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Observer-based friction compensation in heavy-duty parallel robot control

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Abstract

This paper presents an experimental study on friction compensation for the high-precision tracking control of parallel manipulators. A Luenberger-like observer (LLO) and an extended state observer (ESO) are designed and implemented in real-time control of a 6-DoF heavy-duty Stewart-Gough platform (SGP). The dynamic Lu-Gre model is used in the identification of friction. Performances of the proposed observer-based friction compensators are compared to those of a model-based compensator in computed torque control. Experimental results show that the observer-based compensators significantly improve the tracking performances in high speed motions. Among the investigated observers, the ESO results in minimum RMS error in position tracking. Improvement in position tracking at velocity reversals of the individual leg motions is also observed with the contribution of observer-based compensation. The observer error dynamics is exponentially stable, and the convergence rate can be arbitrarily increased by tuning the observer gain.

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Abbreviations

D (X) ∈ R 6×6 :

Linertia matrix

C (X, Ẋ) ∈ R 6×6 :

Matrix of Coriolis and centrifugal forces

G (X) ∈ R 6×1 :

Vector of gravitational forces

F (Ẋ) ∈ R 6×1 :

Vector of equivalent friction forces

\({\mathcal{J}^T}(X) \in {R^{6 \times 6}}\) :

Jacobian matrix

f ∈ R 6×1 :

Vector of external forces

X = ⌊ x y z ∝ β y⌋T ∈ R 6×1 :

Position vector

Ẋ = [v ω]T ∈ R 6×1 :

Velocity vector

Ẍ = [a α]T ∈ R 6×1 :

Acceleration vector

p i B :

ith center of a universal joint at the moving platform (MP) in frame {P}

d B :

Distance of the center of {P} of the MP in {B}

qi :

ith center of a universal joint at the MP in {B}

b i B :

ith center of a universal joint at the base platform in {B}

\(R_P^B\) :

Rotation matrix of {P} with respect to {B}

L i :

ith vector from the origin of the {D} to the origin of {U}

s i :

ith linear module unit vector

l i :

ith linear module length

ω :

Angular velocity vector of the MP

α :

Angular acceleration vector of the MP

g :

Vector of gravitational acceleration

a p :

Combined linear acceleration vector of the MP

v p :

Combined linear velocity vector of the MP

m p :

Mass of the MP

m U :

Mass of the moving piston of a linear module

m D :

Mass of the lower part of a linear module

f ext :

External force vector at the MP

T ext :

External torque vector at the MP

f u :

Force vector of the ith linear module at the universal joint

E 3×3 :

3×3 identity matrix

J eq :

Equivalent rotational inertia

J rotor :

Inertia inside a linear module

J screw :

Ball screw shaft inertia

J mech :

Inertia of other rotating mechanical components, such as inner rings of bearings, electromechanical brake disc

P ω :

Pitch gain

F c :

Coulomb friction

F v :

Viscous friction

F s :

Static friction

σ 0 :

Stiffness

σ 1 :

Microdamping

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Authors and Affiliations

  1. Mechanical Eng. Dept., Istanbul Technical University, MA1 Gumussuyu/Istanbul, 34437, Turkey

    Kamil Vedat Sancak & Zeki Yagiz Bayraktaroglu

  2. ALTINAY Robot Technologies Inc., Istanbul Industry and Trade Free Zone, Tuzla/Istanbul, 34957, Turkey

    Kamil Vedat Sancak

Authors
  1. Kamil Vedat Sancak
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  2. Zeki Yagiz Bayraktaroglu
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Correspondence to Kamil Vedat Sancak.

Additional information

Kamil Vedat Sancak obtained his Aeronautical Engineering B.Sc. and Robotics M.Sc. degrees from Istanbul Technical University, Turkey. He is currently a Ph.D. student at the Mechanical Engineering Department, Istanbul Technical University, and preparing a thesis on the control of heavy duty parallel manipulator. He has been employed as a robotics researcher at the TUBITAK-MAM (Scientific and Technological Research Council of Turkey-Marmara Research Center) in 1991–2000. He has worked in robotics research companies. In 2013, he joined the Altinay Robot Technologies company as the engineering manager. His research interests include design, development, and control of parallel and serial manipulators. In recent years, he has focused on projects of collaborative and assistive robotics.

Zeki Yagiz Bayraktaroglu obtained his B.Sc. degree in Mechanical Engineering from the Istanbul Technical University, Istanbul, Turkey, the M.Sc. in Robotics from the Ecole Nationale Supérieure d’Arts et Métiers, Paris, France and Ph.D. in Robotics from the University of Versailles Saint Quentin-en-Yvelines, Versailles, France, in 1997, 1998, and 2002, respectively. He is currently an Associate Professor of the Department of Mechanical Engineering, Istanbul Technical University.

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Sancak, K.V., Bayraktaroglu, Z.Y. Observer-based friction compensation in heavy-duty parallel robot control. J Mech Sci Technol 35, 3693–3704 (2021). https://doi.org/10.1007/s12206-021-0738-2

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  • DOI: https://doi.org/10.1007/s12206-021-0738-2

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