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.
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References
George Thuruthel T, Ansari Y, Falotico E, Laschi C (2018) Control strategies for soft robotic manipulators: a survey. Soft Robot 5(2):149–163
Wooten MB, Walker ID (2017) Robot ropes for disaster response operations. In: 2017 IEEE global humanitarian technology conference (GHTC), pp 1–1
Walker ID, University C (2017) Use of continuum robots for remote inspection operations. In: Computing conference, pp 1382–1385
Nahar D, Yanik PM, Walker ID (2017) Robot tendrils: long, thin continuum robots for inspection in space operations. In: IEEE aerospace conference, pp 1–8
Kim Y, Cheng SS, Desai JP (2018) Active stiffness tuning of a spring-based continuum robot for MRI-guided neurosurgery. IEEE Trans Robot 34:18–28
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 2:1656–1663
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 1989–1995
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 3:1793–1800
Ouyang B, Liu Y, Tam H, Sun D (2018) Design of an interactive control system for a multisection continuum robot. IEEE/ASME Trans Mechatron 23:2379–2389
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 4945–4950
Dehghani M, Moosavian SAA (2014) Compact modeling of spatial continuum robotic arms towards real time control. Adv Robot 28(1):15–26
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 130:109–122
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 11–16
Rone WS, Ben-Tzvi P (2014) Continuum robot dynamics utilizing the principle of virtual power. IEEE Trans Robot 30:275–287
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 5660–5665
Falkenhahn V, Hildebrandt A, Neumann R, Sawodny O (2017) Dynamic control of the bionic handling assistant. IEEE/ASME Trans Mechatron 22:6–17
Amouri A, Zaatri A, Mahfoudi C (2018) Dynamic modeling of a class of continuum manipulators in fixed orientation. J Intell Robot Syst 91:413–424
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 31:1483–1496
Gravagne IA, Rahn CD, Walker ID (2003) Large deflection dynamics and control for planar continuum robots. IEEE/ASME Trans Mechatron 8:299–307
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 361–369
Ivanescu M, Popescu D, Popescu N (2015) A decoupled sliding mode control for a continuum arm. Adv Robot 29(13):831–845
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
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):695–722
Mousa A, Khoo S, Norton M (2018) Robust control of tendon driven continuum robots. In: 15th International workshop on variable structure systems (VSS), pp 49–54
Alqumsan AA, Khoo S, Norton M (2019) Robust control of continuum robots using cosserat rod theory. Mech Mach Theory 131:48–61
Zak SH (2002) Systems and control. Oxford University Press, Oxford
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):2388–2404
Rubin MB (2000) Cosserat rods. Springer, Dordrecht, pp 191–310
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 79:38–47
Nuti S, Ruimi A, Reddy J (2014) Modeling the dynamics of flaments for medical applications. Int J Non-Linear Mech 66:139–148
Hoffman JD (1992) Numerical methods for engineers and scientists. McGraw-Hill, New York
Sobottka GA, Lay T, Weber A (2008) Stable integration of the dynamic cosserat equations with application to hair modeling. J WSCG 16:73–80
Rucker DC, Webster RJ III (2011) Statics and dynamics of continuum robots with general tendon routing and external loading. IEEE Trans Robot 27:1033–1044
Sontag ED (1998) Mathematical control theory: deterministic finite dimensional systems, 2nd edn. Springer, New York, pp 57–60
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):7985–8004
Won M, Hedrick JK (1996) Multiple-surface sliding control of a class of uncertain nonlinear systems. Int J Control 64:693–706
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The Titan Xp used for this research was donated by the NVIDIA Corporation. The authors also wish to thank Xenon Systems Pty Ltd for the XENON/CSIRO GPU support program for this project.
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Abu Alqumsan, A., Khoo, S. & Norton, M. Multi-surface sliding mode control of continuum robots with mismatched uncertainties. Meccanica 54, 2307–2316 (2019). https://doi.org/10.1007/s11012-019-01072-6
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DOI: https://doi.org/10.1007/s11012-019-01072-6