Abstract

The best exoskeleton control strategy depends on the task, motivating the development and analysis of an exoskeleton capable of position, force, and impedance control. In this paper, we implement and compare the three controller types via sliding mode control on a custom-built pneumatic cylinder ankle exoskeleton. To evaluate each controller's performance, the exoskeleton was tested on the benchtop and with human subject experiments. With the position controller, the exoskeleton achieved an root-mean-square error (RMSE) of under 5 deg for both the benchtop and human tests. It had a bandwidth of approximately 12 rad/s. The force controller tracked sinusoidal trajectories acceptably well at low frequencies (15% of force range at 6 rad/s), with a bandwidth of approximately 24 rad/s. The error was significantly higher (RMSE of 24% of force range) for the more biologically relevant trajectory. The impedance controller demonstrated the desired spring-like behavior, with position RMSE generally under 5 deg compared to expected position. All three controllers worked equally well for benchtop and human tests. Thus, a pneumatically powered ankle exoskeleton with sliding mode control is capable of accurate position and impedance control and is capable of marginally acceptable force control.

References

1.
Aliman
,
N.
,
Ramli
,
R.
, and
Haris
,
S. M.
,
2017
, “
Design and Development of Lower Limb Exoskeletons: A Survey
,”
Rob. Auton. Syst.
,
95
, pp.
102
116
.10.1016/j.robot.2017.05.013
2.
Schröder
,
J.
,
Truijen
,
S.
,
Criekinge
,
T.
, and
Saeys
,
W.
,
2019
, “
Feasibility and Effectiveness of Repetitive Gait Training Early After Stroke: A Systematic Review and Meta-Analysis
,”
J. Rehabil. Med.
,
51
(
2
), pp.
78
88
.10.2340/16501977-2505
3.
Miller
,
L. E.
,
Zimmermann
,
A. K.
, and
Herbert
,
W. G.
,
2016
, “
Clinical Effectiveness and Safety of Powered Exoskeleton-Assisted Walking in Patients With Spinal Cord Injury: Systematic Review With Meta-Analysis
,”
Med. Dev. Evid. Res.
,
9
, pp.
455
466
.10.2147/MDER.S103102
4.
Meng
,
W.
,
Liu
,
Q.
,
Zhou
,
Z.
,
Ai
,
Q.
,
Sheng
,
B.
, and
Shane
,
S.
,
2015
, “
Recent Development of Mechanisms and Control Strategies for Robot-Assisted Lower Limb Rehabilitation
,”
Mechatronics
,
31
, pp.
132
145
.10.1016/j.mechatronics.2015.04.005
5.
Hussain
,
S.
,
Xie
,
S. Q.
, and
Liu
,
G.
,
2011
, “
Robot Assisted Treadmill Training: Mechanisms and Training Strategies
,”
Med. Eng. Phys.
,
33
(
5
), pp.
527
533
.10.1016/j.medengphy.2010.12.010
6.
Krebs
,
H. I.
,
Michmizos
,
K. P.
,
Monterosso
,
L.
, and
Mast
,
J.
,
2016
, “
Pediatric Anklebot: Pilot Clinical Trial
,”
IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics
, Singapore, June 26–29, pp.
662
666
.10.1109/BIOROB.2016.7523701
7.
Li
,
Z.
,
Huang
,
B.
,
Ye
,
Z.
,
Deng
,
M.
, and
Yang
,
C.
,
2018
, “
Physical Human-Robot Interaction of a Robotic Exoskeleton by Admittance Control
,”
IEEE Trans. Ind. Electron.
,
65
(
12
), pp.
9614
9624
.10.1109/TIE.2018.2821649
8.
Pratt
,
G.
, and
Williamson
,
M.
,
1995
, “
Series Elastic Actuators
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots
, Pittsburgh, PA, Aug. 5–9, pp.
399
406
.10.1109/IROS.1995.525827
9.
Huo
,
W.
