffness of hip joints is considered sufficiently big, since their
physical compliance is relatively insignificant.
In the light of the above stated facts, we model the robot as a
4-link 3-DoF system as displayed in Fig. 1(c), in which ankle
joints are driven via variable stiffness actuators, knee joints
driven are via passively compliant actuators, and hip joints are
driven via stiff-by-nature actuators. Since both legs move in asynchronized manner, the ankle joint stiffness in this model isequivalently distributed to the left and right ankle joints of therobot. This approach was confirmed to be feasible in practicefor a passively compliant humanoid [17].
III. BALANCE C ONTROL S TRATEGY
In order to avoid complex and computationally heavyalgorithms, abstracted models with reduced dimensionality
are often used in a way so as to capture the important

f

k2

Xzmp

k3
P
Fn

d
m

f

α

r

z
P
Xzmp

x

Fnx
Fnz

Fig. 3. XoR is modeled as a torsional spring-loaded flywheel pendulum. It
can characterize both approximated angular momentum and physical stiffness.
Flywheel disk orients in an identical manner with the pendulum. Any
disturbance applied on the robot may be represented by d that acts along
the α axis. Reaction force Fn can be decomposed to Fnx and Fnz .

characteristics of multi-body robots for a given task [12],[16], [33]. In line with this strategy, a torsional spring-loaded
flywheel model, illustrated in Fig. 3, is utilized to combine
the concepts presented in [12] and [33]. In this approach, aflywheel disk with a constant rotational inertia of If and a total
mass of m is considered to emulate the robot. Flywheel mass
is condensed at the robot’s CoM position and it is in contact
with the floor through a telescopic leg and a rectangular foot.
Friction between the foot and the floor is sufficient to prevent
foot slips. As the generalized coordinates, leg length r, andangular position with the vertical z-axis, α, are assigned. A
torsional spring, with a varying stiffness of kf , connects theleg to the vertical z-axis. When α=α0 , the spring is in therest state. The parameter d represents the overall disturbancetorque acting on the robot CoM, due to external pushes, andas well as due to modeling uncertainties.
The model offers two beneficial properties. i) Unlike point
mass pendulums, it can encapsulate the approximated angularmomentum, which is crucial in describing the postural equilibrium. Though the rotational inertia of the robot is joint state
dependent (composite rigid body inertia), one can conjecture
a constant value by considering the target motion range and
CAD data [33]. ii) It can embody the physical stiffness of
the robot with the presence of torsional spring. To this end,
a mapping between the torsional spring stiffness (kf ) andjoint space stiffness (k2 , k3 ) will be addressed in the next
subsection.

A. Equations of Motion
To derive equations of motion, Lagrangian mechanics isused. r and α are the generalized coordinates.

IEEE TRANSACTIONS ON MECHATRONICS

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 1
1
m ṙ2 + r2 α̇2 + If α̇2
(1)
2
2
1
2
kf (α − α0 ) + mgr cos α(2)
Uf m =
2
1
Df m =
bf α̇2(3)
2
In these equations, Tf m and Uf m stand for total kinetic
energy and total potential energy. Df m is Rayleigh’s dissipation function which is used to embody the frictionaland other damping effects through α. The related damping
coefficient is bf . Calculating the Lagrangian of the system via
Lf m = Tf m − Uf m , the equations of motion can be yielded
as follows.
Tf m

=

∂Lf m
∂Df m
d ∂Lf m
−
+
= Fn
(4)
dt ∂ ṙ∂r∂ ṙ
d ∂Lf m
∂Lf m
∂Df m
−
+
= Mn
(5)
dt ∂ α̇∂α∂ α̇
Eqs. (4) and (5) respectively stand for translational androtational motion. Fn and Mn are reaction force and moment
acting on the system, see Fig. 3. As described earlier, thefriction between the foot and floor is considered to be sufficient
to prevent foot slips; therefore, we give our full attention to
postural balance which can be described using (5). In thiscase, reaction moment can be expressed in terms of x-axis
ZMP, (Xzmp ), and vertical reaction force, (Fnz ) [11].
Mn = Fnz Xzmp + d(6)

