This paper presents a sliding mode controller for a 2DOF planar pneumatic manipulator actuated by pleated pneumatic artificial muscle actuators. It is argued that it is necessary to account for the pressure dynamics of muscles and valves. A relatively detailed system model that includes pressure dynamics is established. Since the model includes actuator dynamics, feedback linearization was necessary to design a sliding mode controller. The feedback linearization and subsequent controller design are presented in detail, and the controller’s performance is evaluated, both in simulation and experimentally. Chattering was found to be quite severe, so the introduction of significant boundary layers was required.
1.
Chou
, C. P.
, and Hannaford
, B.
, 1996, “Measurement and Modelling of McKibben Pneumatic Artificial Muscles
,” IEEE Trans. Rob. Autom.
1042-296X, 12
(1
), pp. 90
–102
.2.
Inoue
, K.
, 1987, “Rubbertuators and Applications for Robots
,” Proceedings of the 4th International Symposium on Robotic Research
, pp. 57
–63
.3.
Klute
, G. K.
, Czerniecki
, J. M.
, and Hannaford
, B.
, 2002, “Artificial Muscles: Actuators for Biorobotic Systems
,” Int. J. Robot. Res.
0278-3649, 21
(4
), pp. 295
–309
.4.
Klute
, G. K.
, and Hannaford
, B.
, 2000, “Accounting for Elastic Energy Storage in McKibben Artificial Muscle Actuators
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 122
(2
), pp. 386
–388
.5.
Liu
, W.
, and Rahn
, C. R.
, 2003, “Fiber-Reinforced Membrane Models of McKibben Actuators
,” Trans. ASME, J. Appl. Mech.
0021-8936, 70
(6
), pp. 853
–859
.6.
Manuello Bertetto
, A.
, and Ruggiu
, M.
, 2004, “Characterization and Modeling of Air Muscles
,” Mech. Res. Commun.
0093-6413, 31
(2
), pp. 185
–194
.7.
Repperger
, D. W.
, Philips
, C. A.
, Johnson
, D. C.
, Harmon
, R. D.
, and Johnson
, K.
, 1997, “A Study of Pneumatic Muscle Technology for Possible Assistance in Mobility
,” Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
, Vol. 5
, pp. 1884
–1887
.8.
Schulte
, H. F.
, 1961, “The Characteristics of the McKibben Artificial Muscle
,” The Application of External Power in Prosthetics and Orthotics
, National Academy of Sciences-National Research Council
, Washington, DC
, Publication 874, pp. 94
–115
.9.
Tondu
, B.
, and Lopez
, P.
, 2000, “Modeling and Control of McKibben Artificial Muscle Robot Actuators
,” IEEE Control Syst. Mag.
0272-1708, 20
(2
), pp. 15
–38
.10.
Verrelst
, B.
, Van Ham
, R.
, Vanderborght
, B.
, Lefeber
, D.
, Daerden
, F.
, and Van Damme
, M.
, 2006, “Second Generation Pleated Pneumatic Artificial Muscle and Its Robotic Applications
,” Adv. Rob.
0169-1864, 20
(7
), pp. 783
–805
.11.
Daerden
, F.
, and Lefeber
, D.
, 2001, “The Concept and Design of Pleated Pneumatic Artificial Muscles
,” Int. J. Fluid Power
1439-9776, 2
(3
), pp. 41
–50
.12.
Bicchi
, A.
, and Tonietti
, G.
, 2004, “Fast and Soft Arm Tactics: Dealing With the Safety-Performance Trade-Off in Robot Arms Design and Control
,” IEEE Rob. Autom. Mag.
1070-9932, 11
(2
), pp. 22
–33
.13.
Bicchi
, A.
, Tonietti
, G.
, Bavaro
, M.
, and Piccigallo
, M.
, 2003, “Variable Stiffness Actuators for Fast and Safe Motion Control
,” Proceedings of the International Symposium on Robotics Research Springer Tracts in Advanced Robotics (STAR)
, B.
Siciliano
, O.
Khatib
, and F.
Groen
, eds., Springer-Verlag
.14.
Ikuta
, K.
, Ishii
, H.
, and Nokata
, M.
, 2003, “Safety Evaluation Method of Design and Control for Human-Care Robots
,” Int. J. Robot. Res.
