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adfa, p. 1, 2011.
© Springer-Verlag Berlin Heidelberg 2011
Development of Series Elastic Actuators for Physical
Rehabilitation Devices
Nhat Tan Pham1, Van Tien Anh Nguyen1, Nhat Dang Khoa Nguyen1,
Tan Tien Nguyen2, and Sang Bong Kim3
1 HiTech Mechatronics Lab, Hochiminh City Univ. of Technology (HCMUT), Vietnam
{phamnhattan309, nvtienanh, dangkhoa.bk11}@gmail.com
2 Bach Khoa Research Center for Manufacturing Eng., HCMUT, Vietnam
nttien@hcmut.edu.vn
3 Dept. of Mechanical and Automotive Eng., Pukyong National Univ., Korea
kimsb@pknu.ac.kr
Abstract. Active training in rehabilitation requires that the actuator of robotic
devices must have ability to control the physical interaction with the patient. This
paper studies the characteristic of Series Elastic Actuator (SEA) and proposes
using this actuator for active training. The results showed that, by a simple con-
troller, SEA shows potential of good interactive force/torque control. And be-
cause of its low cost and simplicity, it can make the rehabilitation robotic devices
more affordable to many patients.
Keywords: Series Elastic Actuator, Rehabilitation, Cerebral Palsy
1 Introduction
Rehabilitation Robotic devices for motor skill training quickly became important
beside conventional rehabilitation which based on functional training with physiother-
apists. These devices bring significant benefit to patients living with motor impairment
which caused by cerebral palsy, Parkinson's disease, spinal cord injury, stroke , trau-
matic brain injury , amyotrophic lateral sclerosis, etc. [1]
Neuroscience has proved that the brain has neuroplasticity capacity, so by intensive
and active training based on motor learning principle, the brain can recover from dam-
age structure and connections which lead to motor impairment [2].
Intensive training is the repetition of simple tasks that require the patient focus to
complete. Robotic devices are suitable for this training because of ability to operate
frequently, daily and less costly compared to conventional training with physiotherapist
[3]. When combination with interactive video games, the patient can focus on their
tasks which lead to enhancement of recovery of motor function [4]. Robotic devices
also have benefit of collecting feedback information for evaluation and modification of
training task by physiotherapist (Fig. 1).
Active training means that, during a training task, the patients move follow a trajec-
tory with their effort, their cognition of doing this task. Research showed that, for opti-
mal motor skills learning and recovery process, the patients should be as active as pos-
sible and the level of assistance of a task should be decreased over time [5].
The assistance in training can be classified into four types:
Passive: task with fully assistance from device or physiotherapist.
Assist-as-needed: sufficient assistance.
Active-free: no assistance, patients complete the task by themselves.
Active-resisted: resist completing the task of patients [6].
For active training, robotic devices must have the capability to adjust the level of
assistance from assist-as-needed, active-free to active-resisted. This means that the ac-
tuator of robotic devices must have good qualification for interaction control including
interactive force/torque control, mechanical impedance/admittance control. And Series
Elastic Actuator is one of actuators that can satisfy these requirement.
Physiotherapist Patient
Robotic device
Diagnostic
Physical
Rehabilitation
Fig. 1. Physical rehabilitation using robotic devices
2 Series Elastic Actuator Principle
Series Elastic Actuator (SEA) is first presented in 1995 showing the good quality
of interaction control for natural task [7]. Since then, SEA has applied to many interac-
tive robotic problem such as: stable walking of humanoid robot, safety cooperating with
human of industrial robot and active training of rehabilitation.
Compare to conventional stiffness actuator use in rehabilitation such as electronic
motor with gearbox in Continuous Passive Motion devices (CPM devices), SEA also
has the same stiffness part but with additional compliance part like compression spring
placed serially and interacting with patient’s part such as hand, ankle, knee. (Fig. 2)
T
M
ω
M
DC Moto r
Gearbox
J
eq
, n, η, B
Compress ion spring
T
L
ω
o
T
L
ω
L
Patient
Complia nce part
K
s
Load
Stiffness part
K
T,
K
EMF
V
IN
R
L
V
EMF
+
–+
–
I
Fig. 2. SEA model
Modeling and control
Stiffness part of SEA supply energy in form of velocity source or force/torque
source. In this paper, stiffness part including DC motor and gearbox is built and con-
trolled as a velocity source for easy implementation.