In (6), d stands for the resultant external moment that may
occur due to disturbances. Plugging (6) into (5), the equationof motion is yielded.
Fnz Xzmp + d =+2(mr + If )α̈ + 2mrṙα̇ + kf (α − α0 )bf α̇ − mgr sin α(7)

At the right hand side of (7), the rate change of angularmomentum that is associated with the rotational inertia ischaracterized via If α̈ term. Physical stiffness is captured withkf (α − α0 ) term.
B. From Flywheel Stiffness to Ankle Stiffness: The Mapping
While (7) reveals the mathematical relation between the
ZMP (Xzmp ) and flywheel stiffness (kf ) in addition to otherterms, it is still required to construct a mapping from flywheel
stiffness (kf ) to ankle joint stiffness (k3 ). To this end, thefollowing equation is used.
T +kf = (Jrt (q) ) Kr (Jrt (q))+(8)

In (8), the superscript + stands for the Moore-Penrose
pseudo inverse. Recall that the model we use includes only asingle torsional spring through α, with a time-varying stiffness
parameter kf ; see Fig. 3. There is no translational springthrough r. Hence, the stiffness matrix of the model has only

ref

+Xzmp

cp

cmd

Xzmp

Xzmp
+
PD
+

Fnz

Force Sensing+d-Eq. (11)..
..
(mr2+I f )α + 2mrrα r,α.
+bf α - mgr sinα

1
α-α
0
+

des

kf Mapping k3
k f k3Eq. (10)

Robot

DisturbanceFig. 4.
Our ZMP-based real-time balance controller is based on thevariable physical ankle stiffness modulation. Superscripts cmd and refdenote command (controller output) and reference (desired) signals. Positionand stiffness control of PAMs [34] is not included in this illustration. The
disturbance d represents the resultant external moment that may occur due toany kind of disturbance, e.g., external pushes, modeling uncertainties, etc.

one element: kf . Kr in (8) is a matrix whose diagonal
elements store the stiffness values of our robot (k2 , k3 ). Notethat hip joints do not include physical compliance, thus they
are not considered in the mapping as explained in section
II. Joint state-dependent Jrt (q) is the Jacobian matrix thatkinematically maps α to joint coordinates.
∂α ∂αJrt (q) =∂q2 ∂q3(9)

In order to extract the kinematic relation between α andjoint coordinates, one can utilize coordinate transformationfrom polar to Cartesian coordinates and forward kinematics.
With (9) at one hand, we can solve (8) to obtain k3 in termsof k2 and kf .
2
2
2
2
kf Jrt1+ Jrt2− k2 Jrt1
k3 =
2
Jrt2

(10)

Jrt1 and Jrt2 are the first and second elements of Jrt (q)and they can be calculated using joint angle measurements.
Variations in k2 can be estimated using the PAM model
parameters and torque measurements [34]. Finally, one canobtain k3 via (10) for a given kf , together with the estimatedk2 , so as to achieve the mapping kf 7→ k3 .
C. Stable ZMP Feedback Control via Varying Ankle Stiffness
Fig. 4 displays the ZMP feedback control strategy. In order
to embody ZMP feedback via the utilization of varying ankle
stiffness, we primarily define τcp which includes the rest of
the terms that appear due to inertia, gravity and damping.
τcp = (mr2 + If )α̈ + 2mrṙα̇ + bf α̇ − mgr sin α(11)

If we compute τcp using the actual r and α, along withthe required time derivatives, and add it up as a compensation
block as shown in Fig. 4, we can hypothetically cancel out
these terms. On this matter, any modeling and parameter
uncertainty would contribute to the disturbance d, which
represents the resultant disturbance, including external pushes.
Note that actual r and and α can be computed using joint angle
measurements. α̈ is obtained with approximate differentiation.

