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Constant force tracking using online stiffness and reverse damping force of variable impedance controller for robotic polishing

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Abstract

This paper proposes a novel constant force tracking control scheme based on an impedance controller with online stiffness and reverse damping force (OSRDF) to track desired force. An interaction contact force between the robot end-effector and its environment was represented and analyzed using the full mechanical second-order system and individual spring model. A position-based impedance controller is used to receive a contact force signal to track the constant desired force. The proposed approach tracks the desired contact force and reference trajectory based on reference position and velocity. This OSRDF controller is implemented by adjusting the online stiffness parameter and merging the inverse damping force with the force tracking error to compensate for the unknown environment and reduce the force error to zero. A Lyapunov function is applied to investigate the stability of the OSRDF impedance controller during implementation. Simulation studies and experimental tests on a seven degree of freedom (7DOF) robot manipulator are performed to evaluate the efficiency of the proposed method compared to the traditional constant impedance controller. The results showed the validity and effectiveness of the OSRDF method and revealed a relationship between the end-effector velocity and force tracking error. The proposed approach improves force tracking accuracy with simpler computational processes in simulation and practice.

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Abbreviations

\(B_r\) :

Robot damping (N\(\cdot\)s/m)

\(C(w,\dot{w})\) :

Coriolis and centrifugal torques (N.rad)

\(F_d\) :

Desired force (N)

\(F_e\) :

Environment force (N)

\({F_{X_d}}\) :

Force error after compensation (N)

\(F_c\) :

Compensated force (N)

\({F_{\hat{f}}}\) :

Cartesian space friction forces (N)

G(w):

Gravitational torque (N.rad)

J :

Jacobian matrix

\(K_r\) :

Robot stiffness (N/m)

\(K_e\) :

Environment stiffness (N/m)

\(\hat{M}\) :

Inertia matrix in Cartesian space (N\(\cdot\)s\(^2\)/m)

\(M_r\) :

Robot inertia (N\(\cdot\)s\(^2\)/m)

M(w) :

Positive symmetric inertia matrix (N\(\cdot\)s\(^2\)/rad)

\(T_s\) :

Sampling time (s)

\(u(w,\dot{w})\) :

Overall torques (N.rad)

\(\hat{u}\) :

Estimated of overall torques (N.rad)

V :

Lyapunov variable

\(\hat{V}\) :

Estimated of inertia matrix (kg)

X :

Cartesian displacement (m)

\(\dot{X}\) :

Cartesian velocity (m/s)

\(\ddot{X}\) :

Cartesian acceleration (\(m/s^2\) )

\(X_e\) :

Environment location (m)

\(X_d\) :

Desired position (m)

\(X_t\) :

Command position (m)

\(X^b_s\) :

Position before spring (m)

\(X^a_s\) :

Position after spring (m)

Z :

Mechanical impedance

w :

Displacement vector (rad)

\(\dot{w}\) :

Velocity vector (rad/s)

\(\ddot{w}\) :

Acceleration vector (rad/\(s^2\))

\(\omega _n\) :

Natural frequency (rad)

\(\zeta\) :

Damping ratio

\({\sigma _f}\) :

Friction forces (N)

\({\sigma _e}\) :

External disturbance (N)

\(\delta X\) :

Correction trajectory (m)

\(\delta X_e\) :

Correction environment trajectory (m)

\(\delta F\) :

Force error (N)

\(e_{ss}^X\) :

Steady-state position error (m)

\(K^ \oplus\) :

Online stiffness (N/m)

\(\delta F^{\prime }\) :

Force error after compensation (N)

References

  1. Realyvásquez-Vargas A, Arredondo-Soto KC, García-Alcaraz JL, Márquez-Lobato BY, Cruz-García J (2018) Introduction and configuration of a collaborative robot in an assembly task as a means to decrease occupational risks and increase efficiency in a manufacturing company. Robot Comput Integr Manuf 57:315–328. https://doi.org/10.1016/j.rcim.2018.12.015

    Article  Google Scholar 

  2. Middleton RH, Goodwin GC, Longman RW (1989) A method for improving the dynamic accuracy of a robot performing a repetitive task. Int J Robot Res 8(5):67–74. https://doi.org/10.1177/027836498900800506

