Continuum robots have great application value and broad prospects in various fields due to their dexterity and compliance. To fully exploit their advantages, it is crucial to develop an effective, accurate and robust control system for them. However, research on continuum robot control is still in its infancy and there are many problems remaining unsolved in this field. In particular, this paper focuses on the task-space behavior and the generic control of heterogeneous continuum robots. First, a controller is proposed to achieve the kinematic motion control and visual servoing of continuum robots with predefined task-space behavior. The predefined behavior is twofold: prescribed task-space error and predefined convergence time. Then, the proposed controller is integrated with a velocity-level kinematic mapping estimator to obtain a model-free control system, which is applicable to heterogeneous continuum robots. Furthermore, a re-adjustable performance function is proposed to ensure the effectiveness and robustness of the proposed control system in the presence of external disturbance. Finally, extensive simulations and experiments are performed based on heterogeneous continuum robots, including the cable-driven continuum robot, the parallel continuum robot, the concentric-tube robot, the flexible endoscope, and the pneumatic continuum robot. Our results demonstrate that the task-space error of heterogeneous continuum robots complies with the prescribed boundaries and converges to steady state in predefined time, which reveals the efficacy of the proposed control method.
AmouriAZaatriAMahfoudiC (2018) Dynamic modeling of a class of continuum manipulators in fixed orientation. Journal of Intelligent and Robotic Systems91(3): 413–424.
2.
AndersonPLHendrickRJRoxMF, et al. (2023) Exceeding traditional curvature limits of concentric tube robots through redundancy resolution. The International Journal of Robotics Research43(1): 53–68.
3.
AristidouALasenbyJ (2011) FABRIK: a fast, iterative solver for the inverse kinematics problem. Graphical Models73(5): 243–260.
4.
Ayala-CarrilloJEParra-VegaVOlguín-DíazE, et al. (2023) Cascade control for robust tracking of continuum soft robots with finite-time convergence of pneumatic system. IEEE Control Systems Letters7: 577–582.
5.
BechlioulisCPRovithakisGA (2008) Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Transactions on Automatic Control53(9): 2090–2099.
6.
BedellCLockJGoslineA, et al. (2011) Design optimization of concentric tube robots based on task and anatomical constraints. IEEE international conference on robotics and automation, Shanghai, China, 9–13 May 2011.
7.
BiezeTMLargilliereFKruszewskiA, et al. (2018) Finite element method-based kinematics and closed-loop control of soft, continuum manipulators. Soft Robotics5(3): 348–364.
8.
BosmanJBiezeTMLakhalO, et al. (2015) Domain decomposition approach for FEM quasistatic modeling and control of continuum robots with rigid vertebras. IEEE international conference on robotics and automation, Seattle, WA, USA, 26–30 May 2015.
9.
BoushakiMNLiuCPoignetP (2014) Task-space position control of concentric-tube robot with inaccurate kinematics using approximate Jacobian. IEEE international conference on robotics and automation, Hong Kong, China, 31 May 2014.
10.
BoutchouangAHBMelinguiAAhandaJJBM, et al. (2022) Learning-based approach to inverse kinematics of wheeled mobile continuum manipulators. IEEE/ASME Transactions on Mechatronics27(5): 3451–3462.
11.
BruderDGillespieBDavid RemyC, et al. (2019) Modeling and control of soft robots using the Koopman operator and model predictive control. Robotics: Science and Systems22. DOI: 10.15607/RSS.2019.XV.060.
12.
BruderDFuXGillespieRB, et al. (2021) Data-driven control of soft robots using Koopman operator theory. IEEE Transactions on Robotics37(3): 948–961.
13.
BrysonCERuckerDC (2014) Toward parallel continuum manipulators. IEEE international conference on robotics and automation, Hong Kong, China, 31 May 2014.
14.
BuX (2023) Prescribed performance control approaches, applications and challenges: a comprehensive survey. Asian Journal of Control25(1): 241–261.
15.
ChenYWuBJinJ, et al. (2021) A variable curvature model for multi-backbone continuum robots to account for inter-segment coupling and external disturbance. IEEE Robotics and Automation Letters6(2): 1590–1597.
16.
Della SantinaCBicchiARusD (2020a) On an improved state parametrization for soft robots with piecewise constant curvature and its use in model based control. IEEE Robotics and Automation Letters5(2): 1001–1008.
17.
Della SantinaCKatzschmannRKBicchiA, et al. (2020b) Model-based dynamic feedback control of a planar soft robot: trajectory tracking and interaction with the environment. The International Journal of Robotics Research39(4): 490–513.
18.
DemirSOCulhaUKaracakolAC, et al. (2021) Task space adaptation via the learning of gait controllers of magnetic soft millirobots. The International Journal of Robotics Research40(12-14): 1331–1351.