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5

(12)

Having computed kfdes via (12), we utilize (10) to obtain thecorresponding ankle stiffness. The corresponding ankle stiffness is realized in accordance with the simultaneous positionand variable stiffness controller that is reported in [34].
In order to prove the stability of the controller disclosed inFig. 4, we use Lyapunov’s theory. First, placing (12) into (7)yields the following.
cmd
Fnz Xzmp + d − Fnz Xzmp
=0

cmd
ref
Xzmp
= Xzmp+ Kp ez + Kd ėz(14)

Positive PD gains, Kp and Kd , are assigned by respectingrefthe Hurwitz criterion. ez = ez (t) is ZMP error; ez = Xzmp−
Xzmp . Combining (13) and (14) results as follows.
1 + Kpd−ez
Fnz KdKd(15)

The Lyapunov function V (ez ) and its time derivative alongsystem trajectories, (15), are derived as below.
1 2
εe
2 z

V (ez )=V̇ (ez )= εez ėz = −ε(16)
1 + Kp 2
de +εez (17)
Kd z
Fnz KdIn (16)-(17), ε is a sufficiently small number. Considering
the Young’s inequality argument, the following condition is
met for a sufficiently small coefficient c1 > 0 and a sufficiently
large coefficient c2 > 0 [35],V̇ (ez ) ≤

2

(a)
0.0

-0.2
(i)
-0.4

(ii)
(iii)

-0.6
-0.16

Variable Stiffness
Opt. Const. Stiffness
0.0
0.16
Flywheel Angle [rad]

0.32

55
(i)
50

(b)

(ii)

45

(iii)

40
4

5

6
time [s]78Fig. 5. Numerical simulations were conducted using the torsional springloaded flywheel model to compare the proposed and the optimal constant
stiffness strategies. 3 distinct external disturbances are implemented to theflywheel CoM. a) Phase diagram, b) Ankle stiffness.

(13)

cmd
The command signal Xzmp
is constructed via a PD controller with feedforward, see Fig. 4.

ėz =

60
Ankle Stiffness [Nm/radrad]

cmd
Fnz Xzmp− τcp
kfdes =
α − α00.2
Flywheel Angular Rate [rad/s]

Keeping this in mind, the desired flywheel stiffness, kfdes ,is designed as follows, see Fig. 4.

2−c1 kez k + c2 kδ(t)k ,(18)

where δ(t) = ε FnzdKd ez . k·k denotes the Euclidean norm. It
follows from [36] that the system (13) is Input to State Stable(ISS) with respect to time-varying disturbance δ(t). This also
indicates a notion of robustness for the system (13) through thecharacterization of the ISS concept. For example, the following
expression (definition of ISS) holds true for some K function
Υ and for some KL function Ω [36].
kez (t)k ≤ Ω(kez (0)k , t) + Υ(kδ(t)k∞ )(19)

In (19), k·k∞ denotes the infinity norm of the signal k·(t)kover time. Intuitively speaking, the definition of ISS requiresthat for t large, the state must be bounded by some functionof the amplitude of the inputs. This to say the norm of thestate eventually enters in a ball of radius Υ(kδ(t)k∞ ).