The dynamic of stiffness part is showed as Eq. 1 with the virtual input included
controllable voltage input and a load compensation term as Eq. 2.
()
()=
đ..+(. +.). +(.+.)
(1)
= +.
.
. ≈
.
.
(2)
Generally, in low frequency, the second-order system (Eq. 1) can be approximated
to a first-order system (Eq. 3) with high precision.
()
()=
(3)
Velocity source is based on a velocity controller which include a feedback term and
a feedforward term as follows:
=1
._.().
(4)
()=()
() =1
1+ /(_ )
(5)
The system is always stable when _ ≥ and as show in Fig. 3, it independence
from interactive torque TL if the load is still inside the operational region of the DC
motor.
0 0.5 1 1.5 2 2.5 3 3.5 4
Speed
(rad/s)
0
0.01
0.02 With load compe sation
0 0.5 1 1.5 2 2.5 3 3.5 4
Speed
(rad/s)
-2
0
2Without load com pesatio n
Time (s)
0 0.5 1 1.5 2 2.5 3 3.5 4
Load
(N.m)
0
2
4Load
Fig. 3. Simulation of velocity source with pulse loads.
As present in the research [8], this velocity source is apply to control the interactive
force/torque as following controller
= _.()
(6)
The interactive force depends on the reference force and the movement of the load
()=.._.()
+.._ ()..
+.._
(7)
Fig. 4. Simulink model of force control base on a velocity source
Simple loop gains are applied in the controllers for evaluate the main characteristic
of the SEA. For better quality of controller, these loop gains in velocity controller and
force controller then placed by PID controller (as showed in Fig. 4), with the same
proportional term as gain to ensure stability, small integral term to compensator settling
error and small derive term to decrease system oscillation.
Placing a compliance part causes to lower mechanical output impedance, and giving
interesting characteristic for interaction control of SEA that include:
Lower force bandwidth but better suitable for reality implementation of force con-
trol
As showed in equation, when the load is fixed,
()
()=1
.._ +1
(8)
The cutoff frequency of this system is .._. Increasing stiffness Ks also in-
crease the force bandwidth. But in reality, increasing stiffness (output impedance) re-
quire higher resolution of sensors and higher quality of gearbox (less backlash, high
efficiency) and electronic motor (no cogging, small inertia, less friction). For rehabili-
tation training task operating in low frequency, using compliance element decrease the
requirement of high quality system [8]. Especially, the interactive force can be meas-
ured through the displacement of the spring. That make SEA low cost, and affordable
for rehabilitation devices.
Shock tolerant and back-drive ability.
The main reason that SEA is good at interactive force control is that the movement
of the load is less affect to the interactive force when compare to stiffness actuator
because of its low output impedance.
()=()
()=
+.
(9)
Decreasing the stiffness decreases the overall output impedance. In high fre-
quency, the output impedance is the stiffness of the spring (Eq. 10)
( → ∞)=
(10)
When shock or impact at high frequency by a load with momentum , low stiffness
Ks extents the impact time which is proportional to the time constant
.
= .(0)=.
≈ .
(11)
High shock tolerant and low output impedance cause the SEA having back-drivabil-
ity and safety. SEA only applies small interactive force on the load and suitable for
active-free training where the SEA doesn’t affect the movement of the patient.
Requirement of faster electronic motor
To ensure the good performance, every operational point (operating locus) of DC
motor much be inside its operational region. Compare to stiffness actuator, SEA much
require the higher velocity for the same task because of the compliance. Institutionally,
lower output compliance good for interactive force control but also means the DC mo-
tor much move faster for the same force trajectory compare to stiffness actuator. As
showed in Fig. 5, choosing the smallest stiffness and ensuring the operating locus of
DC motor is still inside operating region.
Torque (mN.m)
0 50 100 150 20 0 250
Velocity (rpm)
0
1000
2000
3000
4000
5000
6000
7000
8000
Fig. 5. Examples of choosing spring stiffness.