,
Mohammed
,
S.
,
Moreno
,
J. C.
, and
Amirat
,
Y.
,
2016
, “
Lower Limb Wearable Robots for Assistance and Rehabilitation: A State of the Art
,”
IEEE Syst. J.
,
10
(
3
), pp.
1068
1081
.10.1109/JSYST.2014.2351491
10.
Young
,
A. J.
, and
Ferris
,
D. P.
,
2017
, “
State of the Art and Future Directions for Lower Limb Robotic Exoskeletons
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
25
(
2
), pp.
171
182
.10.1109/TNSRE.2016.2521160
11.
Bryan
,
G. M.
,
Franks
,
P. W.
,
Klein
,
S. C.
,
Peuchen
,
R. J.
, and
Collins
,
S. H.
,
2021
, “
A Hip-Knee-Ankle Exoskeleton Emulator for Studying Gait Assistance
,”
Int. J. Rob. Res.
,
40
(
4–5
), pp.
722
746
.10.1177/0278364920961452
12.
Huang
,
T.-H.
,
Zhang
,
S.
,
Yu
,
S.
,
MacLean
,
M. K.
,
Zhu
,
J.
,
Di Lallo
,
A.
,
Jiao
,
C.
,
Bulea
,
T. C.
,
Zheng
,
M.
, and
Su
,
H.
,
2022
, “
Modeling and Stiffness-Based Continuous Torque Control of Lightweight Quasi-Direct-Drive Knee Exoskeletons for Versatile Walking Assistance
,”
IEEE Trans. Rob.
,
38
(
3
), pp.
1442
1459
.10.1109/TRO.2022.3170287
13.
Goo
,
A.
,
Laubscher
,
C. A.
, and
Sawicki
,
J. T.
,
2022
, “
Hybrid Zero Dynamics Control of an Underactuated Lower-Limb Exoskeleton for Gait Guidance
,” ASME
J. Dyn. Syst., Meas., Control
,
144
(
6
), p.
061008
.10.1115/1.4053946
14.
Moltedo
,
M.
,
Bacek
,
T.
,
Junius
,
K.
,
Vanderborght
,
B.
, and
Lefeber
,
D.
,
2016
, “
Mechanical Design of a Lightweight Compliant and Adaptable Active Ankle Foot Orthosis
,”
Proceedings of the IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics
, Singapore, June 26–29, pp.
1224
1229
.10.1109/BIOROB.2016.7523798
15.
Moltedo
,
M.
,
Cavallo
,
G.
,
Baček
,
T.
,
Lataire
,
J.
,
Vanderborght
,
B.
,
Lefeber
,
D.
, and
Rodriguez-Guerrero
,
C.
,
2019
, “
Variable Stiffness Ankle Actuator for Use in Robotic-Assisted Walking: Control Strategy and Experimental Characterization
,”
Mech. Mach. Theory
,
134
, pp.
604
624
.10.1016/j.mechmachtheory.2019.01.017
16.
Yu
,
S.
,
Huang
,
T. H.
,
Yang
,
X.
,
Jiao
,
C.
,
Yang
,
J.
,
Chen
,
Y.
,
Yi
,
J.
, and
Su
,
H.
,
2020
, “
Quasi-Direct Drive Actuation for a Lightweight Hip Exoskeleton With High Backdrivability and High Bandwidth
,”
IEEE/ASME Trans. Mechatronics
,
25
(
4
), pp.
1794
1802
.10.1109/TMECH.2020.2995134
17.
Elery
,
T.
,
Rezazadeh
,
S.
,
Nesler
,
C.
, and
Gregg
,
R. D.
,
2020
, “
Design and Validation of a Powered Knee-Ankle Prosthesis With High-Torque, Low-Impedance Actuators
,”
IEEE Trans. Rob.
,
36
(
6
), pp.
1649
1668
.10.1109/TRO.2020.3005533
18.
Erdogan
,
A.
,
Celebi
,
B.
