Design, Modeling and Control of a Series Elastic Actuator for anAssistive Knee Exoskeleton

Nikos C. Karavas, Nikos G. Tsagarakis and Darwin G. CaldwellIstituto Italiano di Tecnologia (IIT)

Abstract— This paper introduces the design, modeling andcontrol of a novel inherently compliant actuator with theability to manually reconfigure the level of stiffness (CompAct-ARS). CompAct-ARS is intended to be utilized in assistivedevices for legs, which will aid users in different motion taskssuch as walking, sit-to-stand movement and squatting and willdemonstrate the benefits of passive compliance. The actuatormodeling design and mechanics are introduced. Experimentaland simulation data are used in order to determine the designspecifications of the actuator for its use in a knee exoskeletonsystem. Finally an assistive control strategy is introduced thatwill allow the proposed system to provide motion assistance tothe subject knee.

I. INTRODUCTION

Lower limb exoskeletons can be used for human perfor-

mance augmentation, assistive locomotion and rehabilitation

purposes. Human performance augmenting exoskeletons can

enhance the user’s capability to carry heavy loads and/or

increase the muscle activation during different motion tasks

[1], [2], [3]. Assistive exoskeletons are aimed at assistive am-

bulation for individuals with impaired legs [4], [5], although

they can also be used to assist sound function. On the other

hand the goal of rehabilitation exoskeletons [6], [7] is to

provide a gait rehabilitation solution to patients preferably

when residing outside the clinic and without the support of

a physiotherapist.

These robotic devices have mutual requirements regarding

their actuation performance, the weight and size of both

actuator and structure, the wearability of their design and

the safety of the user. Researchers who are focused on the

development of exoskeletons have made efforts to address

these aspects. However, there still remain limitations to be

overcome before this technology can be used effectively [8].

As exoskeletons are devices wearable by humans, safety of

interaction is crucial requirement in preventing both injury

and discomfort [9]. The enabling technology and the control

strategy are the keys to achieve safety and adaptability

of physical human-robot interaction (pHRI). To date the

majority of the presented exoskeletons employ stiff actuators,

which impose on the exoskeletons significant limitations

related to safety issues and the ability to interact with

human. This substantially relies on the fact that the high

frequency output impedance of a stiff actuator is dominated

The authors are within the Department of AdvancedRobotics, Istituto Italiano di Tecnologia, via Morego, 30, 16163Genova {nikolaos.karavas, nikos.tsagarakis,darwin.caldwell}@iit.it

by the reflected inertia of the rotor. For this purpose, safe-

oriented control techniques have been proposed to improve

the dynamic behavior of stiff actuation during pHRI [10],

however there are ineffective for frequencies above the closed

loop bandwidth of the control system.

Introducing inherent compliance to the actuation system

decouples the inertia of the motor drive from the output link

and renders the output mechanical impedance lower across

the frequency spectrum [11]. Thus, the robot improves its

ability to intrinsically absorb impacts and enhances physical

human-robot interaction. In addition, due to the presence

of the employed passive elements which can store and

release energy during one cycle of a periodical motion,

compliant robots can be more energy efficient as compared

to traditional stiff actuated systems. This feature is critical

in the creation of energetically autonomous exoskeletons for

locomotion.

In order to achieve the features described above, our

primary goal is to build an inherently compliant lower body

exoskeleton to be used as a lower limb assistive device. First

step along this path is the development of a compliant knee

exoskeleton, which will provide motion assistance both to pa-

tients with impaired legs and healthy individuals for different

motion tasks such as walking, standing up-sitting down and

squatting. The realization of such a compliant exoskeleton

remains a challenging task requiring more compact, modular

and high performance actuation units. This paper presents the

design, modeling and control of CompAct-ARS (Actuator

with Reconfigurable Stiffness). CompAct-ARS is an intrinsic

compliant actuator with manually reconfigurable stiffness

which has the ability to provide the required assistive torques

to the knee joints of the wearer.

II. COMPACT-ARS

A. Functional Principle of CompAct-ARS

CompAct-ARS as mentioned above is a series elastic

actuator with the ability to regulate off-line the level of

stiffness in as wide a range as needed. This feature permits

the experimentation with different compliance levels and

the adaptation of the joint to fit specific task requirements.

The elimination of active tuning of the spring stiffness

through a second motor was performed to reduce the weight

and dimensions of the unit. The working principle of the

CompAct-ARS is based on the CompAct-VSA (Variable

Stiffness Actuator) [12], which uses a lever arm mechanism

with a variable pivot axis. As it is shown in Fig. 1 the springs

are kept fixed while the position of the pivot is changing.