0278-3649, 22
(5
), pp. 281
–297
.15.
Kulic
, D.
, and Croft
, E. A.
, 2006, “Real-Time Safety for Human-Robot Interaction
,” Rob. Auton. Syst.
0921-8890, 54
(1
), pp. 1
–12
.16.
Lim
, H.-O.
, and Tanie
, K.
, 2000, “Human Safety Mechanisms of Human-Friendly Robots: Passive Viscoelastic Trunk and Passively Movable Base
,” Int. J. Robot. Res.
0278-3649, 19
(4
), pp. 307
–335
.17.
Zinn
, M.
, Roth
, B.
, Khatib
, O.
, and Salisbury
, J. K.
, 2004, “A New Actuation Approach for Human Friendly Robot Design
,” Int. J. Robot. Res.
0278-3649, 23
(4–5
), pp. 379
–398
.18.
Balasubramanian
, S.
, Ward
, J.
, Sugar
, T.
, and He
, J.
, 2007, “Characterization of the Dynamic Properties of Pneumatic Muscle Actuators
,” Proceedings of the 2007 IEEE Tenth International Conference on Rehabilitation Robotics
, pp. 764
–770
.19.
Gordon
, K. E.
, Sawickia
, G. S.
, and Ferris
, D. P.
, 2006, “Mechanical Performance of Artificial Pneumatic Muscles to Power an Anklefoot Orthosis
,” J. Biomech.
0021-9290, 39
, pp. 1832
–1841
.20.
Surentu
, J.
, Tuijthof
, J. M. G.
, and Herder
, J. L.
, 2007, “Optimized Artificial Muscles for an Inherently Safe Robotic Arm
,” Proceedings of the 2007 IEEE Tenth International Conference on Rehabilitation Robotics
, pp. 1070
–1076
.21.
Noritsugu
, T.
, and Tanaka
, T.
, 1997, “Application of a Rubber Artificial Muscle Manipulator as a Rehabilitation Robot
,” IEEE/ASME Trans. Mechatron.
1083-4435, 2
(4
), pp. 259
–267
.22.
Tondu
, B.
, Ippolito
, S.
, Guiochet
, J.
, and Daidie
, A.
, 2005, “A Seven-Degrees-of Freedom Robot-Arm Driven by Pneumatic Artificial Muscles for Humanoid Robots
,” Int. J. Robot. Res.
0278-3649, 24
(4
), pp. 257
–274
.23.
Tsagarakis
, N. G.
, and Caldwell
, G.
, 2003, “Development and Control of a “Soft-Actuated” Exoskeleton for Use in Physiotherapy and Training
,” Auton. Rob.
0929-5593, 15
, pp. 21
–33
.24.
Tzafestas
, C. S.
, M’Sirdi
, N. K.
, and Manamani
, N.
, 1997, “Adaptive Impedance Control Applied to a Pneumatic Legged Robot
,” J. Intell. Robotic Syst.
0921-0296, 20
, pp. 105
–129
.25.
Vanderborght
, B.
, Verrelst
, B.
, Van Ham
, R.
, and Lefeber
, D.
, 2006, “Controlling a Bipedal Walking Robot Actuated by Pleated Pneumatic Artificial Muscles
,” Robotica
0263-5747, 24
(4
), pp. 401
–410
.26.
Zhang
, W.
, Accorsi
, M. L.
, and Leonard
, J. W.
, 2005, “Analysis of Geometrically Nonlinear Anisotropic Membranes: Application to Pneumatic Muscle Actuators
,” Finite Elem. Anal. Design
0168-874X, 41
, pp. 944
–962
.27.
Schröder
, J.
, Kawamura
, K.
, Gockel
, T.
, and Dillmann
, R.
, 2003, “Improved Control of a Humanoid Arm Driven by Pneumatic Actuators
,” Proceedings of Humanoids 2003
.28.
Thanh
, T. D. C.
, and Ahn
, K. K.
, 2006, “Intelligent Phase Plane Switching Control of Pneumatic Artificial Muscle Manipulators With Magneto-Rheological Brake
,” Mechatronics
0957-4158, 16
, pp. 85
–95
.29.
Thanh
, T. D. C.