,
Satici
,
A. C.
, and
Patoglu
,
V.
,
2017
, “
AssistOn-Ankle: A Reconfigurable Ankle Exoskeleton With Series-Elastic Actuation
,”
Auton. Robots
,
41
(
3
), pp.
743
758
.10.1007/s10514-016-9551-7
19.
Yu
,
H.
,
Huang
,
S.
,
Chen
,
G.
,
Pan
,
Y.
, and
Guo
,
Z.
,
2015
, “
Human-Robot Interaction Control of Rehabilitation Robots With Series Elastic Actuators
,”
IEEE Trans. Rob.
,
31
(
5
), pp.
1089
1100
.10.1109/TRO.2015.2457314
20.
Sawicki
,
G. S.
, and
Ferris
,
D. P.
,
2009
, “
A Pneumatically Powered Knee-Ankle-Foot Orthosis (KAFO) With Myoelectric Activation and Inhibition
,”
J. NeuroEng. Rehabil.
,
6
(
1
), p.
23
.10.1186/1743-0003-6-23
21.
Zhang
,
M.
,
Xie
,
S. Q.
,
Li
,
X.
,
Zhu
,
G.
,
Meng
,
W.
,
Huang
,
X.
, and
Veale
,
A. J.
,
2018
, “
Adaptive Patient-Cooperative Control of a Compliant Ankle Rehabilitation Robot (CARR) With Enhanced Training Safety
,”
IEEE Trans. Ind. Electron.
,
65
(
2
), pp.
1398
1407
.10.1109/TIE.2017.2733425
22.
Jouppila
,
V.
,
Andrew Gadsden
,
S.
, and
Ellman
,
A.
,
2014
, “
Experimental Comparisons of Sliding Mode Controlled Pneumatic Muscle and Cylinder Actuators
,”
ASME J. Dyn. Syst., Meas., Control
,
136
(
4
), p.
044503
. 10.1115/1.4026873
23.
Ohta
,
P.
,
Valle
,
L.
,
King
,
J.
,
Low
,
K.
,
Yi
,
J.
,
Atkeson
,
C. G.
, and
Park
,
Y.-L.
,
2018
, “
Design of a Lightweight Soft Robotic Arm Using Pneumatic Artificial Muscles and Inflatable Sleeves
,”
Soft Rob.
,
5
(
2
), pp.
204
215
.10.1089/soro.2017.0044
24.
Cao
,
Y.
,
Huang
,
J.
,
Xiong
,
C.-H.
,
Wu
,
D.
,
Zhang
,
M.
,
Li
,
Z.
, and
Hasegawa
,
Y.
,
2020
, “
Adaptive Proxy-Based Robust Control Integrated With Nonlinear Disturbance Observer for Pneumatic Muscle Actuators
,”
IEEE/ASME Trans. Mechatronics
,
25
(
4
), pp.
1756
1764
.10.1109/TMECH.2020.2997041
25.
Richer
,
E.
, and
Hurmuzlu
,
Y.
,
2000
, “
A High Performance Pneumatic Force Actuator System: Part I-Nonlinear Mathematical Model
,” ASME
J. Dyn. Syst., Meas., Control
,
122
(
3
), pp.
416
425
.10.1115/1.1286336
26.
Richer
,
E.
, and
Hurmuzlu
,
Y.
,
2000
, “
High Performance Pneumatic Force Actuator System: Part II-Nonlinear Controller Design
,” ASME
J. Dyn. Syst., Meas., Control
,
122
(
3
), pp.
426
434
.10.1115/1.1286366
27.
Shorter
,
K. A.
,
Kogler
,
G. F.
,
Loth
,
E.
,
Durfee
,
W. K.
, and
Hsiao-Wecksler
,
E. T.
,
2011
, “
A Portable Powered Ankle-Foot Orthosis for Rehabilitation
,”
J. Rehabil. Res. Dev.
,
48
(
4
), pp.