The Fourth IEEE RAS/EMBS International Conferenceon Biomedical Robotics and BiomechatronicsRoma, Italy. June 24-27, 2012

978-1-4577-1198-5/12/$26.00 ©2012 IEEE 1813

Thus, the apparent stiffness at the lever arm is adjusted

theoretically from zero to infinite by moving the pivot point.

If the pivot moves to the end of the lever which is connected

to the springs the stiffness turns to zero, whereas if it moves

to the other end the stiffness turns to infinite and the lever

becomes rigid.

Pivot

extF

SF

Spring 1 Spring 2

SK = ∞

0SK =

Fig. 1. Concept of working principle of CompAct-ARS; Stiffness isadjusted by varying the location of the pivot.

B. Mechatronic Design

As series elastic actuator, CompAct-ARS is consisted

by two subassemblies: the elastic module and the motor

housing. The motor housing subassembly includes among

others a Kollmorgen RBE1810 frameless brushless motor

and a harmonic drive CSD 25 with gear ratio 100:1. The

elastic module contains the compliance elements and the

lever arm mechanism with the reconfigurable pivot point

(Fig. 2(b), 2(c), 2(d)). As it is shown in Fig. 2(a), the location

of the pivot can be altered by tuning two set screws and so

the apparent stiffness at the output load can be reconfigured

according the application.

The employed springs are pre-compressed half of the

maximum compression which is 20 mm. The selection of

the springs’ constant ks and their maximum displacement

is described in subsection III-B. In addition, the actuator

contains four position sensors and one torque sensor. One

16 bit optical encoder (Avago Technologies) mounted on the

elastic module measures the angular deflection of the link

while a potentiometer (Austria Microsystems) measures the

pivot position. On the other hand, the motor housing sub-

assembly employs two encoders and one torque sensor. The

torque sensor, which utilizes semiconductor strain gauges,

measures the torque provided by the motor. One 12 bit

optical incremental encoder (MicroE Systems) monitors the

position of the motor and one magnetic absolute encoder

(Austria Microsystems with 12 bit of resolution) measures

the position of the motor after the harmonic drive.

C. Stiffness Modeling

The stiffness model of the CompAct-ARS is derived from

the lever arm mechanism which was described in subsection

II-A and is demonstrated with more details in Fig. 3. Suppose

that the lever arm is at its equilibrium position and we apply

an external torque τext which rotates the lever arm with an

angle φ with respect to the pivot (P). As a result, the springs

(a)

(b)

Spring Lever Arm

(c)

Spring Cover

Cam Roller Set Screw

(d)

(e)

Fig. 2. a) Section of the CAD assembly of CompAct-ARS. b) Horizontalsection view of the elastic module. c), d) Views of the first prototype’selastic module. e) Overall view of CompAct-ARS.

are displaced by xs and consequently generate a force Fsapplied in (Γ) given by

Fs = 2ksl1 tanφ (1)

where l1 is the distance form the pivot (P) to point (Δ) which

is the connection point between the springs and the lever at

lever’s equilibrium position. The perpendicular force to the

1814

lever arm is Fs cosφ . Due to the lever mechanism, a force

Fl = Fs cosφPΓAP

= 2ksl21 tanφ

1

AP(2)

is therefore applied in (A), where PΓAP is the amplification

ratio and

AP =√

R2 +d2 +2Rd cosθs (3)

where R = AO, d is the distance from the center of rotation

of the joint (O) to the pivot (P) and θs = q−θe is the angular

deflection of the elastic transmission defined as the difference

between the angle of the output link q and the angle of the

motor θe after the reduction drive. The resultant force FEalong the perpendicular to AO is

FE =Fl

cosε=

Fl

cos(θs −φ)=

2ksl21 tanφ

APcos(θs −φ)(4)

As sinφ = RAP sinθs the (4) becomes

FE =2ksl2

1 sinφAPcosφ cos(θs −φ)

=2ksRl2

1 sinθs

AP2 cosφ cos(θs −φ)(5)

Thus, the elastic torque τE = FER which at the equilibrium

counterbalances the external torque is

τE =2ksR2l2

1 sinθs

AP2 cosφ cos(θs −φ)(6)

The allowable range of the deflection of the elastic transmis-

sion θs is from 0 to 0.2 rad. For this small range of deflection

the elastic torque expression can be simplified as

τE =2ksR2l2

1θs

l22

(7)

Finally the stiffness of the elastic mechanism KS = ∂τE∂θs

is

Β

Δ

O

A

P

ΓsF

sϑ

ϕ

ϕ

extτ

Eτ

ε

EF

lF

cossF ϕ

Sk

Sk

1l

2l

d

R

sx

Fig. 3. Schematic of the CompAct-ARS functional principle.

formulated such as

KS =2ksR2l2

1

l22

= 2ksα2R2 (8)

where α = l1l2

is the ratio of the lever arm.