D. Numerical Simulation
In order to observe the differences regarding convergenceproperties of the proposed balancing strategy with respect tothe optimal constant stiffness strategy [16], we ran numericalsimulations. In these simulations, disturbances with 3 distinct
amplitudes were horizontally implemented to the flywheel
CoM for a period of 10 [ms]: i) 50 [N], ii) 100 [N], iii)
150 [N]. Fig. 5 depicts the results in which purple and green
lines show phase diagrams and ankle stiffness variations forthe proposed balancing strategy and optimal constant stiffness
strategy, respectively.
Observing Fig. 5(a), the proposed strategy always converged
faster to the equilibrium, compared to the optimal constant
stiffness strategy. This was indeed expected, because, when
the stiffness was constant, the CoM needed to travel longer
to extend the deflection (α-α0 ), so as to cope with the
disturbance. In contrast, the proposed strategy dynamicallymodulated the stiffness; therefore, the compensation torqueto handle the disturbance could be exerted with comparatively
less angular deflection. This allowed the CoM to travel less,resulting in a more favorable balancing strategy as the CoM
deviated less from its desired path.
In addition, ankle stiffness appeared to decrease at thetime of impact to cope with the disturbance, see Fig. 5(b).
It decreased even more when the disturbance amplitude wasgreater. This was an expected behavior as the disturbancecould be dissipated more effectively in higher intrinsic compliance.
IV. E XPERIMENT R ESULTS
A series experiments were conducted on the bipedal exoskeleton XoR for the proof of concept evaluation. Twoexperimental protocols were considered: 1) The robot wasbalanced using the proposed method in which physical ankle
stiffness was modulated. This experiment protocol is tagged as
VSS. 2) The robot was balanced using the method reported in[16], which allows the computation of the optimal constantankle stiffness by means of a cost function to optimallyminimize ZMP squared. This experiment protocol is tagged as
OCS. Using this method, the optimal constant ankle stiffness
was calculated as 58 [Nm/rad] for our robot.

Ankle Stiffness [Nm/rad]

48
24
0
-24
-48
-72

(a)

-96
60

Variable Stiff.
Opt. Const. Stiff.

56

52

(b)

48
6
3
0
-3

(c)

Flywheel Angle Error [rad]-6

Mechanical Power [W]x-axis ZMP Error [cm]

72

0.28

0.3

0.14

-0.14

(d)

-0.28

Norm. Air Consumption

The following conditions kept the same in both protocols.
a) The CoM position reference was assigned as a quiet
standing state; r = r0 = 0.65 [m] and α = α0 = 4.8◦ .
The method proposed in [34] was used for the position andstiffness control of PAM-powered joints.
b) A pendulum with a tip mass of 4 [kg] and a cable length of
1.25 [m] was released towards the approximate robot CoM bymeans of an external disturbance source. It was released froman initial angular distance of 15◦ with zero initial velocity.
The pendulum tip mass struck the robot when the pendulum
angle is approximately 0◦ .
c) The pendulum was set free 3 times in a successive manner,with an equal amount of delay in between each hit.
d) Experiments were strictly conducted in 3-D. No tethering,nor supporting mechanism was utilized. The robot also singlehandedly bore a bundle of pneumatic and electrical cables
attached to its pelvis from the back.
Fig. 6 displays the main results, where solid green andpurple lines depict the data collected from OCS and VSS,
respectively. Yellow hatched areas indicate the periods inwhich the pendulum hits the robot to perturb its state, andthen the robot reacts to recover from that perturbation.
Horizontal reaction force measurements are provided in Fig.
6(a). This plot shows that the robot motion was disturbed
equally in each experiment protocol; see the circled reaction
force peaks. The difference is apparent during the recovery
stage. The robot was able to dissipate the disturbance when
the proposed balancing strategy was used. In the case of
VSS, The horizontal reaction force response stayed within theband of ±24 [N], and settled relatively faster. In contrast, thismeasurement varied between -50∼75 [N], in the case of OCS.
Fig. 6(b) depicts the physical ankle stiffness variations. As
stated previously, the optimal constant ankle stiffness wascomputed as 58 [Nm/rad] for the case OCS. In the proposed
strategy, the ankle joint stiffness was modulated in accordancewith the balance control strategy disclosed in section III. Whenthe robot motion was perturbed via the pendulum hits, theankle stiffness showed a variance between 48∼58 [Nm/rad].
When there was no disturbance, it stayed within the vicinityof the optimal constant stiffness. In order to maintain thebalance when disturbed, the higher intrinsic compliance isof importance [10], [25]. By virtue of the decreased ankle
stiffness, the disturbance could be effectively dissipated.
ZMP error variations are presented in Fig. 6(c) for thehorizontal x-axis. For OCS and VSS, ZMP error varied between -4∼6 [cm] and -1∼2 [cm], respectively. As the proposed
method was able to dissipate the external disturbances, ZMP
error was well contained for the case of VSS. Compared to
the OCS case, peak-to-peak ZMP error was reduced for about
70%. That being said, the robot maintained dynamic balancein both cases, as the ZMP error stayed within the support
polygon boundaries.
CoM position error, i.e., flywheel angle deflection plots
are given in Fig. 6(d). In the case of OCS, flywheel angle
deflection (α−α0 ) was the only physical quantity that supports
the dissipation of the external disturbance. This enforced the
CoM to travel more and caused it to deviate from its desired
path. In contrast, the proposed balance controller modulated