3 Apply SEA to Rehabilitation Devices
3.1 Real problem of the patient
In this paper, the rehabilitation devices are designed for a patient with spastic cerebral
palsy (CP). This disease is caused by the damage of motor system which leads to muscle
tightness at the right wrist and left ankle as showed in Fig. 6. Intensity active training
is needed to recovery the connection between motor system and the muscles.
The patient needs passive training as traditional physical therapy (Fig. 7) to maintain
the range of motion (ROM) of the impairment joints; and with increasing in difficulty
from assist as needed training to resisted training for the recovery.
Fig. 6. The muscle tightness at right wrist and left ankle of the patient
Fig. 7. Passive training at the right wrist
Rehabilitation devices based on SEA are designed for all above types of training.
For passive training, the devices must support enough force/torque to the extension and
flexion movement of the left wrist and right ankle at full ROM when the patient relaxes
their muscle (Fig. 8).
70
o
0
o
90
o
Torque
(a)
0
1000
2000
3000
30
o
60
o
90
o
0
o
70
o
Torque (mN.m)
(b)
Fig. 8. Torque supplied during passive training of full ROM for dorsiflexion of wrist joint (a)
when the patient relaxes the muscles. Measured directly by the wrist devices (b).
The requirement of supplying torque for passive training always larger than active-
free and assist-as-needed. For active-resisted training, the more strong motor, the more
resistive level that the SEA can produce to make more difficult to the patient.
Assume that the passive training happen at low speed, the minimum requirement of
SEA for wrist devices
Output torque: 2
Frequency at full ROM: 0.2
3.2 Mechanical design of ankle and wrist rehabilitation device
Two type of SEA are designed for rehabilitation devices including rotary SEA for
wrist device and linear SEA for ankle device showed in Fig. 9. The interactive
force/torque is determined through measuring the displacement of the compression
springs by a potentiometer. This measure is used for controller.
Load
Gear box
DC motor
Motor
Belt transmission
Load
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
(a) (b)
Fig. 9. Mechanical design of rotary SEA (a) and linear SEA (b) including: (1) DC motor with
encoder; (2) transmission; (3) compression spring with potentiometer; (4) connect to a load.
Both devices using DC motor, model NISCA NA4056. Through the transmission, it
can produce approximately 6 stall torque and 4/ no load speed for the wrist
device; 10 stall torque and 2/ no load speed for the ankle device.
(a)
(b)
Fig. 10. Rehabilitation devices based on SEA for the wrist joint (a) and the ankle joint (b)
3.3 Control strategy for assistance
Passive training base on position control of the stiffness part (ignore small displacement
of the compliant part), the movement of patient is forced to follow the sinusoid trajec-
tory. The minimum torque is required for passive training showed in Fig. 8, and it de-
pends on the position of the wrist.
BRAIN
Red dot following game
Connect ion
Impairme nt
Eye
Feedback
Torque T
L
Movement ω
L
REHABILI TATION
DEVICE
Trajectory of red dot
WRIST
SCORE: 0
Fig. 11. Mechanism of a training task
Dorsiflexion angle (degree)
-10 0 10 20 30 40 50 60 70
Torque (mN.m)
0
500
1000
1500
2000
2500 Full support
Torque f or passive training
Desired torque
Dorsiflexion angle (degree)
-10 0 10 20 30 40 50 60 70
Torque (mN.m)
0
500
1000
1500
2000
2500 Assit-As-Need ed
Torque f or passive training
Desired torque
-10 0 10 20 30 40 50 60 70
-500
0
500
1000
1500
2000
2500 Activ e-free
Dorsiflexion angle (degree)
Torque (mN.m)
Torque f or passive training
Desired torque
Dorsiflexion angle (degree)
-10 0 10 20 30 40 50 60 70
-500
0
500
1000
1500
2000
2500 Active-resisted
Torqu e (mN .m)
Torque f or passive training
Desired torque
Fig. 12. Desired torque for each training type.
In passive training, the movement of impairment joint doesn’t depend on cognition
of the patient. For recovery process, the patient needs active training. This means that
the patient must show their effort when doing a training task.
A training task (as showed in Fig. 11) is designed in form of an interactive game.
The goal is make the patient follows a reference trajectory by their effort with a support
or a resistance from the devices.