III. KNEE EXOSKELETON APPLICATION

A. Knee Exoskeleton Specifications

Acquiring the knowledge behind the biomechanics of hu-

man lower limbs plays crucial role in the design of exoskele-

tons and orthotic devices for locomotion. Many researchers

have used Clinical Gait Analysis (CGA) data as a primary

basis for the design specifications of the exoskeletons [1],

[13]. From open literature it is possible to perceive that

running and standing up motion are the most demanding

tasks in terms of torque, power and range of motion of

the human knee joint [14], [15], [16]. Therefore, some of

the specifications for the proposed actuation unit have been

obtained from simulation and experimental data of the sit-

stand-sit movement cycle.

Si�ng pose

Standing pose

[ , ]t tm I

[ , ]th thm I

[ , ]t tm I

[ , ]sh shm I [ , ]

sh shm I

[ , ]th thm I

q

Mass kg

Shank 4.04

Thigh 10.4

Pelvis 6.15

Torso

Human 82.5

41.32

( )shm

( )thm

( )pm

( )tm

( )hm

Hτ

Aτ

Kτ

Fig. 4. Sit-stand-sit movement cycle of the human leg.

For this purpose, a simulation model of human has been

developed. This 6 DOF (hip, knee, ankle) planar model

can replicate the sit-stand-sit motion of the human in the

sagittal plane (Fig. 4). For the simulations a male of 82.5

kg with 1.85 m height has been considered according to the

anthropometric data in [17]. The lumped mass models of

the shank, thigh, pelvis and torso have also been considered

according to the anthropometric data in [17]. To derive

the torque characteristics of each joint of the human leg

two different types of joint trajectories were used. Firstly,

parametric trajectories based on literature biomechanics data

[16], [18], [19], [20] were used as input to the human

model. Fig. 5 demonstrates the parametric trajectories and

the corresponding torque characteristics for the standing

up motion. For evaluation and comparison the following

experiment took place: a healthy subject with a weight of 81

kg (this is close to the simulated model weight of 82.5 kg)

was instructed to repeatedly stand up and sit down without

hand assistance (worst case/highest torques). A Vicon motion

capture system with 6 cameras operating at 250 Hz was

used to monitor the trackers’ position and reconstruct the

trajectories of their hip, knee, and ankle joints of both legs.

These trajectories were used as input to the simulation model

in order to obtain the torque characteristics and correspond

to the continuous motion of standing up, sitting down and

standing up (Fig. 6). Note that Fig. 5 and Fig. 6 demonstrate

also the ankle and hip trajectories to allow full comparison

of the simulation results. However, for the actuator design

1815

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.62468

101214161820

Ank

le A

ngle

[de

g]

t [s]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

−60

−50

−40

−30

−20

−10

0

10

20

Ank

le T

orqu

e [N

m]

t [s]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

102030405060708090

100

Kne

e A

ngle

[de

g]

t [s]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

−100−90−80−70−60−50−40−30−20−10

0

Kne

e To

rque

[N

m]

t [s]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

20

40

60

80

100

120

Hip

Ang

le [

deg]

t [s]0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

−20−10

01020304050607080

Hip

Tor

que

[Nm

]

t [s]

Fig. 5. Parametric trajectories and the corresponding torques of each jointfor the standing up motion.

only the knee trajectories have been considered.

In Fig. 5 and Fig. 6 it is possible to notice that the

task of standing up is performed approximately over the

same duration both in parametric and Vicon trajectories.

Thus, it is reasonable to compare the two knee torque

characteristics obtained with different joint input trajectories

fact which results that the maximum torque, which the knee

joint requires, is around 100 Nm (omitting the high peaks

in Fig. 6). This torque value, which can also be confirmed

by biomechanics data in the literature [16], [18], [20], was

used as torque specification for the knee actuator design.

