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PD-adaptive variable impedance constant force control of macro-mini robot for compliant grinding and polishing

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Abstract

In order to realize the compliant grinding and polishing of complex surfaces, the traditional impedance control cannot adjust the system impedance, so the force tracking deviation is large, the adaptive variable impedance control can adapt to the environmental changes to adjust the system impedance and realize the stable tracking of the contact force, but the overshoot is too large. In this paper, the constant force control of compliant grinding and polishing processing is studied on the designed macro-mini robotic system, and an adaptive variable impedance control algorithm with pre-PD adjustment is proposed. The control law is used to update the damping term in the impedance parameters of the system, and realize the constant force control process in which the grinding and polishing head is approximately perpendicular to the machined surface, and the stability and convergence of the force control algorithm are proved. Through simulation and experiment, the four algorithms of impedance control, adaptive impedance control, adaptive variable impedance control and the proposed PD-adaptive variable impedance control are compared and analyzed in the force tracking performance of plat surface, sloped surface and curved surface, and then in the grinding and polishing experiments to verify the grinding and polishing force tracking error, the force tracking errors of the other three control algorithms are controlled within 2.08 N, 1.30 N, and 1.34 N, and the overshoot amounts to 19.2%, 56.3%, and 11.1%. The proposed algorithm can control the force tracking error within 0.78 N, the overshoot is less than 4.5%, which verifies that the proposed force control algorithm is more superior in force control performance and is suitable for force control scenarios of actual grinding and polishing.

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Data availability

The data of this study are available from the first author or corresponding author upon reasonable request.

Abbreviations

x, mm:

Offline trajectory

θ d , rad:

Desired angle value of the six-axis joint of the robot

θ c , rad:

Actual control angle value of the six-axis joint of the robot

θ m , rad:

Actual angle value of the six-axis joint of the robot

∆f, N:

Force error

f r , N:

Expected contact force

f e , N:

Actual contact force

k e , N/m:

Environmental stiffness

m d , kg:

Mass coefficient

∆b, N/(m/s):

Damping compensation coefficient

b d , N/(m/s):

Damping coefficient

x m , mm:

Displacement obtained by the positive kinematics of the robot

x r , mm:

Motion reference trajectory

x e , mm:

Actual environmental position

e, mm:

Position error

\(\widehat{{e}}\) , mm:

Estimated position error

f r ’, N:

Variable contact force

\({\widehat{{x}}}_{{e}}\), mm:

Estimated environmental position

\({\widehat{e}}_{{ss}}\) , ——:

Steady-state error

e 1, mm:

Calculated desired displacement

e 2 , mm:

Specified displacement of the voice coil motor movement

e 3 , mm:

Actual displacement of the voice coil motor movement

x d , mm:

Actual displacement of the end effector

M d , Kg:

Mass coefficient matrix

B d , N/(m/s):

Damping coefficient matrix

K d , N/m:

Stiffness coefficient matrix

F e , N:

Actual contact force matrix

F r , N:

Expected contact force matrix

X d , mm:

Actual displacement matrix of the end effector

k d , N/m:

Stiffness coefficient

X r , mm:

Expected environmental position matrix

η, ——:

Sampling time of the controller

σ, ——:

Update rate

λ, ——:

Adjustment control parameter

k p1 , ——:

Contact force coefficient

k d1 , ——:

Contact force error coefficient

\(\delta {{x}}_{{e}}\), mm:

Environmental position disturbance

v e, mm/s:

Speed of the macro-robot

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Funding

This work was supported by National Key R&D Program of China (2018YFB1308900), the Key Project of Tianjin Applied Basic Research Multi-Investment Fund Project (21JCZDJC00870), and Tianjin Postgraduate Research and Innovation Project (2021YJSS094).

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Authors and Affiliations

  1. Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China

    Guilian Wang, Yuxin Deng, Haibo Zhou & Xu Yue

  2. National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China

    Guilian Wang, Yuxin Deng, Haibo Zhou & Xu Yue

Authors
  1. Guilian Wang
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  2. Yuxin Deng
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  3. Haibo Zhou
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  4. Xu Yue
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Contributions

Guilian Wang: resources, instructing, review; Yuxin Deng: conceptualization, writing original draft, validation; Haibo Zhou: instructing, review; Xu Yue: methodology.

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Correspondence to Haibo Zhou.

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Wang, G., Deng, Y., Zhou, H. et al. PD-adaptive variable impedance constant force control of macro-mini robot for compliant grinding and polishing. Int J Adv Manuf Technol 124, 2149–2170 (2023). https://doi.org/10.1007/s00170-022-10405-x

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