Research Papers

Flatness-Based Control of a Two Degrees-of-Freedom Platform With Pneumatic Artificial Muscles

[+] Author and Article Information
David Bou Saba

Laboratoire Ampère CNRS,
INSA Lyon,
Université de Lyon,
Villeurbanne, Cedex 69621, France
e-mail: david.bou-saba@insa-lyon.fr

Paolo Massioni

Laboratoire Ampère CNRS,
INSA Lyon,
Université de Lyon,
Villeurbanne, Cedex 69621, France
e-mail: paolo.massioni@insa-lyon.fr

Eric Bideaux

Laboratoire Ampère CNRS,
INSA Lyon,
Université de Lyon,
Villeurbanne, Cedex 69621, France
e-mail: eric.bideaux@insa-lyon.fr

Xavier Brun

Laboratoire Ampère CNRS,
INSA Lyon,
Université de Lyon,
Villeurbanne, Cedex 69621, France
e-mail: xavier.brun@insa-lyon.fr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 15, 2018; final manuscript received September 6, 2018; published online October 5, 2018. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 141(2), 021003 (Oct 05, 2018) (10 pages) Paper No: DS-18-1024; doi: 10.1115/1.4041445 History: Received January 15, 2018; Revised September 06, 2018

Pneumatic artificial muscles (PAMs) are an interesting type of actuators as they provide high power-to-weight and power-to-volume ratio. However, their efficient use requires very accurate control methods taking into account their complex and nonlinear dynamics. This paper considers a two degrees-of-freedom platform whose attitude is determined by three pneumatic muscles controlled by servovalves. An overactuation is present as three muscles are controlled for only two degrees-of-freedom. The contribution of this work is twofold. First, whereas most of the literature approaches the control of systems of similar nature with sliding mode control, we show that the platform can be controlled with the flatness-based approach. This method is a nonlinear open-loop controller. In addition, this approach is model-based, and it can be applied thanks to the accurate models of the muscles, the platform and the servovalves, experimentally developed. In addition to the flatness-based controller, which is mainly a feedforward control, a proportional-integral (PI) controller is added in order to overcome the modeling errors and to improve the control robustness. Second, we solve the overactuation of the platform by an adequate choice for the range of the efforts applied by the muscles. In this paper, we recall the basics of this control technique and then show how it is applied to the proposed experimental platform. At the end of the paper, the proposed approach is compared to the most commonly used control method, and its effectiveness is shown by means of experimental results.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Daerden, F. , and Lefeber, D. , 2002, “ Pneumatic Artificial Muscles: Actuators for Robotics and Automation,” Eur. J. Mech. Environ. Eng., 47(1), pp. 11–21.
Shen, W. , and Shi, G. , 2011, “ An Enhanced Static Mathematical Model of Braided Fibre-Reinforced Pneumatic Artificial Muscles,” Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng., 225(3), pp. 212–225.
Ba, D. , Dinh, T. , and Ahn, K. , 2016, “ An Integrated Intelligent Nonlinear Control Method for a Pneumatic Artificial Muscle,” IEEE/ASME Trans. Mechatronics, 21(4), pp. 1835–1845. [CrossRef]
Zhu, X. , Tao, G. , Yao, B. , and Cao, J. , 2008, “ Adaptive Robust Posture Control of Parallel Manipulator Driven by Pneumatic Muscles With Redundancy,” IEEE/ASME Trans. Mechatronics, 13(9), pp. 441–450.
Aschemann, H. , and Schindele, D. , 2008, “ Sliding-Mode Control of a High-Speed Linear Axis Driven by Pneumatic Muscle Actuators,” IEEE Trans. Ind. Electron., 55(11), pp. 3855–3864. [CrossRef]
Cai, D. , and Dai, Y. , 2000, “ A Sliding Mode Controller for Manipulator Driven by Artificial Muscle Actuator,” IEEE International Conference on Control Applications, pp. 668–673.
Shen, X. , 2010, “ Nonlinear Model-Based Control of Pneumatic Artificial Muscle Servo Systems,” Control Eng. Pract., 18(3), pp. 311–317. [CrossRef]
Ahn, K. , and Anh, H. , 2007, “ A New Approach for Modelling and Identification of the Pneumatic Artificial Muscle Manipulator Based on Recurrent Neural Networks,” Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng., 221(8), pp. 1101–1121. [CrossRef]
Shi, G. , and Shen, W. , 2013, “ Hybrid Control of a Parallel Platform Based on Pneumatic Artificial Muscles Combining Sliding Mode Controller and Adaptive Fuzzy CMAC,” Control Eng. Pract., 1(1), pp. 76–86. [CrossRef]
Robinson, R. , Kothera, C. , Sanner, R. , and Wereley, N. , 2016, “ Nonlinear Control of Robotic Manipulators Driven by Pneumatic Artificial Muscles,” IEEE/ASME Trans. Mechatronics, 21(1), pp. 55–68. [CrossRef]
Rahman, R. , and Sepehri, N. , 2017, “ Design and Experimental Evaluation of a Dynamical Adaptive Backstepping-Sliding Mode Control Scheme for Positioning of an Antagonistically Paired Pneumatic Artificial Muscles Driven Actuating System,” Int. J. Control, 90(2), pp. 249–274. [CrossRef]
Chou, C.-P. , and Hannaford, B. , 1996, “ Measurement and Modeling of McKibben Pneumatic Artificial Muscles,” IEEE Trans. Rob. Autom., 12(1), pp. 90–102. [CrossRef]
Tondu, B. , and Lopez, P. , 2000, “ Modeling and Control of McKibben Artificial Muscle Robot Actuators,” Control Syst., IEEE, 20(2), pp. 15–38. [CrossRef]
Sermeno Mena, S. , Sesmat, S. , and Bideaux, E. , 2012, “ Parallel Manipulator Driven by Pneumatic Muscles,” Eighth International Conference on Fluid Power (8th IFK), Dresden, Germany, Mar. 26–28.
Schindele, D. , and Aschemann, H. , 2012, “ Model-Based Compensation of Hysteresis in the Force Characteristic of Pneumatic Muscles,” 12th IEEE International Workshop on Advanced Motion Control (AMC), Sarajevo, Bosnia-Herzegovina, Mar. 25–27, pp. 1–6.
Fliess, M. , Lévine, J. , Martin, P. , and Rouchon, P. , 1995, “ Flatness and Defect of Non-Linear Systems: Introductory Theory and Examples,” Int. J. Control, 61(6), pp. 1327–1361. [CrossRef]
Bou Saba, D. , Bideaux, E. , Brun, X. , and Massioni, P. , 2016, “ A Complete Model of a Two Degree of Freedom Platform Actuated by Three Pneumatic Muscles Elaborated for Control Synthesis,” ASME Paper No. FPMC2016-1706.
Olaby, O. , Brun, X. , Sesmat, S. , Redarce, T. , and Bideaux, E. , 2005, “ Characterization and Modeling of a Proportional Valve for Control Synthesis,” JFPS International Symposium on Fluid Power, Tsukuba, Japan, Nov. 7–10, pp. 771–776.
Rouchon, P. , 2005, “ Flatness Based Control of Oscillators,” ZAMM-J. Appl. Math. Mech./Z. Angew. Math. Mech., 85(6), pp. 411–421. [CrossRef]
Martin, P. , Murray, R. M. , and Rouchon, P. , 2003, “ Flat Systems, Equivalence and Trajectory Generation,” Technical Report https://authors.library.caltech.edu/28021/1/mmr03-cds.pdf.
Rouchon, P. , Fliess, M. , Lévine, J. , and Martin, P. , 1993, “ Flatness, Motion Planning and Trailer Systems,” 32nd IEEE Conference on Decision and Control, San Antonio, TX, Dec. 15–17, pp. 2700–2705.
Lévine, J. , and Nguyen, D. , 2003, “ Flat Output Characterization for Linear Systems Using Polynomial Matrices,” Syst. Control Lett., 48(1), pp. 69–75. [CrossRef]
Isidori, A. , 2013, Nonlinear Control Systems, Springer Science & Business Media, Berlin.


