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Adaptive back stepping fast terminal sliding mode control of robot manipulators actuated by pneumatic artificial muscles: continuum modelling, dynamic formulation and controller design

  • H. KhajehsaeidEmail author
  • B. Esmaeili
  • R. Soleymani
  • A. Delkhosh


Pneumatic Artificial Muscles (PAMs) also called braided pneumatic actuators were invented by Mckibben to help the Polio patients. When the internal bladder is pressurized the actuator gets shorter which can produce a tensile force. PAMs are widely used in bio robotic as well as industrial, medical and rehabilitation robotic applications due to their salient advantages such as high power to weight ratio, flexibility and low cost. However, PAMs exhibit highly non-linear characteristics due to nonlinear mechanical properties of the inner tube and geometrically complex behavior of the outer shell. To use PAMs in engineering applications it is necessary to have an accurate relationship between produced axial force, contraction ratio and applied internal pressure. In this work, a continuum mechanics based model is extended to calculate actuation force of PAMs which is essential in calculation of the required internal pressure as the input signal for control of PAM-based systems. Moreover, dynamic model of a 2-link robot manipulator actuated by PAMs is presented and an adaptive back stepping fast terminal sliding mode controller is applied. Robustness of the utilized method against external disturbances and parameter uncertainties is also investigated. Comparing the model results with experimental data, it is observed the model well predicts mechanical behavior of PAMs. Furthermore, positions and tracking errors are compared with results of an adaptive sliding mode controller. Simulation results obviously demonstrate fast and accurate tracking performance of the applied controller. The developed model can be widely used in design of rehabilitation and also industrial robotic systems.


Pneumatic artificial muscle Continuum mechanics Nonlinear elasticity Sliding mode control Back stepping control Fast terminal 



This Project is supported by a research Grant of the University of Tabriz (Number 817).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Engineering–Emerging TechnologiesUniversity of TabrizTabrizIran

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