, and Ahn
, K. K.
, 2006, “Nonlinear PID Control to Improve the Control Performance of 2 Axes Pneumatic Artificial Muscle Manipulator Using Neural Network
,” Mechatronics
0957-4158, 16
(9
), pp. 577
–587
.30.
Caldwell
, D. G.
, Medrano-Cerda
, G. A.
, and Goodwin
, M. J.
, 1995, “Control of Pneumatic Muscle Actuators
,” IEEE Control Syst.
1066-033X, 15
(1
), pp. 40
–48
.31.
Lilly
, J. H.
, 2003, “Adaptive Tracking for Pneumatic Muscle Actuators in Bicep and Tricep Configurations
,” IEEE Trans. Neural Syst. Rehabil. Eng.
1534-4320, 11
(3
), pp. 333
–339
.32.
Medrano-Cerda
, G. A.
, Bowler
, C. J.
, and Caldwell
, D. G.
, 1995, “Adaptive Position Control of Antagonistic Pneumatic Muscle Actuators
,” Proceedings of the International Conference on Intelligent Robots and Systems
, Vol. 1
, pp. 378
–383
.33.
Nouri
, A. S.
, Gauvert
, C.
, Tondu
, B.
, and Lopez
, P.
, 1994, “Generalized Variable Structure Model Reference Adaptive Control of One-Link Artificial Muscle Manipulator in Two Operating Modes
,” Proceedings of the 1994 IEEE International Conference on Systems, Man, and Cybernetics
, Vol. 2
, pp. 1944
–1950
.34.
Tonietti
, G.
, and Bicchi
, A.
, 2002, “Adaptive Simultaneous Position and Stiffness Control for a Soft Robot Arm
,” Proceedings of the IEEE International Symposium Intelligent Robots and Systems
, pp. 1992
–1997
.35.
Repperger
, D. W.
, Philips
, C. A.
, and Krier
, M.
, 1999, “Controller Design Involving Gain Scheduling for a Large Scale Pneumatic Muscle Actuator
,” Proceedings of the 1999 IEEE International Conference on Control Applications
, pp. 285
–290
.36.
Guihard
, M.
, and Gorce
, P.
, 1999, “Dynamic Control of an Artificial Muscle Arm
,” Proceedings of the 1999 IEEE International Conference on Systems, Man and Cybernetics
, Vol. 4
, pp. 813
–818
.37.
Hildebrandt
, A.
, Sawodny
, O.
, Neumann
, R.
, and Hartmann
, A.
, 2005, “Cascaded Control Concept of a Robot With Two Degrees of Freedom Driven by Four Artificial Pneumatic Muscle Actuators
,” Proceedings of the 2005 American Control Conference
, Portland, OR
, pp. 680
–685
.38.
Ahn
, K. K.
, and Nguyen
, H. T. C.
, 2007, “Intelligent Switching Control of a Pneumatic Muscle Robot Arm Using Learning Vector Quantization Neural Network
,” Mechatronics
0957-4158, 17
, pp. 255
–262
.39.
Eskiizmirliler
, S.
, Tondu
, B.
, and Darlot
, C.
, 2001, “Motor Control of a Limb Segment Actuated by Artificial Muscles
,” Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society
, Vol. 1
, pp. 865
–868
.40.
Hesselroth
, T.
, Sarkar
, K.
, van der Smagt
, P. P.
, and Schulten
, K.
, 1994, “Neural Network Control of a Pneumatic Robot Arm
,” IEEE Trans. Syst. Man Cybern.
0018-9472, 24
(1
), pp. 28
–38
.41.
Balasubramanian
, K.
, and Rattan
, K.
, 2005, “Trajectory Tracking Control of a Pneumatic Muscle System Using Fuzzy Logic
,” Proceedings of NAFIPS 2005—Annual Meeting of the North American Fuzzy Information Processing Society
, pp. 472
–477
.42.
Balasubramanian
, K.
, and Rattan
, K. S.
, 2003, “Feedforward Control of a Non-Linear Pneumatic Muscle System Using Fuzzy Logic
,” Proceedings of The 12th IEEE International Conference on Fuzzy Systems
, Vol. 1
, pp. 272
–277
.43.
Balasubramanian
, K.
