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Meccanica

, Volume 54, Issue 14, pp 2307–2316 | Cite as

Multi-surface sliding mode control of continuum robots with mismatched uncertainties

  • Ahmad Abu AlqumsanEmail author
  • Suiyang Khoo
  • Michael Norton
Article
  • 73 Downloads

Abstract

In this paper, we tackle the control problem of continuum robots with mismatched uncertainties. Uncertainties that affect systems through any of their states and may not be directly accessed by their controllers. These uncertainties emerge in a system either due to unmodeled dynamics, practical limitations, or external disturbances. Continuum robots possess highly nonlinear dynamic behaviour due to their elastic nature and operate within undefined or congested environments, exposing them to such uncertainties. However, mismatched uncertainties in the continuum robots’ field, are yet to be addressed. Here, we tackle this problem and propose the first robust control for continuum robots that assures its robustness property under mismatched uncertainties. To this end, we first derive the dynamic model for our continuum robot by considering it as an elastic rod and then applying Cosserat rod theory. This will result in a general dynamic model that does not require any design or operative assumption. Next, we design our robust controller utilizing multi-surface sliding mode control, a method capable of handling nonlinear systems under mismatched uncertainties. Finally, we include simulations to validate our controller’s performance.

Keywords

Robust control Multi-surface sliding mode control Continuum robot Cosserat rod Mismatched uncertainties 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    George Thuruthel T, Ansari Y, Falotico E, Laschi C (2018) Control strategies for soft robotic manipulators: a survey. Soft Robot 5(2):149–163CrossRefGoogle Scholar
  2. 2.
    Wooten MB, Walker ID (2017) Robot ropes for disaster response operations. In: 2017 IEEE global humanitarian technology conference (GHTC), pp 1–1Google Scholar
  3. 3.
    Walker ID, University C (2017) Use of continuum robots for remote inspection operations. In: Computing conference, pp 1382–1385Google Scholar
  4. 4.
    Nahar D, Yanik PM, Walker ID (2017) Robot tendrils: long, thin continuum robots for inspection in space operations. In: IEEE aerospace conference, pp 1–8Google Scholar
  5. 5.
    Kim Y, Cheng SS, Desai JP (2018) Active stiffness tuning of a spring-based continuum robot for MRI-guided neurosurgery. IEEE Trans Robot 34:18–28CrossRefGoogle Scholar
  6. 6.
    Dwyer G, Chadebecq F, Amo MT, Bergeles C, Maneas E, Pawar V, Poorten EV, Deprest J, Ourselin S, De Coppi P, Vercauteren T, Stoyanov D (2017) A continuum robot and control interface for surgical assist in fetoscopic interventions. IEEE Robot Autom Lett 2:1656–1663CrossRefGoogle Scholar
  7. 7.
    Qu T, Chen J, Shen S, Xiao Z, Yue Z, Lau HYK (2016) Motion control of a bio-inspired wire-driven multi backbone continuum minimally invasive surgical manipulator. In: IEEE international conference on robotics and biomimetics (ROBIO), pp 1989–1995Google Scholar
  8. 8.
    Chikhaoui MT, Granna J, Starke J, BurgnerKahrs J (2018) Toward motion coordination control and design optimization for dual-arm concentric tube continuum robots. IEEE Robot Autom Lett 3:1793–1800CrossRefGoogle Scholar
  9. 9.
    Ouyang B, Liu Y, Tam H, Sun D (2018) Design of an interactive control system for a multisection continuum robot. IEEE/ASME Trans Mechatron 23:2379–2389CrossRefGoogle Scholar
  10. 10.
    Mahl T, Mayer AE, Hildebrandt A, Sawodny O (2013) A variable curvature modeling approach for kinematic control of continuum manipulators. In: American control conference, pp 4945–4950Google Scholar
  11. 11.
    Dehghani M, Moosavian SAA (2014) Compact modeling of spatial continuum robotic arms towards real time control. Adv Robot 28(1):15–26CrossRefGoogle Scholar
  12. 12.
    Chen L, Yang C, Wang H, Branson DT, Dai JS, Kang R (2018) Design and modeling of a soft robotic surface with hyperelastic material. Mech Mach Theory 130:109–122CrossRefGoogle Scholar
  13. 13.
    Lee K, Leong MCW, Chow MCK, Fu H, Luk W, Sze K, Yeung C, Kwok K (2017) Fem-based soft robotic control framework for intracavitary navigation. In: IEEE international conference on real-time computing and robotics (RCAR), pp 11–16Google Scholar
