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Adaptive robust control of fully constrained cable robots: singular perturbation approach

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Abstract

In this paper, adaptive robust control of fully constrained cable-driven parallel robots with elastic cables is studied in detail. A composite controller is proposed for the system under the assumption of linear axial spring model as the dominant dynamics of the cables and in presence of model uncertainties. The proposed controller which is designed based on the singular perturbation theory, consists of two main parts. An adaptive robust controller is designed to counteract the unstructured and parametric uncertainties of the robot and a fast control term which is added to control the longitudinal vibrations of the cables. Moreover, to ensure that all cables remain in tension, the proposed control algorithm benefits from internal force concept. Using the results of the singular perturbation theory, the stability of the overall closed-loop system is analyzed through Lyapunov second method, and finally, the effectiveness of the proposed control algorithm is verified through some simulations on a planar cable-driven parallel robot.

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Abbreviations

\({{\varvec{x}}}\) :

The generalized coordinates vector

\({{\varvec{x}}}_{d}\) :

The reference trajectories vector

\({{\varvec{S}}}\) :

The sliding surface vector

\({{\varvec{L}}}_2\) :

The cables length vector

\({{\varvec{L}}}_1\) :

The tensioned cables length vector

\({{\varvec{L}}}_0\) :

The cables length vector at \({{\varvec{x}}}=0\)

\({{\varvec{q}}}\) :

The vector of motors shaft position

\({\varvec{\rho }}\) :

The upper bound of the robot uncertainties

\({{\varvec{I}}}_{m}\) :

The moments of inertia matrix of the motors

\({{\varvec{K}}}\) :

The stiffness matrix of the cables

\({{\varvec{F}}}_{d}\) :

The coefficient matrix of viscous friction

r :

The radius of the actuator drum

n :

The degrees of freedom of the robot

\({{\varvec{M}}}\) :

The mass matrix of the robot

\({{\varvec{C}}}\) :

The Coriolis and centrifugal terms

\({{\varvec{G}}}\) :

The vector of gravity terms

\({{\varvec{F}}}_{s}\) :

The vector of Coulomb friction terms

\({{\varvec{T}}}_{d}\) :

The vector of disturbance terms

\({{\varvec{J}}}\) :

The Jacobian matrix of the robot

\({{\varvec{Q}}}\) :

The vector of internal forces

\({{\varvec{F}}}\) :

The Cartesian force control law

\({{\varvec{u}}}\) :

The vector of motors input torque

\({\varvec{\epsilon }}\) :

The threshold width of the sliding surface

\({{\varvec{K}}}_v\) :

The gain matrix of the fast control term

\({{\varvec{K}}}_{D}\) :

The gain matrix of the Cartesian control law

\({\varvec{\Lambda }}\) :

The constant matrix of the sliding surface

\({\varvec{\Gamma }}\) :

The constant matrix of the adaptation law

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Authors and Affiliations

  1. Advanced Robotics and Automated Systems (ARAS), Faculty of Electrical Engineering, Industrial Control Center of Excellence, K.N. Toosi University of Technology, Tehran, Iran

    Reza Babaghasabha & Hamid D. Taghirad

  2. Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

    Mohammad A. Khosravi

Authors
  1. Reza Babaghasabha
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  2. Mohammad A. Khosravi
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  3. Hamid D. Taghirad
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Correspondence to Reza Babaghasabha.

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Babaghasabha, R., Khosravi, M.A. & Taghirad, H.D. Adaptive robust control of fully constrained cable robots: singular perturbation approach. Nonlinear Dyn 85, 607–620 (2016). https://doi.org/10.1007/s11071-016-2710-8

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