6x-axis Reaction Force [N]IEEE TRANSACTIONS ON MECHATRONICS

0
-0.3

(e)

-0.6
0.9

0.6

(f)

0.3

0

25

50
Time [s]75Fig. 6.
White areas show delay (rest) periods. Yellow hatched areas
indicate the periods in which the robot was hit by the pendulum, and then it
reacted to turn back to the quiet standing state. a) Horizontal reaction force
measurements. b) Physical ankle stiffness variations. c) ZMP error variations
through x-axis. d) Flywheel angular deflections through α axis. e) Total
mechanical power plots. f) Normalized air mass consumption plots.

IEEE TRANSACTIONS ON MECHATRONICS

7

Flywheel Angle Rate [rad/s]

Variable Stiff.

0.22 Opt. Const. Stiff.
0.11
0
-0.11
-0.22
-0.19

-0.08 0.03
0.14 0.25
Flywheel Angle [rad]0.36

Fig. 7.
Phase diagrams through α axis. It is plotted for 3 successive
perturbations and the related recovery period. Compared to the OCS case, theCoM converged faster to the quiet standing state when the proposed strategy
was employed.

the ankle stiffness in accordance with the ZMP feedback, so
as to dissipate the perturbation effectively. As a consequence,
CoM position error was contained well as the flywheel angle
deflected comparatively less.
Fig. 6(e) depicts the total mechanical power. Since the CoM
needed to travel less in the case of VSS, the peak-to-peakmechanical power showed a 50% decrease, compared to the
OCS case. Hence, the mechanical power reduction appears
to be another advantage of using the proposed method forbalancing bipedal systems.
Air mass consumption variations are estimated using ideal
gas law and normalized with respect to maximum value; see
Fig. 6(f). Examining this figure, the system demanded 70%
more air mass in the case of VSS. The main reason behind
this increase is that the simultaneous position and stiffness
control utilizes the actuator redundancy in the antagonisticarchitecture, which leads to more aggressive changes in PAM
pressure levels. While this negative result should be noted, theincrease in supply air is not inherent to this control strategy.
We discuss this aspect later in section V.
Fig. 7 illustrates the phase diagrams which were constructedusing the experiment data. These phase diagrams indicatethat the CoM converged to the equilibrium (quiet standing)much faster in the case of VSS. This result well agrees
with numerical simulations presented in Fig. 5. In principle,
the proposed balancing strategy modulates the variable ankle
stiffness in a way so as to dissipate the external disturbance
more effectively, which enables the flywheel angular deflection
to be contained more. This helps to decrease CoM position
error.
V. D ISCUSSION AND C ONCLUDING R EMARKSThis paper presented a biologically-inspired novel balance
controller that makes use of the ’variable physical’ stiffness
for the first time in the legged robot control literature to
the authors’ knowledge. Through the use of torsional springloaded flywheel model, balance recovery via ZMP feedback