    Article  Google Scholar 

  3. Qiao H, Wang M, Su J, Jia S, Li R (2014) The concept of attractive region in environment and its application in high-precision tasks with low-precision systems. IEEE/ASME Trans Mechatron 20(5):2311–2327. https://doi.org/10.1109/TMECH.2014.2375638

    Article  Google Scholar 

  4. Heyer C (2010) Human-robot interaction and future industrial robotics applications. In 2010 IEEE/RSJ International Conference. IEEE, pp 4749–4754. https://doi.org/10.1109/IROS.2010.5651294

  5. Xu Z, Li S, Zhou X, Cheng T (2019) Dynamic neural networks based adaptive admittance control for redundant manipulators with model uncertainties. Neurocomputing 357:271–281. https://doi.org/10.1016/j.neucom.2019.04.069

    Article  Google Scholar 

  6. Han B, Zoppi M, Molfino R (2013) Variable impedance actuation using biphasic media. Mech Mach Theory 62:1–2. https://doi.org/10.1016/j.mechmachtheory.2012.11.001

    Article  Google Scholar 

  7. Ochoa H, Cortesao R (2021) Impedance control architecture for robotic-assisted mold polishing based on human demonstration. IEEE Trans Ind Electron. https://doi.org/10.1109/TIE.2021.3073310

    Article  Google Scholar 

  8. Lakshminarayanan S, Kana S, Mohan DM, Manyar OM, Then D, Campolo D (2021) An adaptive framework for robotic polishing based on impedance control. Int J Adv Manuf Technol 112(1):401–417. https://doi.org/10.1007/s00170-020-06270-1

    Article  Google Scholar 

  9. Peng J, Yang Z, Ma T (2019). Position/force tracking impedance control for robotic systems with uncertainties based on adaptive jacobian and neural network. https://doi.org/10.1109/ROBOT.1996.506953

    Article  Google Scholar 

  10. Yunfei D, Tianyu R, Hu K, Wu D, Chen K (2020) Contact force detection and control for robotic polishing based on joint torque sensors. Int J Adv Manuf Technol 107(5–6):2745–2756. https://doi.org/10.1007/s00170-020-05162-8

    Article  Google Scholar 

  11. Kim T, Yoo S, Kim HS, Kim J (2018) Design and force-tracking impedance control of a 2-DOF wall-cleaning manipulator using disturbance observer and sliding mode control. In 2018 IEEE International Conference on Robotics and Automation (ICRA). IEEE, pp 4079–4084. https://doi.org/10.1109/ICRA.2018.8460897

  12. Kronthaler P, Woittennek F (2019) Force regulation for pick-and-place units by use of adaptive impedance control in the semiconductor-industry with experimental results. IFAC-Papers OnLine 52(15):621–626. https://doi.org/10.1016/j.ifacol.2019.11.745

    Article  Google Scholar 

  13. Prats M, del Pobil ÁP, Sanz PJ (2013) Robot-environment interaction. In Robot Physical Interaction Through the Combination of Vision, Tactile and Force Feedback. Springer, Berlin, Heidelberg, pp 7–17. https://doi.org/10.1007/978-3-642-33241-82

  14. Dachang Z, Baolin D, Puchen Z, Shouyan C (2020). Constant force PID control for robotic manipulator based on fuzzy neural network algorithm. https://doi.org/10.1155/2020/3491845

    Article  Google Scholar 

  15. Mills JK (1996) Simultaneous control of robot manipulator impedance and generalized force and position. Mech Mach Theory 31(8):1069–1080. https://doi.org/10.1016/0094-114X(96)84599-X

    Article  Google Scholar 

  16. Chen F, Zhao H, Li D, Chen L, Tan C, Ding H (2019) Robotic grinding of a blisk with two degrees of freedom contact force control. Int J Adv Manuf Technol 101(1):461–474. https://doi.org/10.1016/0094-114X(96)84599-X

    Article  Google Scholar 

  17. Ahmed Al-Dujaili MA (2013) Study of the relation between types of the quality costs and its impact on productivity and costs: a verification in manufacturing industries. Total Qual Manag Bus Excell 24(3–4):397–419. https://doi.org/10.1080/14783363.2012.669552

