Abstract

Artificial muscles (AMs) traditionally rely on pneumatic sources of fluid power. The use of hydraulics can increase the power and force to weight and volume ratios of AM actuators. This paper develops a control-centric third-order single-input single-output (SISO) lumped-parameter dynamic model and sliding mode position controller based on Filippov's principle of equivalent dynamics for a braided hydraulic artificial muscle (HAM) actuator. The model predicts the nonlinear behavior of the HAM free contraction and captures the fluid and actuator nonlinear dynamic interactions in addition to the braid deformation. Model simulations are compared to experimental results for quasi-static pressurization, isometric pressurization, and open-loop square wave commands at 0.25, 0.5, and 1 Hz. Experiments of sine wave tracking at 0.25, 0.5, and 1 Hz and continuous square wave tracking at 0.067 Hz are conducted using a sliding mode controller (SMC) derived from the model. The SMC achieves a steady-state error of 6 μm at multiple setpoints within the actuator's 17 mm stroke. Compared to a proportional-integral-derivative (PID) controller, the SMC root-mean-square (RMS) error, mean error, and absolute maximum error are reduced on average by 53%, 61%, and 44%, respectively, demonstrating the benefit of model-based approaches for controlling HAMs.

References

References
1.
Yoshinada
,
H.
,
Yamazaki
,
T.
,
Suwa
,
T.
,
Naruse
,
T.
, and
Ueda
,
H.
,
1991
, “
Seawater Hydraulic Actuator System for Underwater Manipulator
,”
Fifth International Conference on Automation and Robotics
, Vol.
2
,
Pisa, Italy
,
June 19–22
, pp.
1300
1335
.10.1109/ICAR.1991.240458
2.
Zengmeng
,
Z.
,
Jiaoyi
,
H.
,
Zhengwen
,
S.
,
Yongjun
,
G.
, and
Jian
,
M.
,
2014
, “
Analysis and Simulation on Drive Characteristics of High-Strength Water Hydraulic Artificial Muscles
,”
Adv. Mater. Res.
,
889–890
, pp.
448
492
. 10.4028/www.scientific.net/AMR.889-890.488
3.
Zengmeng
,
Z.
,
Yongjun
,
G.
, and
Jiaoyi
,
H.
,
2014
, “
Drive Characteristics Analysis and Test System Design for Water Hydraulic Artificial Muscle
,”
Appl. Mech. Mater.
,
511–512
, pp.
737
742
.10.4028/www.scientific.net/AMM.511-512.737
4.
Bryant
,
M.
,
Fitzgerald
,
J.
,
Miller
,
S.
,
Saltzman
,
J.
,
Kim
,
S.
,
Lin
,
Y.
, and
Garcia
,
E.
,
2014
, “
Climbing Robot Actuated by Meso-Hydraulic Artificial Muscles
,”
SPIE
9057
, p. 90570H.10.1117/12.2046368
5.
Chipka
,
J. B.
,
Meller
,
M. A.
, and
Garcia
,
E.
,
2015
, “
Efficiency Testing of Hydraulic Artificial Muscles With Variable Recruitment Using a Linear Dynamometer
,”
Proc. SPIE
,
9429
(
16
), p.
942916
.10.1117/12.2084460
6.
Iwata
,
K.
,
Suzumori
,
K.
, and
Wakimoto
,
S.
,
2012
, “
A Method of Designing and Fabricating McKibben Muscles Driven by 7 MPa Hydraulics
,”
Int. J. Autom. Technol.
,
6
(
4
), pp.
482
487
.10.20965/ijat.2012.p0482
7.
Sangian
,
D.
,
Naficy
,
S.
,
Spinks
,
G.
, and
Tondu
,
B.
,
2015
, “
The Effect of Geometry and Material Properties on the Performance of a Small Hydraulic McKibben Muscle System
,”
Sens. Actuators
,
234
, pp.
150
157
.10.1016/j.sna.2015.08.025
8.
Ku
,
K. K.
,
Bradbeer
,
R.
,
Lam
,
K.
, and
Yeung
,
L.