  14. 14.
    Rone WS, Ben-Tzvi P (2014) Continuum robot dynamics utilizing the principle of virtual power. IEEE Trans Robot 30:275–287CrossRefGoogle Scholar
  15. 15.
    Hisch F, Giusti A, Althoff M (2017) Robust control of continuum robots using interval arithmetic. IFAC-PapersOnLine. In: 20th IFAC world congress, vol 50(1), pp 5660–5665Google Scholar
  16. 16.
    Falkenhahn V, Hildebrandt A, Neumann R, Sawodny O (2017) Dynamic control of the bionic handling assistant. IEEE/ASME Trans Mechatron 22:6–17CrossRefGoogle Scholar
  17. 17.
    Amouri A, Zaatri A, Mahfoudi C (2018) Dynamic modeling of a class of continuum manipulators in fixed orientation. J Intell Robot Syst 91:413–424CrossRefGoogle Scholar
  18. 18.
    Falkenhahn V, Mahl T, Hildebrandt A, Neumann R, Sawodny O (2015) Dynamic modeling of bellows-actuated continuum robots using the eulerlagrange formalism. IEEE Trans Robot 31:1483–1496CrossRefGoogle Scholar
  19. 19.
    Gravagne IA, Rahn CD, Walker ID (2003) Large deflection dynamics and control for planar continuum robots. IEEE/ASME Trans Mechatron 8:299–307CrossRefGoogle Scholar
  20. 20.
    Ivanescu M, Nitulescu M, Nguyen VDH, Florescu M (2017) Dynamic control for a class of continuum robotic arms. In: New advances in mechanisms, mechanical transmissions and robotics. Springer, Cham, pp 361–369Google Scholar
  21. 21.
    Ivanescu M, Popescu D, Popescu N (2015) A decoupled sliding mode control for a continuum arm. Adv Robot 29(13):831–845CrossRefGoogle Scholar
  22. 22.
    Hadi Sadati SM, Shiva A, Ataka A, Naghibi SE, Walker ID, Althoefer K, Nanayakkara T (2016) A geometry deformation model for compound continuum manipulators with external loading. In: 2016 IEEE international conference on robotics and automation (ICRA), Stockholm, pp 4957–4962. https://ieeexplore.ieee.org/document/7487702
  23. 23.
    Godage IS, Medrano-Cerda GA, Branson DT, Guglielmino E, Caldwell DG (2016) Dynamics for variable length multisection continuum arms. Int J Robot Res 35(6):695–722CrossRefGoogle Scholar
  24. 24.
    Mousa A, Khoo S, Norton M (2018) Robust control of tendon driven continuum robots. In: 15th International workshop on variable structure systems (VSS), pp 49–54Google Scholar
  25. 25.
    Alqumsan AA, Khoo S, Norton M (2019) Robust control of continuum robots using cosserat rod theory. Mech Mach Theory 131:48–61CrossRefGoogle Scholar
  26. 26.
    Zak SH (2002) Systems and control. Oxford University Press, OxfordzbMATHGoogle Scholar
  27. 27.
    Khoo S, Xie L, Zhao S, Man Z (2014) Multi-surface sliding control for fast finite time leader follower consensus with high order siso uncertain nonlinear agents. Int J Robust Nonlinear Control 24(16):2388–2404MathSciNetCrossRefGoogle Scholar
  28. 28.
    Rubin MB (2000) Cosserat rods. Springer, Dordrecht, pp 191–310Google Scholar
  29. 29.
    Arbind A, Reddy J (2016) Transient analysis of cosserat rod with inextensibility and unshearability constraints using the least squares finite element model. Int J Non-Linear Mech 79:38–47CrossRefGoogle Scholar
  30. 30.
    Nuti S, Ruimi A, Reddy J (2014) Modeling the dynamics of flaments for medical applications. Int J Non-Linear Mech 66:139–148CrossRefGoogle Scholar
  31. 31.
    Hoffman JD (1992) Numerical methods for engineers and scientists. McGraw-Hill, New YorkzbMATHGoogle Scholar
  32. 32.
    Sobottka GA, Lay T, Weber A (2008) Stable integration of the dynamic cosserat equations with application to hair modeling. J WSCG 16:73–80Google Scholar
  33. 33.
    Rucker DC, Webster RJ III (2011) Statics and dynamics of continuum robots with general tendon routing and external loading. IEEE Trans Robot 27:1033–1044CrossRefGoogle Scholar
  34. 34.
    Sontag ED (1998) Mathematical control theory: deterministic finite dimensional systems, 2nd edn. Springer, New York, pp 57–60CrossRefGoogle Scholar
  35. 35.
    Zhang Q, Wang C, Su X, Xu D (2018) Observer-based terminal sliding mode control of non-affine nonlinear systems: finite-time approach. J Frankl Inst 335(16):7985–8004MathSciNetCrossRefGoogle Scholar
  36. 36.
    Won M, Hedrick JK (1996) Multiple-surface sliding control of a class of uncertain nonlinear systems. Int J Control 64:693–706MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of EngineeringDeakin UniversityGeelongAustralia

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