The spikes observed in Fig. 6, which were amplified by

the numerical differentiation used for obtaining the motion

acceleration, are due to the noise of the Vicon system’s

tracking. In addition, analysis of the torque-velocity require-

ments using these simulation results was conducted in order

to determine the suitable selection of the pair DC motor-

harmonic drive but this analysis is not presented due to the

paper length constraint.

B. Selection of Actuator Design Variables and Design Anal-ysis

In this subsection, the selection of the design variables of

the actuator and its performance analysis are described with

particular focus on the application of a knee exoskeleton

device. Both are based on simulation of the stiffness model

introduced in subsection II-C. The fundamental design pa-

rameters which affect the behavior of the actuator in terms

of stiffness, elastic torque and stored potential energy are

0 2 4 6 8 10 12 14−5

0

5

10

15

20

25

Ank

le A

ngle

[de

g]

t [s]0 2 4 6 8 10 12 14

−160

−120

−80

−40

0

40

Ank

le T

orqu

e [N

m]

t [s]

0 2 4 6 8 10 12 140

102030405060708090

100

Kne

e A

ngle

[de

g]

t [s]0 2 4 6 8 10 12 14

−180−160−140−120−100−80−60−40−20

0

Kne

e To

rque

[N

m]

t [s]

0 2 4 6 8 10 12 140

102030405060708090

100

Hip

Ang

le [

deg]

t [s]0 2 4 6 8 10 12 14

−20

0

20

40

60

80

Hip

Tor

que

[Nm

]

t [s]

Fig. 6. Trajectories obtained from Vicon capture system and the corre-sponding torques of each joint.

Fig. 7. Video frames of the standing up motion during the experiment.

the spring rate ks, the length of the lever arm L = l1 + l2and the maximum displacement of the springs xsmax . As it is

described in subsection III-A the torque specification for the

actuator is 100 Nm. At this point authors are not aware of

any study regarding the stiffness range of human knee joint

during walking or sit-stand-sit movement. In [21] there is an

attempt to specify the characteristic stiffness of the knee in

flexion and extension modes during gait cycle. According

to that, we adopt a suitable range of stiffness from 300

Nm/rad to 600 Nm/rad. The passive deflection of the elastic

mechanism θs is given by

θs =τE

KS(9)

and thus the required angular deflection for the actuator

is shown in Fig. 8(a). However, one feature of the func-

tional principle of the actuator is that the maximum angular

deflection θs is constrained by the maximum allowable

1816

displacement xsmax of the pre-compressed springs and varies

as function of the pivot position l1. Fig. 8(a) depicts the

achievable deflection θs for different values of maximum

spring displacement xsmax . It is obvious that by increasing the

maximum displacement of the springs the angular deflection

increases as well. However, the free length of the springs

is increasing which leads to size increment and also for

a given spring diameter the constant of the spring ks is

decreasing. This will have implications to the size of the

actuator assembly. Thus, a proper trade off should be made

according to the application of the actuator in order to

determine the design parameters of the springs. In Fig. 8(b)

it is shown the utilizable range of l1 for different values

of the lever arm length L. By selecting greater lever length

the distance that the pivot needs to cover for stiffness range

300 Nm/rad - 600 Nm/rad increases as well which improves

accuracy but on the other hand increases the dimensions of

the actuator. In Table I the selected design variables for the

realization of the first prototype of CompAct-ARS to be used

in the knee exoskeleton device are presented.

TABLE I

DESIGN VARIABLES OF COMPACT-ARS

Description Symbol Value UnitLever Arm Length L 52 mm

Radius R 26 mmUtilizable Range of l1 r 3.6 mm

Spring rate ks 55 N/mmSpring Diameter ds 24 mm

Spring free length ls 60 mmAllowable Spring Displacement (Max) xsmax 10 mm

The stiffness KS of the elastic mechanism, as formulated

in (8), is shown in Fig. 8(c) with respect to the variation

of the pivot position l1 for different values of spring’s rate

ks while the desired stiffness range is marked. It is also

worthy to mention that the mechanically allowable stiffness

range at the elastic transmission of the prototype is from

200 Nm/rad to 800 Nm/rad (see Table II) and is limited due

to the size of the actuator. Finally, in Fig. 8(e) is evaluated

the performance of CompAct-ARS in terms of elastic torque

as formulated in (6). It is possible to see that the maximum

elastic torque τE which the elastic module can provide to the

output link is 80 Nm (for spring’s rate ks = 55KN/m). This

torque value is close to the maximum torque that knee joint

need for standing up and greater than the required torque

during gait cycle. Finally, Table II depicts the specifications

of the actuator.