,
2008
, “
Exploration for Novel Uses of Air Muscles as Hydraulic Muscles for Underwater Actuator
,”
Oceans 2008 MTS/IEEE
,
Kobe, Japan
,
Apr. 8–11
, pp.
1
6
.10.1109/OCEANSKOBE.2008.4530989
9.
Meller
,
M. A.
,
Bryant
,
M. J.
, and
Garcia
,
E.
,
2013
, “
Energetic and Dynamic Effects of Operating Fluid on Fluidic Artificial Muscles
,”
ASME
Paper No. SMASIS2013-3210.https://asmedigitalcollection.asme.org/SMASIS/proceedings-abstract/SMASIS2013/56048/V002T06A019/282027
10.
Sangian
,
D.
,
Naficy
,
S.
, and
Spinks
,
G. M.
,
2016
, “
Thermally Activated Paraffin-Filled McKibben Muscles
,”
J. Intell. Mater. Syst. Struct.
,
27
(
18
), pp.
2508
2509
.10.1177/1045389X16633766
11.
Xiang
,
C.
,
Giannaccini
,
M. E.
,
Theodoridis
,
T.
,
Hao
,
L.
,
Neft-Meziani
,
S.
, and
Davis
,
S.
,
2016
, “
Variable Stiffness McKibben Muscles With Hydraulic and Pneumatic Operating Modes
,”
J. Adv. Rob.
,
30
(
13
), pp.
889
899
.10.1080/01691864.2016.1154801
12.
Mori
,
M.
,
Suzumori
,
K.
,
Seita
,
S.
,
Takahashi
,
M.
,
Hosoya
,
T.
, and
Kusumoto
,
K.
,
2009
, “
Development of Very High Force Hydraulic McKibben Artificial Muscle and Its Applications to Shape-Adaptable Power Hand
,”
IEEE International Conference on Robotics and Biomimetics
,
Guilin, China
, Dec. 19–23, pp.
1457
1462
.10.1109/ROBIO.2009.5420382
13.
Chapman
,
E.
,
Macleod
,
M.
, and
Bryant
,
M.
,
2015
, “
Electrohydraulic Modeling of a Fluidic Artificial Muscle Actuation System for Robot Locomotion
,”
ASME
Paper No. SMASIS2015-8834.10.1115/SMASIS2015-8834
14.
Tiwari
,
R.
,
Meller
,
M.
,
Wajcs
,
K.
,
Moses
,
C.
,
Reveles
,
I.
, and
Garcia
,
E.
,
2012
, “
Hydraulic Artificial Muscles
,”
J. Intell. Mater. Syst. Struct.
,
23
(
3
), pp.
301
312
.10.1177/1045389X12438627
15.
Mori
,
M.
,
2010
, “
Development of Power Robot Hand With Shape Adaptability Using Hydraulic McKibben Muscles
,”
IEEE International Conference on Robotics and Automation
,
Anchorage, AK
,
May 3–7
, pp.
1162
1168
.10.1109/ROBOT.2010.5509489
16.
Department of Energy
,
2012
, “
Estimating the Impact (Energy Emissions and Economics) of the United States Fluid Power Industry
,”
Oak Ridge National Laboratory and UT-Battelle
,
Oak Ridge, TN
.10.2172/1061537
17.
Hannaford
,
B.
, and
Winters
,
J.
,
1990
, “
Multiple Muscle Systems: Biomechanics and Movement Organization
,”
Actuator Properties and Movement Control: Biological and Technical Models
,
Springer-Verlag
,
New York
, pp.
101
120
.
18.
Slightam
,
J. E.
, and
Nagurka
,
M. L.
,
2019
, “
Theoretical Modeling, Analysis, and Experimental Results of a Hydraulic Artificial Muscle Prototype
,”
ASME
Paper No. FPMC2019-1654.10.1115/FPMC2019-1654
19.
Meller
,
M. A.
,
Bryant
,
M.
, and
Garcia
,
E.
,
2014
, “
Reconsidering the McKibben Muscle: Energetics, Operating Fluid, and Bladder Material
,”
J. Intell. Mater. Syst. Struct.
,
25
(
18
), pp.