is addressed by means of physical ankle stiffness modulation.
This phenomenon is also observed in humans [21], [30]–[32].
The proposed controller outperformed the optimal constantankle stiffness strategy in dissipating the external disturbances.
This property enabled the robot to exhibit satisfactory balance recovery behavior in terms of convergence rate to theequilibrium state, well-contained ZMP/CoM position error andreduced mechanical power.
That being said, air mass consumption rate appears toincrease. While this should be noted as a limitation, thisbehavior is not inherent to the implemented balance controller.
Rather, it is attributed to the nature of antagonistic setups.
In [37], Carloni et al. presented a port-based analysis whichsuggested that a certain portion of power flow is internallystored, and therefore cannot be used to do work, during
the nominal operation of variable stiffness actuators withantagonistic setups. Since PAMs must be antagonisticallycoupled to generate bidirectional joint torque, increased air
mass consumption rate is inevitable, in particular, when the
stiffness is modulated.
Numerical simulations also showed that the proposed
method outperforms the optimal constant ankle stiffness
method. After disturbing three times with different amplitudes,
the CoM travels less when returning to the equilibrium position in each case. This is in good agreement with the experiment results. Moreover Fig. 6(a) indicates that the horizontal
impact was around 100 [N] in our experiments. This caused adrop in ankle stiffness up to 48.5 [Nm/rad]. A comparable dropis also seen in the second numeric simulation; implementing
a perturbation of 100 [N] led to a decrease in ankle joint up
to 46.5 [Nm/rad].
The proposed controller utilizes the ankle joint. In [38],Stephen showed that hip strategy could be utilized in addition to ankle strategy. While the proposed method can beaccordingly enhanced for a robot with variable stiffness hip
joints, ankle strategy was observed to be the main and primarystabilization action in humans [39]. The study in [39] alsoemphasized that no ’hip-only’ strategy was observed; rather,
it appears to be an auxiliary stabilization action to support theankle strategy. With this in mind, this study focused on the socalled ankle strategy. Currently, our bipedal exoskeleton XoR
is under hardware maintenance to provide variable stiffness
in all joints. Upon the completion of this modification, auxiliary supportive strategies will be investigated on top of the
proposed controller.
Speaking of auxiliary controllers, Morasso and Sanguineti
defended that ankle stiffness modulation alone is not sufficient
to stabilize human quiet standing [40]. Indeed this is expected,
as the achievable stiffness range has upper and lower bounds
for biological muscles. Akin to their biological counterparts,
PAM-powered joints have certain stiffness operation ranges
as well. Depending on the disturbance amplitude, the desired
ankle stiffness may be out of the operation range, potentiallyhampering the success of the stabilization. Since this is a certain limitation for almost all the muscle-powered systems, one
may utilize additional strategies when the stiffness saturation
occurs. Another possible solution is to use variable stiffness
actuators with theoretically infinite stiffness range, such as theIEEE TRANSACTIONS ON MECHATRONICS

one reported in [23], although such actuators have not been
fully downsized yet to power multi-DoF systems. Therefore,
the maximum disturbance that can be handled by the controller
is hardware-dependent.
After the hardware modification on XoR, the future work
will include the development of the auxiliary strategies, on
top of the proposed baseline stabilizer that utilizes physicalankle stiffness. In addition, human-robot coupled stability will
be scrutinized to eventually address real-time balance control
while the robot is utilized in clinical rehabilitation tests.
ACKNOWLEDGEMENTS
This research was supported by SRPBS of the MEXT, the
New Energy and Industrial Technology Development Organization (NEDO), ImPACT Program of Council for Science,
Technology and Innovation (Cabinet Office, Government ofJapan), the contract with the Ministry of Internal Affairs
and Communications entitled ’Novel and innovative R&D
making use of brain structures’, MEXT KAKENHI 23120004,
JSPS KAKENHI 24700203 and 15H05321, JST-SICP, MICSCOPE, and JSPS-MIZS: Japan-Slovenia Research Co- operative Program. The authors thank A. Inano, N. Nakano, and
G. Lisi for their kind assistance.
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Barkan Ugurlu (S’08-M’10) received his Ph.D.
degree in Electrical and Computer Engineering from
Yokohama National University, Yokohama, Japan, in
March 2010. From May 2010 to March 2013, he wasa Post-Doctoral Researcher, at the Istituto Italiano diTecnologia, Genova, Italy, and Toyota Technological Institute, Nagoya, Japan. Between March 2013
and February 2015, he was a Research Scientist at
the Computational Neuroscience Laboratories, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan. He currently holds
an Assistant Professor position at the Dept. of Mechanical Engineering,
Ozyegin University, Istanbul, Turkey. His research interests include biologicalsensorimotor control and motor recovery, active orthoses and exoskeletons,
robot-aided rehabilitation, and humanoid/quadruped locomotion control.