459
472
.10.1682/JRRD.2010.04.0054
28.
Slotine
,
J.-J. E.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice Hall
,
Englewood Cliffs, NJ
.
29.
Zhu
,
Y.
, and
Barth
,
E. J.
,
2005
, “
Impedance Control of a Pneumatic Actuator for Contact Tasks
,”
IEEE International Conference on Robotics and Automation
, Barcelona, Spain, Apr. 18–22, pp.
987
992
.10.1109/ROBOT.2005.1570245
30.
Taheri
,
B.
,
Case
,
D.
, and
Richer
,
E.
,
2014
, “
Force and Stiffness Backstepping-Sliding Mode Controller for Pneumatic Cylinders
,”
IEEE/ASME Trans. Mechatronics
,
19
(
6
), pp.
1799
1809
.10.1109/TMECH.2013.2294970
31.
Pinto-Fernandez
,
D.
,
Torricelli
,
D.
,
Sanchez-Villamanan
,
M. D. C.
,
Aller
,
F.
,
Mombaur
,
K.
,
Conti
,
R.
,
Vitiello
,
N.
,
Moreno
,
J. C.
, and
Pons
,
J. L.
,
2020
, “
Performance Evaluation of Lower Limb Exoskeletons: A Systematic Review
,”
IEEE Trans. Neural Syst. Rehabil. Eng.
,
28
(
7
), pp.
1573
1583
.10.1109/TNSRE.2020.2989481
32.
Astrom
,
K. J.
, and
Wittenmark
,
B.
,
1997
,
Computer-Controlled Systems: Theory and Design
,
Prentice Hall
, Upper Saddle River, NJ.
33.
Hodgson
,
S.
,
Tavakoli
,
M.
,
Pham
,
M. T.
, and
Leleve
,
A.
,
2015
, “
Nonlinear Discontinuous Dynamics Averaging and PWM-Based Sliding Control of Solenoid-Valve Pneumatic Actuators
,”
IEEE/ASME Trans. Mechatronics
,
20
(
2
), pp.
876
888
.10.1109/TMECH.2014.2326601
34.
Bovi
,
G.
,
Rabuffetti
,
M.
,
Mazzoleni
,
P.
, and
Ferrarin
,
M.
,
2011
, “
A Multiple-Task Gait Analysis Approach: Kinematic, Kinetic and EMG Reference Data for Healthy Young and Adult Subjects
,”
Gait Posture
,
33
(
1
), pp.
6
13
.10.1016/j.gaitpost.2010.08.009
35.
Gabriel
,
R. C.
,
Abrantes
,
J.
,
Granata
,
K.
,
Bulas-Cruz
,
J.
,
Melo-Pinto
,
P.
, and
Filipe
,
V.
,
2008
, “
Dynamic Joint Stiffness of the Ankle During Walking: Gender-Related Differences
,”
Phys. Ther. Sport
,
9
(
1
), pp.
16
24
.10.1016/j.ptsp.2007.08.002
36.
Ren
,
H.
, and
Fan
,
J.
,
2016
, “
Adaptive Backstepping Slide Mode Control of Pneumatic Position Servo System
,”
Chin. J. Mech. Eng.
,
29
(
5
), pp.
1003
1009
.10.3901/CJME.2016.0412.050
37.
Yang
,
J.
,
Sun
,
T.
,
Cheng
,
L.
, and
Hou
,
Z.-G.
,
2023
, “
Spatial Repetitive Impedance Learning Control for Robot-Assisted Rehabilitation
,”
IEEE/ASME Trans. Mechatronics
,
28
(
3
), pp.
1280
1290
.10.1109/TMECH.2022.3221931
38.
Lee
,
H.
, and
Utkin
,
V. I.
,
2007
, “
Chattering Suppression Methods in Sliding Mode Control Systems
,”
Annu. Rev. Control
,
31
(
2
), pp.
179
188
.10.1016/j.arcontrol.2007.08.001
You do not currently have access to this content.