2276
2293
.10.1177/1045389X14549872
20.
Gaylord
,
R.
,
1957
, “
Fluid Actuated Motor System and Stroking Device
,” U.S. Patent No. 2844126.
21.
Chou
,
C.-P.
, and
Hannaford
,
B.
,
1996
, “
Measurement and Modeling of McKibben Pneumatic Artificial Muscles
,”
IEEE Trans. Rob. Autom.
,
12
(
1
), pp.
90
102
.
22.
Tang
,
T.
,
Chong
,
S.
,
Tan
,
M.
,
Chan
,
C.
, and
Sato
,
K.
,
2016
, “
Characterization of Pneumatic Artificial Muscle System in an Opposing Pair Configuration
,”
J. Telecommun., Electron. Comput. Eng.
,
8
(
2
), pp.
73
77
. https://journal.utem.edu.my/index.php/jtec/article/view/960
23.
Liu
,
H.
,
Zhao
,
Y.
,
Jiang
,
F.
, and
Yao
,
X.
,
2015
, “
Pneumatic Muscle Actuator Position Control Based on Sliding Mode Control Algorithms
,”
IEEE International Conference on Information and Automation
,
Lijiang, China
,
Aug. 8–10
, pp.
1115
1120
.10.1109/ICInfA.2015.7279453
24.
Driver
,
T. A.
, and
Shen
,
X.
,
2014
, “
Design and Control of a Sleeve Muscle-Actuated Robot Elbow
,”
ASME J. Dyn. Syst. Meas. Control
,
136
(
4
), p.
041023
.10.1115/1.4026834
25.
Kang
,
B.
,
Kothera
,
C.
,
Woods
,
B.
, and
Wereley
,
N.
,
2009
, “
Dynamic Modeling of McKibben Pneumatic Artificial Muscles for Antagonistic Actuation
,”
International Conference on Robotics and Automation
,
Kobe, Japan
,
May 12–17
, pp.
182
187
.10.1109/ROBOT.2009.5152280
26.
Tondu
,
B.
, and
Lopez
,
P.
,
2000
, “
Modeling and Control of McKibben Artificial Muscle Robot Actuators
,”
IEEE Control Syst. Mag.
,
20
(
2
), pp.
15
38
.10.1109/37.833638
27.
Pitel'
,
J.
, and
Tóthová
,
M.
,
2013
, “
Dynamic Modeling of PAM Based Actuator Using Modified Hill's Muscle Model
,”
IEEE Carpathian Control Conference
,
Rytro, Poland
,
May 26–29
.10.1109/CarpathianCC.2013.6560559
28.
Kerscher
,
T.
,
Albiez
,
J.
,
Zollner
,
J.
, and
Dillmann
,
R.
,
2006
, “
Evaluation of the Dynamic Model of Fluidic Muscles Using Quick-Release
,”
IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics
,
Rytro, Poland
,
May 26–29, Feb. 20–22
, pp.
307
310
.10.1109/BIOROB.2006.1639161
29.
Hosovsky
,
A.
, and
Havran
,
M.
,
2012
, “
Dynamic Modeling of One Degree of Freedom Pneumatic Muscle-Based Actuator for Industrial Applications
,”
Tech. Gazette
,
19
(
3
), pp.
673
681
.https://www.researchgate.net/publication/274698812_Dynamic_Modeling_of_One_Degree_of_Freedom_Pneumatic_Muscle-based_Actuator_for_Industrial_Applications
30.
Robinson
,
R. M.
,
Kothera
,
C. S.
,
Sanner
,
R. M.
, and
Wereley
,
N. M.
,
2016
, “
Nonlinear Control of Robotic Manipulators Driven by Pneumatic Artificial Muscles
,”
IEEE/ASME Trans. Mechatronics
,
21
(
1
), pp.
55
68
.10.1109/TMECH.2015.2483520
31.
Sarosi
,
J.
,
Biro
,
I.
,
Nemeth
,
J.
, and
Cveticanin
,
L.
,
2015
, “
Dynamic Modeling of a Pneumatic Muscle Actuator With Two Directional Motion
,”
Mech. Mach. Theory
,
85
, pp.