19.
DuriezC (2013) Control of elastic soft robots based on real-time finite element method. IEEE international conference on robotics and automation, Karlsruhe, Germany, 6–10 May 2013.
20.
EmaruTImagawaKHoshinoY, et al. (2008) Estimation of velocity and acceleration by nonlinear filter using sliding mode and application to control systems. Asia International Symposium on Mechatronics3: 212–217.
21.
GilbertHBHendrickRJWebsterRJ (2016) Elastic stability of concentric tube robots: a stability measure and design test. IEEE Transactions on Robotics: A Publication of the IEEE Robotics and Automation Society32(1): 20–35.
22.
GiorelliMRendaFCalistiM, et al. (2012) A two dimensional inverse kinetics model of a cable driven manipulator inspired by the octopus arm. IEEE international conference on robotics and automation, St Paul, Minnesota, USA, 14–18 May 2012.
23.
GiorelliMRendaFCalistiM, et al. (2015) Neural network and Jacobian method for solving the inverse statics of a cable-driven soft arm with nonconstant curvature. IEEE Transactions on Robotics31(4): 823–834.
24.
GongZFangXChenX, et al. (2021) A soft manipulator for efficient delicate grasping in shallow water: modeling, control, and real-world experiments. The International Journal of Robotics Research40(1): 449–469.
25.
GouryODuriezC (2018) Fast, generic, and reliable control and simulation of soft robots using model order reduction. IEEE Transactions on Robotics34(6): 1565–1576.
26.
GrassmannRModesVBurgner-KahrsJ (2018) Learning the forward and inverse kinematics of a 6-DOF concentric tube continuum robot in SE(3). IEEE/RSJ international conference on intelligent robots and systems, Madrid, Spain, 1–5 October 2018.
27.
GrassmannRMChenRZLiangN, et al. (2022) A dataset and benchmark for learning the kinematics of concentric tube continuum robots. IEEE/RSJ international conference on intelligent robots and systems, Kyoto, 27 October 2022.
28.
GundermanALSenguptaSSiampliE, et al. (2023) Non-metallic MR-guided concentric tube robot for intracerebral hemorrhage evacuation. IEEE transactions on bio-medical engineering70(10): 2895–2904.
29.
HaggertyDABanksMJKamenarE, et al. (2023) Control of soft robots with inertial dynamics. Science Robotics8: eadd6864.
30.
HanJHanZLiuZ (2020) Adaptive control for a constrained soft manipulator with prescribed performance. IFAC-PapersOnLine53(5): 524–529.
31.
HendrickRJGilbertHBWebsterRJ (2015) Designing snap-free concentric tube robots: a local bifurcation approach. IEEE international conference on robotics and automation, Seattle, WA, USA, 26–30 May 2015.
32.
HuangYLiJZhangX, et al. (2022) A surgeon preference-guided autonomous instrument tracking method with a robotic flexible endoscope based on dVRK platform. IEEE Robotics and Automation Letters7(2): 2250–2257.
33.
JiangHWangZJinY, et al. (2021) Hierarchical control of soft manipulators towards unstructured interactions. The International Journal of Robotics Research40(1): 411–434.
34.
JinYWangYChenX, et al. (2017) Model-less feedback control for soft manipulators. IEEE international conference on intelligent robots and systems, Vancouver, Canada, 24–28 September 2017.
35.
KalidindiHTThuruthelTGLaschiC, et al. (2019) Cerebellum-inspired approach for adaptive kinematic control of soft robots. IEEE international conference on soft robotics, Seoul Korea, 14–18 April 2019.
36.
KolpashchikovDYLaptevNVDanilovVV, et al. (2018) FABRIK-based inverse kinematics for multi-section continuum robots. International conference on mechatronics-mechatronika, Brno, Czech Republic, 5–7 December 2018.
37.
LeeKHFuDKLeongMC, et al. (2017) Nonparametric online learning control for soft continuum robot: an enabling technique for effective endoscopic navigation. Soft Robotics4(4): 324–337.
38.
LiMKangRBransonDT, et al. (2018) Model-free control for continuum robots based on an adaptive Kalman filter. IEEE/ASME Transactions on Mechatronics23(1): 286–297.
39.
LiGSongDXuS, et al. (2019) A hybrid model and model-free position control for a reconfigurable manipulator. IEEE/ASME Transactions on Mechatronics24(2): 785–795.
40.
LiWChengTYeM, et al. (2020) Kinematic modeling and visual servo control of a soft-bodied magnetic anchored and guided endoscope. IEEE/ASME Transactions on Mechatronics25(3): 1531–1542.
41.
LiangNGrassmannRMLilgeS, et al. (2021) Learning-based inverse kinematics from shape as input for concentric tube continuum robots. IEEE international conference on robotics and automation, Yokohama, Japan, 13 May 2021.