For active training, depend on the assistant level of the device, it controls the inter-
active torque TL as a function of extension angle of the joint (Fig. 12). Desired torque
trajectory is modified to suit with each patient and treatment method.
3.4 Performance
Bode Diagram
Frequen cy (rad/s)
10
0
10
1
10
2
10
3
-90
-45
0
Phase (de g)
-20
-15
-10
-5
0
5
Magnitude (dB)
Simulation
Amplitude 1,2 N.m
Amplitude 0,6 N.m
From T
d
to T
L
Dorsiflexion angle (degree)
-10 0 10 20 30 40 50 60 70 80
Torque (mN.m)
-500
0
500
1000
1500
2000
2500
3000
Desired torque
Measured torque
(a) (b)
Fig. 13. Performance of SEA torque controller: (a) frequency response of SEA; (b) torque tra-
jectory following.
Active training based on interactive force/torque control of SEA. As mentioned
above, the compliance part of SEA decreases force/torque bandwidth. However, for
rehabilitation application operating at low frequency such as movement of full ROM at
0,2Hz, the current design (Fig. 13a), can easily satisfy the requirement.
A simple controller as Eq. 6 is used so the performance is strongly dependent on the
movement of the patient. Fig. 13b shows the torque following a trajectory during a
training task. Higher quality controller is required for higher performance, but for a
training task where the device interacts with human, this performance is acceptable.
3.5 Assessment of the training result.
To assess the training result, this paper proposes a measuring method. For each assistant
level:
= 1 1
∫| () ()|
1
∫| ()|
(12)
The task-completion rate can describe the effort of the patient to complete a task in
active training. For passive training, the joint is fully supported from the devices, so
task completion rate is always 100%. For active training, the more effort, the higher
task-completion rate (Fig. 14). This rate is tracked for the doctor/physiotherapy.
Passive training
Active-free with
zero effort
Active-free
with effort
Task-completion
rate
0% 100%
Time
100%
0%
Fig. 14. Assessment of the training result.
4 Conclusion
Two rehabilitation device were designed based on the SEA. The wrist device is being
applied to the patient for daily training. The training result is gathered for the assess-
ment of the doctor. The ankle device is still under development. A simple interactive
torque controller based on velocity source and an assessment method was proposed and
experiment for active training task. These devices show potential for physical rehabili-
tation and future research in rehabilitation robotics.
References
1. Krebs, H., Dipietro, L., Levy-Tzedek, S., Fasoli, S., Rykman-Berland, A., Zipse, J.,
Fawcett, J., Stein, J., Poizner, H., Lo, A., Volpe, B., Hogan, N.: A paradigm shift
for rehabilitation robotics. IEEE Eng. Med. Biol. Mag. 27, 61–70 (2008).
2. Nudo, R.J.: Recovery after brain injury: mechanisms and principles. Front. Hum.
Neurosci. 7, (2013).
3. Huang, V.S., Krakauer, J.W.: Robotic neurorehabilitation: a computational motor
learning perspective. J. NeuroEngineering Rehabil. 6, 5 (2009).
4. Lohse, K., Shirzad, N., Verster, A., Hodges, N., Van der Loos, H.F.M.: Video
Games and Rehabilitation: Using Design Principles to Enhance Engagement in
Physical Therapy. J. Neurol. Phys. Ther. 37, 166–175 (2013).
5. Snapp-Childs, W., Casserly, E., Mon-Williams, M., Bingham, G.P.: Active Pro-
spective Control Is Required for Effective Sensorimotor Learning. PLoS ONE. 8,
e77609 (2013).
6. Alcocer, W., Vela, L., Blanco, A., Gonzalez, J., Oliver, M.: Major trends in the de-
velopment of ankle rehabilitation devices. Dyna. 79, 45–55 (2012).
7. Pratt, G.A., Williamson, M.M.: Series elastic actuators. In: Intelligent Robots and
Systems 95.’Human Robot Interaction and Cooperative Robots’, Proceedings. 1995
IEEE/RSJ International Conference on. pp. 399–406. IEEE (1995).
8. Paine, N.A.: High-performance series elastic actuation, https://reposito-
ries.lib.utexas.edu/handle/2152/26938, (2014).