25
34
.10.1016/j.mechmachtheory.2014.11.006
32.
Slightam
,
J. E.
, and
Nagurka
,
M. L.
,
2016
, “
PID Sliding Mode Control of Prolate Flexible Pneumatic Actuators
,”
ASME
Paper No. DSCC2016-9705.10.1115/DSCC2016-9705
33.
Doumit
,
M.
, and
Leclair
,
J.
,
2017
, “
Development and Testing of Stiffness Model for Pneumatic Artificial Muscles
,”
Int. J. Mech. Sci.
,
120
, pp.
30
41
.10.1016/j.ijmecsci.2016.11.015
34.
Slightam
,
J. E.
, and
Nagurka
,
M. L.
,
2017
, “
Robust Control of Pneumatic Artificial Muscles
,”
ASME
Paper No. FPMC2017-4225.https://asmedigitalcollection.asme.org/FPST/proceedings-abstract/FPMC2017/58332/V001T01A009/233785
35.
Kothera
,
C.
,
Jangid
,
M.
,
Sirohi
,
J.
, and
Wereley
,
N.
,
2009
, “
Experimental Characterization and Static Modeling of McKibben Actuators
,”
ASME J. Mech. Des.
,
131
(
9
), p.
091010
.10.1115/1.3158982
36.
Ball
,
E.
, and
Garcia
,
E.
,
2016
, “
Effects of Bladder Geometry on Pnuematic Artificial Muscles
,”
ASME J. Med. Devices
,
10
(
4
), p.
041001
.10.1115/1.4033325
37.
Meller
,
M.
,
Kogan
,
B.
,
Bryant
,
M.
, and
Garcia
,
E.
,
2018
, “
Model-Based Feedforward and Cascade Control of Hydraulic McKibben Muscles
,”
Sens. Actuators, A
,
3
(
23
).
38.
Focchi
,
M.
,
Guglielmino
,
E.
,
Semini
,
C.
,
Parmiggiani
,
A.
,
Tsagarakis
,
N.
,
Vanderborght
,
B.
, and
Caldwell
,
D.
,
2010
, “
Water/Air Performance Analysis of a Fluidic Muscle
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Taipei, Taiwan
,
Oct. 18–22
, pp.
2194
2199
.10.1109/IROS.2010.5650432
39.
Slightam
,
J. E.
,
Nagurka
,
M. L.
, and
Barth
,
E.
,
2018
, “
Sliding Mode Impedance Control of a Hydraulic Artificial Muscle
,”
ASME
Paper No. DSCC2018-9186.10.1115/DSCC2018-9186
40.
Dasmahapatra
,
S.
,
Saha
,
R.
,
Mookherjee
,
S.
, and
Sanyal
,
D.
,
2018
, “
Designing an Input-Linearized Adaptive Sliding Mode Coupled Nonlinear Integral Controller
,”
IEEE/ASME Trans. Mechatronics
,
23
(
6
), pp.
2888
2895
.10.1109/TMECH.2018.2870911
41.
Won
,
D.
,
Kim
,
W.
, and
Tomizuka
,
M.
,
2017
, “
High-Gain-Observer-Based Integral Sliding Mode Control for Position Tracking of Electrohydraulic Servo Systems
,”
IEEE/ASME Trans. Mechatronics
,
22
(
6
), pp.
2695
2704
.10.1109/TMECH.2017.2764110
42.
Sun
,
G.
, and
Ma
,
Z.
,
2017
, “
Practical Tracking Control of Linear Motor With Adaptive Fractional Order Terminal Sliding Mode Control
,”
IEEE/ASME Trans. Mechatronics
,
22
(
6
), pp.
2643
2653
.10.1109/TMECH.2017.2766279
43.
Comber
,
D.
,
Barth
,
E.
, and
Webster
,
R.
, III
,
2014
, “
Design and Control of an MR-Compatible Precision Pneumatic Active Cannula Robot
,”
ASME J. Med. Devices
,
8
(
1
), p.
011003
.10.1115/1.4024832
44.