    Article  Google Scholar 

  18. Bogataj D, Battini D, Calzavara M, Persona A (2019) The ageing workforce challenge: Investments in collaborative robots or contribution to pension schemes, from the multi-echelon perspective. Int J Prod Econ 210:97–106. https://doi.org/10.1016/j.ijpe.2018.12.016

    Article  Google Scholar 

  19. Kilicaslan S, Özgören MK, Ider SK (2010) Hybrid force and motion control of robots with flexible links. Mech Mach Theory 45(1):91–105. https://doi.org/10.1016/j.mechmachtheory.2009.08.004

    Article  MathSciNet  MATH  Google Scholar 

  20. Duan J, Gan Y, Chen M, Dai X (2018) Adaptive variable impedance control for dynamic contact force tracking in uncertain environment. Robot Auton Syst 102:54–65. https://doi.org/10.1016/j.robot.2018.01.009

    Article  Google Scholar 

  21. Sun T, Peng L, Cheng L, Hou ZG, Pan Y (2019) Stability-guaranteed variable impedance control of robots based on approximate dynamic inversion. IEEE Transactions on Systems, Man, and Cybernetics: Systems. https://doi.org/10.1109/TSMC.2019.2930582

    Article  Google Scholar 

  22. Hamedani MH, Sadeghian H, Zekri M, Sheikholeslam F, Keshmiri M (2021) Intelligent Impedance Control using Wavelet Neural Network for dynamic contact force tracking in unknown varying environments. Control Eng Pract 113. https://doi.org/10.1016/j.conengprac.2021.104840

    Article  Google Scholar 

  23. Cao H, Chen X, He Y, Zhao X (2019) Dynamic adaptive hybrid impedance control for dynamic contact force tracking in uncertain environments. IEEE Access 7:83162–74. https://doi.org/10.1109/ACCESS.2019.2924696

    Article  Google Scholar 

  24. Jung S, Hsia TC (1999) Stability and convergence analysis of robust adaptive force tracking impedance control of robot manipulators. In Proceedings 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human and Environment Friendly Robots with High Intelligence and Emotional Quotients (Cat. No. 99CH36289) (Vol. 2, pp. 635-640). IEEE. https://doi.org/10.1109/IROS.1999.812751

  25. Hamedani MH, Zekri M, Sheikholeslam F, Selvaggio M, Ficuciello F, Siciliano B (2021) Recurrent fuzzy wavelet neural network variable impedance control of robotic manipulators with fuzzy gain dynamic surface in an unknown varied environment. Fuzzy Set Syst 416:1–26. https://doi.org/10.1016/j.fss.2020.05.001

    Article  MathSciNet  MATH  Google Scholar 

  26. Rahimi HN, Howard I, Cui L (2018) Neural impedance adaption for assistive human-robot interaction. Neurocomputing 290:50–59. https://doi.org/10.1016/j.neucom.2018.02.025

    Article  Google Scholar 

  27. Jung S, Hsia TC (1998) Neural network impedance force control of robot manipulator. IEEE Trans Ind Electron 45(3):451–461. https://doi.org/10.1109/TCST.2004.824320

    Article  Google Scholar 

  28. Yu X, Li Y, Zhang S, Xue C, Wang Y (2020) Estimation of human impedance and motion intention for constrained human-robot interaction. Neurocomputing 390:268–279. https://doi.org/10.1016/j.neucom.2019.07.104

    Article  Google Scholar 

  29. Huang H, Yang C, Chen CP (2020) Optimal robot-environment interaction under broad fuzzy neural adaptive control. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.2998984

    Article  Google Scholar 

  30. Sabahi F (2018) Introducing validity into self-organizing fuzzy neural network applied to impedance force control. Fuzzy Set Syst 337:113–127. https://doi.org/10.1016/j.fss.2017.09.007

    Article  MathSciNet  MATH  Google Scholar 

  31. Sheng X, Zhang X (2018) Fuzzy adaptive hybrid impedance control for mirror milling system. Mechatronics. 53(20–7):20–27. https://doi.org/10.1016/j.mechatronics.2018.05.008

    Article  Google Scholar 

  32. Park H, Lee J (2004) Adaptive impedance control of a haptic interface. Mechatronics 14(3):237–253. https://doi.org/10.1016/S0957-4158(03)00040-0