Grahic Jump Location
Fig. 2

Axonometric view and view from the top of the top plate, with definition of the axes x, y, z and the rotation angles θx and θy. M1, M2, and M3 are the attachment points of the three PAMs and define the three angular positions ϕ1, ϕ2, and ϕ3 given in the Nomenclature section.

Grahic Jump Location
Fig. 1

The experimental platform

Grahic Jump Location
Fig. 3

Contraction force applied by a muscle as a function of the contraction εi and absolute pressure Pi

Grahic Jump Location
Fig. 4

Mass flow of a servovalve as a function of voltage vi and absolute muscle pressure Pi

Grahic Jump Location
Fig. 11

Muscle contractions for the setpoint tracking using the flatness-based control plus a PI

Grahic Jump Location
Fig. 14

Pressures inside the PAMs during the flatness-based control plus PI experiment

Grahic Jump Location
Fig. 15

Forces applied by the PAMs (estimated using Eq. (6) and the measurements of the pressures and the contractions) with flatness-based control plus a PI

Grahic Jump Location
Fig. 6

Values of m as function of θx and θy

Grahic Jump Location
Fig. 7

Global control scheme

Grahic Jump Location
Fig. 8

Valid range of the efforts, bounded from below by Fmin and from above by Fmax for a given position of the platform, determined by the three contractions εi, i ∈ {1, 2, 3}

Grahic Jump Location
Fig. 9

Simulation result of the evolution of the output F3 when the sliding mode control is used

Grahic Jump Location
Fig. 10

Static setpoint tracking using the flatness-based control plus a PI

Grahic Jump Location
Fig. 12

Trajectory tracking with simple PI control

Grahic Jump Location
Fig. 13

Trajectory tracking with flatness-based control plus a PI

Grahic Jump Location
Fig. 5

Value of z as function of x1 = θx and x2 = θy



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In