Comber
,
D. B.
,
Slightam
,
J. E.
,
Gervasi
,
V. R.
,
Neimat
,
J.
, and
Barth
,
E. J.
,
2016
, “
Design, Additive Manufacture, and Control of a Pneumatic MR-Compatible Needle Driver
,”
IEEE Trans. Rob.
,
32
(
1
), pp.
138
149
.10.1109/TRO.2015.2504981
45.
Slightam
,
J.
, and
Nagurka
,
M.
,
2020
, “
Theoretical Dynamic Modeling and Validation of Braided Pneumatic Artificial Muscles
,”
ASME J. Dyn. Syst. Meas. Control
,
142
(
3
), p.
031008
.10.1115/1.4045475
46.
Slightam
,
J. E.
, and
Nagurka
,
M. L.
,
2018
, “
Modeling of Pneumatic Artificial Muscle With Kinetic Friction and Sliding Mode Control
,”
American Control Conference
,
Milwaukee, WI
, Jun. 27–29, pp.
3342
3347
.10.23919/ACC.2018.8431190
47.
Klute
,
G.
, and
Hannaford
,
B.
,
2000
, “
Accounting for Elastic Energy Storage in McKibben Artificial Muscles
,”
ASME J. Dyn. Syst. Meas. Control
,
122
(
2
), pp.
386
388
.10.1115/1.482478
48.
Thomalla
,
S.
, and
Van De Ven
,
J.
,
2018
, “
Modeling and Implementation of the McKibben Actuator in Hydraulic Systems
,”
IEEE Trans. Rob.
,
34
(
6
), pp.
1593
1602
.10.1109/TRO.2018.2864780
49.
Davis
,
S.
,
Tsagarakis
,
N.
,
Canderle
,
J.
, and
Caldwell
,
D. G.
,
2003
, “
Enhanced Modeling and Performance in Braided Pneumatic Muscle Actuators
,”
Int. J. Rob. Res.
,
22
(
3–4
), pp.
213
227
.10.1177/0278364903022003006
50.
Davis
,
S.
, and
Caldwell
,
D. G.
,
2006
, “
Braid Effects on Contractile Range and Friction Modeling in Pneumatic Artificial Muscles
,”
Int. J. Rob.
,
25
(
4
), pp.
359
369
.10.1177/0278364906063227
51.
Richer
,
E.
, and
Hurmuzlu
,
Y.
,
2000
, “
A 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
52.
Slotine
,
J.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice Hall
,
Upper Saddle River, NJ
.
53.
Slightam
,
J.
,
2019
, “
High Fidelity Dynamic Modeling and Nonlinear Control of Fluidic Artificial Muscles
,” Ph.D. dissertation,
Marquette University
,
Milwaukee, WI
.
54.
Morita
,
R.
,
Nabae
,
H.
,
Endo
,
G.
, and
Suzumori
,
K.
,
2018
, “
A Proposal of a New Rotational-Compliant Joint With Oil-Hydraulic McKibben Artificial Muscles
,”
J. Adv. Rob.
,
32
(
9
), pp.
511
523
.10.1080/01691864.2018.1464946
55.
Horgan
,
C.
, and
Murphy
,
J.
,
2019
, “
Magic Angles in the Mechanics of Fibrous Soft Materials
,”
Mech. Soft Mater.
,
1
(
1
), pp.
1
6
.10.1007/s42558-018-0001-x
56.
Tondu
,
B.
,
2014
, “
Robust and Accurate Closed-Loop Control of Mckibben Artificial Muscle Contraction With a Linear Single Integral Action
,”
Actuators
,
3
(
2
), pp.
142
161
.10.3390/act3020142
57.
Manring
,
N.
,
Muhi
,
L.
,
Fales
,
R.
,
Mehta
,
V.
,
Kuehn
,
J.
, and
Peterson
,
J.
,
2018
, “
Using Feedback Linearization to Improve the Tracking Performance of a Linear Hydraulic-Actuator
,”
ASME J. Dyn. Syst. Meas., Control
,
140
(
1
), p.
011009
.10.1115/1.4037285
You do not currently have access to this content.