    Article  Google Scholar 

  33. Azlan NZ, Yamaura H (2013) Adaptive impedance control for unknown non-flat environment. Int J Mech Mechatron Eng 7(2):191–196. https://doi.org/10.5281/zenodo.1061753

    Article  Google Scholar 

  34. Ding S, Peng J, Zhang H, Wang Y (2021) Neural network-based adaptive hybrid impedance control for electrically driven flexible-joint robotic manipulators with input saturation. Neurocomputing 458:99–111. https://doi.org/10.1016/j.neucom.2021.05.095

    Article  Google Scholar 

  35. Xu K, Wang S, Yue B, Wang J, Peng H, Liu D, Chen Z, Shi M (2020) Adaptive impedance control with variable target stiffness for wheel-legged robot on complex unknown terrain. Mechatronics 69. https://doi.org/10.1016/j.mechatronics.2020.102388

    Article  Google Scholar 

  36. Jung S, Hsia TC, Bonitz RG (2004) Force tracking impedance control of robot manipulators under unknown environment. IEEE Trans Control Syst Technol 12(3):474–483. https://doi.org/10.1109/TCST.2004.824320

    Article  Google Scholar 

  37. Jinjun D, Yahui G, Ming C, Xianzhong D (2019) Symmetrical adaptive variable admittance control for position/force tracking of dual-arm cooperative manipulators with unknown trajectory deviations. Robot Comput Integr Manuf 57:357–369. https://doi.org/10.1016/j.rcim.2018.12.012

    Article  Google Scholar 

  38. Jiang Y, Yang C, Wang Y, Ju Z, Li Y, Su CY (2020) Multi-hierarchy interaction control of a redundant robot using impedance learning. Mechatronics 67. https://doi.org/10.1016/j.mechatronics.2020.102348

    Article  Google Scholar 

  39. Su T, Niu L, He G, Liang X, Zhao L, Zhao Q (2020) Coordinated variable impedance control for multi-segment cable-driven continuum manipulators. Mech Mach Theory 153. https://doi.org/10.1016/j.mechmachtheory.2020.103969

    Article  Google Scholar 

  40. Calanca A, Muradore R, Fiorini P (2017) Impedance control of series elastic actuators: Passivity and acceleration-based control. Mechatronics 47:37–48. https://doi.org/10.1016/j.mechatronics.2017.08.010

    Article  Google Scholar 

  41. Ba K, Yu B, Gao Z, Li W, Ma G, Kong X (2017) Parameters sensitivity analysis of position-based impedance control for bionic legged robots’ HDU. Appl Sci 7(10):1035. https://doi.org/10.3390/app7101035

    Article  Google Scholar 

  42. Song P, Yu Y, Zhang X (2019) A tutorial survey and comparison of impedance control on robotic manipulation. Robotica 37(5):801–836. https://doi.org/10.1017/S0263574718001339

    Article  Google Scholar 

  43. Li E (2016) The robotic impedance controller multi-objective optimization design based on Pareto optimality. In International Conference on Intelligent Computing. Springer, Cham, pp 413–423. https://doi.org/10.1007/978-3-319-42297-8-39

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Acknowledgements

The authors acknowledge support from Staff of Bio-inspired Surface Engineering, School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics.

Funding

This work was funded by the National Natural Science Foundation of China under Grant No. 61503076 and No. 61175113.

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Authors and Affiliations

  1. Institute of Bio-inspired Surface Engineering, College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Yuedaojie, Nanjing, 210016, Jiangsu, China

    Hosham Wahballa, Jinjun Duan & Zhendong Dai

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  1. Hosham Wahballa
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  2. Jinjun Duan
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Contributions

The following lists the authors’ contributions to the manuscript: conceptualization and methodology, H. Wahballa and Z. Dai; software, H. Wahballa and J. Duan; validation, H. Wahballa; formal analysis, J. Duan; writing—original draft preparation, H. Wahballa; writing—review, Z. Dai; visualization, H. Wahballa; supervision, formal analysis, review and edits, Z. Dai. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Zhendong Dai.

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Wahballa, H., Duan, J. & Dai, Z. Constant force tracking using online stiffness and reverse damping force of variable impedance controller for robotic polishing. Int J Adv Manuf Technol 121, 5855–5872 (2022). https://doi.org/10.1007/s00170-022-09599-x

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