, and Rattan
, K. S.
, 2003, “Fuzzy Logic Control of a Pneumatic Muscle System Using a Linearing Control Scheme
,” Proceedings of NAFIPS 2003—22nd International Conference of the North American Fuzzy Information Processing Society
, pp. 432
–436
.44.
Carbonell
, P.
, Jiang
, Z. P.
, and Repperger
, D. W.
, 2001, “A Fuzzy Backstepping Controller for a Pneumatic Muscle Actuator System
,” Proceedings of the 2001 IEEE International Symposium on Intelligent Control
, pp. 353
–358
.45.
Chan
, S. W.
, Lilly
, J. H.
, Repperger
, D. W.
, and Berlin
, J. E.
, 2003, “Fuzzy PD+I Learning Control of a Pneumatic Muscle
,” Proceedings of the 2003 IEEE International Conference of Fuzzy Systems
, pp. 278
–283
.46.
Clapa
, D. J.
, Croft
, E. A.
, and Hodgson
, A. J.
, 2006, “Equilibrium Point Control of a 2-DOF Manipulator
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 128
, pp. 134
–141
.47.
Carbonell
, P.
, Jiang
, Z. P.
, and Repperger
, D. W.
, 2001, “Nonlinear Control of a Pneumatic Muscle Actuator: Backstepping vs Sliding-Mode
,” Proceedings of the 2001 IEEE International Conference on Control Applications
, pp. 167
–172
.48.
Kimura
, T.
, Hara
, S.
, Fujita
, T.
, and Kagawa
, T.
, 1997, “Feedback Linearization for Pneumatic Actuator Systems With Static Friction
,” Control Eng. Pract.
0967-0661, 5
(10
), pp. 1385
–1394
.49.
Cai
, D.
, and Dai
, Y.
, 2003, “A Sliding Mode Controller for Manipulator Driven by Artificial Muscle Actuator
,” Electron. Commun. Jpn.
0424-8368, 86
(11
), pp. 57
–64
.50.
Lilly
, J. H.
, and Quesada
, P. M.
, 2004, “A Two-Input Sliding-Mode Controller for a Planar Arm Actuated by Four Pneumatic Muscle Groups
,” IEEE Trans. Neural Syst. Rehabil. Eng.
1534-4320, 12
(3
), pp. 349
–359
.51.
Lilly
, J. H.
, and Yang
, L.
, 2005, “Sliding Mode Tracking for Pneumatic Muscle Actuators in Opposing Pair Configuration
,” IEEE Trans. Control Syst. Technol.
1063-6536, 13
(4
), pp. 550
–558
.52.
Repperger
, D. W.
, Johnson
, K. R.
, and Philips
, C. A.
, 1998, “A VSC Position Tracking System Involving a Large Scale Pneumatic Muscle Actuator
,” Proceedings of the 37th IEEE Conference on Decision & Control
, pp. 4302
–4307
.53.
Sira-Ramírez
, H.
, Lopez
, P.
, and Tondu
, B.
, 1996, “On the Robust Stabilization and Tracking for Robotic Manipulators With Artificial Muscles
,” Int. J. Syst. Sci.
0020-7721, 27
(11
), pp. 1067
–1075
.54.
Yang
, L.
, 2006, “Sliding Mode Control of Robotics Systems Actuated by Pneumatic Muscles
,” Ph.D. thesis, University of Louisville, Louisville, KY.55.
Hamerlain
, M.
, 1995, “An Anthropomorphic Robot Arm Driven by Artificial Muscles Using a Variable Structure Control
,” Proceedings of the 1995 IEEE/RJS International Conference of Intelligent Robots and Systems
, Vol. 1
, pp. 550
–555
.56.
Van Damme
, M.
, Daerden
, F.
, and Lefeber
, D.
, 2005, “A Pneumatic Manipulator Used in Direct Contact With an Operator
,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation
, Barcelona, Spain
, pp. 4505
–4510
.57.
Daerden
, F.
, and Lefeber
, D.
, 2002, “Pneumatic Artificial Muscles: Actuators for Robotics and Automation
,” European Journal of Mechanical and Environmental Engineering
, 47
(1
), pp. 11
–22
.58.
Verrelst
, B.