IV. ASSISTIVE CONTROL OF KNEE EXOSKELETON

In this section the assistive control is introduced. Fig.

9 presents a schematic of a simplified human body model

attached at the level of the knee with the compliant actuator

CompAct-ARS. In comparison to Fig. 4 and to simplify the

presentation of the assistive control concept the masses of the

thigh and the torso have been combined into a single body of

inertia Iu and mass mu. According to this representation the

300 350 400 450 500 550 60002468

101214161820

K [Nm/rad]

Def

lect

ion

θ s [deg

]

theta desiredxs

max

= 5 mm

xsmax

= 10 mm

xsmax

= 15 mm

(a)

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 620

30

40

50

60

70

80

90

Leve

r Arm

Len

gth

L [m

m]

Utilizable Range of l1 [mm]

(b)

0 0.01 0.02 0.03 0.04 0.05 0.060

100200300400500600700800900

1000

l1 [m]

KS [N

m/ra

d]

ks= 40000 N/m

ks= 55000 N/m

ks= 70000 N/m

Desired StiffnessRange

(c)

0.020.03

0.04

−0.2

0

0.20

200400600800

1000

l1 [m]

Stiffness of Elastic Mechanism

θs [rad]

KS [N

m/ra

d]

(d)

0 2 4 6 8 10 12404550556065707580859095

100

Deflection θs [deg]

Ela

stic

torq

ueτ E

[N

m]

ks= 40000 N/mks= 55000 N/mks= 70000 N/m

(e)

Fig. 8. a) Variation of the angular deflection θs versus stiffness KS fordifferent values of the spring’s rate. b) The utilizable range of l1 withinstiffness range 300 Nm/rad to 600 Nm/rad for different values of length Lof lever arm. c) Stiffness of the elastic mechanism calculated as in (8). d)Stiffness KS as a function of pivot position and angular deflection. e) Elastictorque τE versus deflection.

TABLE II

SPECIFICATIONS OF COMPACT-ARS

Description Symbol Value UnitElastic Torque (Max) τE 80 Nm

Torque of motor (Max) τM 1.53 NmElastic Deflection (Max) θs 11 deg

Elastic Energy (Max) Us 5.5 JAllowable Stiffness Range KS 200 ∼ 800 Nm/rad

Diameter DA 90 mmOverall Length LA 135 mmTotal Weight WA 2.1 kg

motion of the overall system (Human + Knee Exoskeleton)

can be described by the following formula:

IΘ̈+DΘ̇+KΘ+G= τ (10)

where I = diag(Iu, Ie) ∈ R2x2 with Iu being the combined

inertia of the human body, and Ie is the inertia of the knee

exoskeleton motor reflected after the reduction drive. In

addition D ∈ R2x2 is the damping matrix, K ∈ R2x2 is a

symmetric stiffness matrix, G ∈ R2x1 is the gravity matrix

and τ ∈ R2x1 represents the torque vector. In matrix form

1817

Fig. 9. Schematic of simplified human body model attached with the kneeexoskeleton.

(10) can be written as follows:

[Iu 0

0 Ie

][q̈θ̈e

]+

[DS −DS−DS De +DS

][q̇θ̇e

]

+

[KS −KS−KS KS

][qθe

]=

[τh −muglu sinq

τe

](11)

where θe = θmN , θ̇e = θ̇m

N and τe = Nτm are the position,

velocity and torque of the exoskeleton motor respectively

reflected at the link side after the gear reduction (N =100 : 1). In addition, Ie = N2Jm is the reflected after the

reduction drive motor inertia and De = N2(Dm +Kτ Kbem f

Rm) is

the damping of the exoskeleton motor reflected also after

the reduction drive. Kτ and Kbem f are the torque sensitivity

and back EMF constant, Rm is the stator resistance and Dmis the physical damping of the motor. Finally, q, q̇ are the

position and velocity of the knee joint and τh, is the torque

applied by the human. Finally, DS represents the physical

damping in parallel to the actuator spring KS and lu is the

distance from the knee center to the center of mass of the

combined human body. To realize the assistive during the

sitting to standing pose transition we considered a scheme

where the reference torque for the assistive exoskeleton τris derived by the combination of two main components. The

first component τcg is a model based component which is

responsible to partially compensate the gravitational torques

while the second term is an assistive term generated based

on the user’s intended motion. We can write:

τr = τcg + τa = βτg + τa (12)

where τg = mglu sinq is the gravitational torque, β is the

gravity compensation scaling coefficient and τa is the assis-

tive component. A block diagram of the control scheme is

presented in Fig. 10. To generate the assistive torques we

consider the following control law:

τa = Ka(qe −q)−Daq̇ (13)

where qe represents the equilibrium of the assistive spring

damper network (Ka,Da). To generate assistive forces to-

wards the direction of motion here we select to update the

equilibrium position qe in accordance to the user’s intended

Fig. 10. Block diagram of the system and control scheme

motion. The user’s intention in the real system can be

obtained by monitoring the user applied torque. This can be

done by using model based techniques as well as monitoring

the interaction forces between the exoskeleton and user thigh

or through the measurement of electromyographic (EMG)

signals. Based on these an estimated user torque φ(τh) which

is a function of the real torque applied by the human τhcan be obtained. Having derived the estimated user torque

the following formula was used to derive the new desired

position vector qe using the measured force signal.

δqe =

⎧⎨⎩

k f (φ(τh)−a) τh > a0 −a < τh < ak f (φ(τh)+a) τh < a

(14)

qe = qe−1 +δqe (15)

where k f and a are the sensitivity constant and the noise

dead band constant respectively. By injecting the desired

equilibrium position qe derived from (15), into (13) assistive

forces augmenting the user desired actions/motions can be

generated that are governed by the stiffness Ka of the spring

damper network. Combining (13) and (12) the overall control

law can be formulated for the sitting to standing transition

task:

τr = βτg +Ka(qe −q)−Daq̇ (16)

The torque delivered to the human knee from the exoskeleton

is equal to:

τe = KS(θe −q) (17)

Considering that the output torque τe should track the refer-

ence torque given by (16) we can write:

τe = KS(θe −q) = βτg +Ka(qe −q)−Daq̇ (18)

From (18) the desired position of the exoskeleton motor θecan be obtained to track the reference torque τe.

θe =βτg

KS+

Ka

KS(qe −q)− Da

KSq̇+q (19)

The assistive control scheme described by (14), (15),(18)

and (19) was validated through simulation studies. Fig. 11(a)

shows the trajectories generated (spring/damper equilibrium

qe, knee angle q and motor angle θe) from a simulated pulse

1818

shape user torque φ(τh) = 10Nm applied for a period of 0.6

s and a sensitivity coefficient in (14), k f = 0.25. The equilib-

rium position qe is derived by (14) and (15) and the desired

position of the exoskeleton θe is estimated by (19). The trend

of the knee angle q towards the equilibrium position qe is

depicted in Fig. 11(a). Additionally, in Fig. 11(b) are shown

the triggering user torque φ(τh) (in this simulated verification

of the assistive control scheme a step type user torque input

was considered) and the attracting torque τa generated by the

assistive spring damper network (Ka = 200Nm/rad, Da =600Nmsec/rad). Finally, the gravity torque τg and the total

reference force required by the exoskeleton are displayed

considering the gravity compensation scaling coefficient β =1, see (18). The human parameters used in the simulation

study were mu = 30kg and lu = 0.4m.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

time (sec)

(rad

) qeq

θe

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−50

0

50

100

150

time (sec)

(Nm

)

φ(τh)τaτgτr = τg + τa

(b)

Fig. 11. a) Trajectories of the equilibrium position of the assistive network,knee and exoskeleton. b) Torques generated by the device in response tothe user applied torque

V. CONCLUSIONS AND FUTURE WORKS

In this work a new compliant actuator (CompAct-ARS)

was developed and its application to a knee exoskeleton

assistive device was presented. Fundamental starting point

was to derive the mechanical requirements of the actuator

from simulation and experimental data of the standing up and

sitting down. Beneficial feature of the actuator is its ability

to regulate off-line the level of stiffness in order to achieve

suitable passive torque-to-angular displacement profiles for

different users and/or different motion tasks. Finally, the knee

exoskeleton associated with assistive control strategy will

provide motion assistance to the knee of the user.

The principle of operation and design of the actuator

were presented followed by the introduction of the assistive

control scheme. Results from simulations demonstrated the

functionality of the assistive control. Experimental trials will

be carried out shortly using the assistive scheme presented. In

particular, the work will focus on the experimental evaluation

of the knee exoskeleton during sit-to-stand movement cycle

for different stiffness level. Its performance in terms of

power, torque and stored energy will be evaluated through

trials.

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