Corinne Doppmann received her B.Sc. and M.Sc.
degrees in Microengineering from the École polytechnique fédérale de Lausanne (EPFL), Switzerland. In 2014, she was an intern student working
on her Master Thesis on exoskeleton robots at
the Computational Neuroscience Laboratories, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan. Since then, she has
been with National Instruments Switzerland GmbH,
Ennetbaden, Switzerland, where she is currently
working as an Applications Engineer.

Masashi Hamaya received his B.E. degree from
Kobe University, Kobe, Japan, in 2013. He is currently working toward the M.S. degree in the Graduate School of Frontier Biosciences, Osaka University, Osaka, Japan. He is also currently with the
Department of Brain Robot Interface, ATR Computational Neuroscience Laboratories, Kyoto, Japan.
His research interests include active exoskeleton
robots and optimal control.

9Paolo Forni received his B.S.E. in Computer Science and Control Engineering from the Universityof Rome, Italy, in 2012, and the M.Sc. in Control
Engineering from Delft University of Technology,
The Netherlands, in 2014. He is currently pursuing
the Ph.D. degree in the Control and Power group in
Imperial College, London, U.K. His main researchinterests are in stability of nonlinear dynamical systems, and control of port-Hamiltonian systems.

Tatsuya Teramae received his Ph.D. in Engineering from Tottori University, Japan, in 2011. He iscurrently a researcher at the Department of Brain
Robot Interface, ATR Computational Neuroscience
Laboratories, Kyoto, Japan. His research interests
include optimal control and human machine interfaces. He is a member of the Society of Instrument
and Control Engineers, Japan, and the Institute ofElectrical Engineers of Japan.

Tomoyuki Noda received his Ph.D. degree in Engineering from the Graduate School of Osaka University, Osaka, Japan, in 2009. He then joined the Institute for Neural Computation in University California
San Diego as a visiting Research Scholar. In 2010,
he started to work as a Post-Doctoral Researcher
at the Computational Neuroscience Laboratories of
ATR, Kyoto, Japan. Dr. Noda was nominated for
the Best Video Award at IEEE AAAI 2008, and is
the recipient of the Best Video Award in LAB-RS
2008, regarding the development of a whole bodyhumanoid robot with tactile sensation and compliant joints. He was nominatedfor the Best Paper Award at IEEE Humanoids2012 with his work on a BMIcontrolled exoskeleton.

Jun Morimoto (M’08) received the Ph.D. degree
in Information Science from the Nara Institute of
Science and Technology, Nara, Japan, in 2001. From2001 to 2002, he was a postdoctoral fellow at
the Robotics Institute, Carnegie Mellon University,
Pittsburgh, PA, USA. Since 2002, he has been at
the Advanced Telecommunications Research Institute International, Kyoto, Japan, where he was a
Researcher in the Computational Brain Project, theInternational Cooperative Research Project, Japan
Science and Technology Agency from 2004 to 2009.
He is currently the head of the Department of the Brain Robot Interface, ATR
Computational Neuroscience Laboratories, Kyoto, Japan.