, Van Ham
, R.
, Vanderborght
, B.
, Daerden
, F.
, and Lefeber
, D.
, 2005, “The Pneumatic Biped “LUCY” Actuated With Pleated Pneumatic Artificial Muscles
,” Auton. Rob.
0929-5593, 18
, pp. 201
–213
.59.
Verrelst
, B.
, Vermeulen
, J.
, Vanderborght
, B.
, Van Ham
, R.
, Naudet
, J.
, Lefeber
, D.
, Daerden
, F.
, and Van Damme
, M.
, 2006, “Motion Generation and Control for the Pneumatic Biped “Lucy,”
,” International Journal of Humanoid Robotics
, 3
(1
), pp. 67
–103
.60.
Daerden
, F.
, 1999, “Conception and Realization of Pleated Pneumatic Artificial Muscles and Their Use as Compliant Actuation Elements
,” Ph.D. thesis, Vrije Universiteit Brussel, Brussel, Belgium.61.
Reynolds
, D. B.
, Repperger
, D. W.
, Phillips
, C. A.
, and Bandry
, G.
, 2003, “Modeling the Dynamic Characteristics of Pneumatic Muscle
,” Ann. Biomed. Eng.
0090-6964, 31
(3
), pp. 310
–317
.62.
Khalil
, H. K.
, 2002, Nonlinear Systems
, 3rd ed., Prentice-Hall
, Englewood Cliffs, NJ
.63.
Hung
, J. Y.
, Gao
, W.
, and Hung
, J. C.
, 1993, “Variable Structure Control: A Survey
,” IEEE Trans. Ind. Electron.
0278-0046, 40
(1
), pp. 2
–22
.64.
Perruquetti
, W.
, 2002, Sliding Mode Control in Engineering
, J. P.
Barbot
, ed., Marcel Dekker
, New York
.65.
Slotine
, J.-J.
, and Li
, W.
, 1991, Applied Nonlinear Control
, Prentice-Hall
, Upper Saddle River, NJ
.66.
Utkin
, V. I.
, 1977, “Variable Structure Systems With Sliding Modes
,” IEEE Trans. Autom. Control
0018-9286, 22
, pp. 212
–222
.67.
Daerden
, F.
, Lefeber
, D.
, Verrelst
, B.
, and Van Ham
, R.
, 2001, “Pleated Pneumatic Artificial Muscles: Actuators for Automation and Robotics
,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, Como, Italy
, pp. 738
–743
.68.
Spong
, M. W.
, Hutchinson
, S.
, and Vidyasagar
, M.
, 2006, Robot Modeling and Control
, Wiley
, New York
.69.
Tondu
, B.
, Boitier
, V.
, and Lopez
, P.
, 1994, “Naturally Compliant Robot-Arms Actuated by McKibben Artificial Muscles
,” Proceedings of the 1994 IEEE International Conference on Systems, Man and Cybernetics
, Vol. 3
, pp. 2635
–2640
.70.
Verrelst
, B.
, 2005, “A Dynamic Walking Biped Actuated by Pleated Pneumatic Artificial Muscles: Basic Concepts and Control Issues
,” Ph.D. thesis, Vrije Universiteit Brussel, Brussel, Belgium.71.
Vanderborght
, B.
, Verrelst
, B.
, Van Ham
, R.
, Van Damme
, M.
, Beyl
, P.
, and Lefeber
, D.
, 2008, “Development of a Compliance Controller to Reduce Energy Consumption for Bipedal Robots
,” Auton. Rob.
0929-5593, 24
(4
), pp. 419
–434
.72.
Vanderborght
, B.
, Verrelst
, B.
, Van Ham
, R.
, Van Damme
, M.
, Lefeber
, D.
, Meira
, Y.
, Duran
, B.
, and Beyl
, P.
, 2006, “Exploiting Natural Dynamics to Reduce Energy Consumption by Controlling the Compliance of Soft Actuators
,” Int. J. Robot. Res.
0278-3649, 25
(4
), pp. 343
–358
.73.
Sastry
, S.
, 1999, Nonlinear Systems: Analysis, Stability and Control
, Springer-Verlag
, New York
.Copyright © 2009
by American Society of Mechanical Engineers
You do not currently have access to this content.