42.
LilgeSBurgner-KahrsJ (2023) Kinetostatic modeling of tendon-driven parallel continuum robots. IEEE Transactions on Robotics39(2): 1563–1579.
43.
LilgeSBarfootTDBurgner-KahrsJ (2022) Continuum robot state estimation using Gaussian process regression on SE(3). The International Journal of Robotics Research41(13-14): 1099–1120.
44.
LuARamosFLinJT, et al. (2023) Enabling higher performance concentric tube robots via multiple constant-curvature tubes. International symposium on medical robotics, Atlanta, GA, USA, 19–21 April 2023. DOI: 10.1109/ISMR57123.2023.10130226.
45.
MelinguiALakhalODaachiB, et al. (2015) Adaptive neural network control of a compact bionic handling arm. IEEE/ASME Transactions on Mechatronics20(6): 2862–2875.
46.
NeppalliSCsencsitsMAJonesBA, et al. (2009) Closed-form inverse kinematics for continuum manipulators. Advanced Robotics23(15): 2077–2091.
47.
Oliver-ButlerKTillJRuckerC (2019) Continuum robot stiffness under external loads and prescribed tendon displacements. IEEE Transactions on Robotics35(2): 403–419.
48.
RuckerDCWebster IIIRJ (2011) Statics and dynamics of continuum robots with general tendon routing and external loading. IEEE Transactions on Robotics27(6): 1033–1044.
49.
RuckerDCJonesBAWebsterRJ (2010) A geometrically exact model for externally loaded concentric-tube continuum robots. IEEE Transactions on Robotics: A Publication of the IEEE Robotics and Automation Society26(5): 769–780.
SadatiSHNaghibiSEShivaA, et al. (2021) TMTDyn: a matlab package for modeling and control of hybrid rigid-continuum robots based on discretized lumped systems and reduced-order models. The International Journal of Robotics Research40(1): 296–347.
52.
SantosoJOnalCD (2021) An origami continuum robot capable of precise motion through torsionally stiff body and smooth inverse kinematics. Soft Robotics8(4): 371–386.
53.
SchrammLSintovABoulariasA (2020) Learning to transfer dynamic models of underactuated soft robotic hands. IEEE international conference on robotics and automation, Paris, France, 31 May 2020.
54.
SeeberRHaimovichHHornM, et al. (2021) Robust exact differentiators with predefined convergence time. Automatica134: 109858.
55.
SlawinskiPRSimaanNObsteinKL, et al. (2019) Sensorless estimation of the planar distal shape of a tip-actuated endoscope. IEEE Robotics and Automation Letters4(4): 3371–3377.
56.
TanNYuPZhangX, et al. (2021) Model-free motion control of continuum robots based on a zeroing neurodynamic approach. Neural Networks: The Official Journal of the International Neural Network Society133: 21–31.
57.
TanNYuPHuangK (2023a) Predefined-time convergent motion control for heterogeneous continuum robots. Robotics: Science and Systems, Daegu, Republic of Korea, 10 July 2023. DOI: 10.15607/RSS.2023.XIX.092.
58.
TanNYuPZhongZ, et al. (2023b) Data-driven control for continuum robots based on discrete zeroing neural networks. IEEE Transactions on Industrial Informatics19(5): 7088–7098.
59.
ThamoBHanleyDDhaliwalK, et al. (2023) Data-driven steering of concentric tube robots in unknown environments via dynamic mode decomposition. IEEE Robotics and Automation Letters8(2): 856–863.
60.
ThuruthelTGFaloticoECianchettiM, et al. (2016) Learning global inverse statics solution for a redundant soft robot. International Conference on Informatics in Control, Automation and Robotics, Doctoral Consortium2: 303–310.
61.
George ThuruthelTFaloticoEMantiM, et al. (2017) Learning closed loop kinematic controllers for continuum manipulators in unstructured environments. Soft Robotics4(3): 285–296.
62.
TillJAloiVRuckerC (2019) Real-time dynamics of soft and continuum robots based on Cosserat rod models. The International Journal of Robotics Research38(6): 723–746.
63.
WangYHuJ (2018) Improved prescribed performance control for air-breathing hypersonic vehicles with unknown deadzone input nonlinearity. ISA Transactions79: 95–107.
64.
WangYJuFYunY, et al. (2020) An inspection continuum robot with tactile sensor based on electrical impedance tomography for exploration and navigation in unknown environment. Industrial Robot: The International Journal of Robotics Research and Application47: 121–130.
65.
WangHLiangWLiangB, et al. (2023) Robust position control of a continuum manipulator based on selective approach and Koopman operator. IEEE Transactions on Industrial Electronics70(12): 12522–12532.
66.
WebsterRJJonesBA (2010) Design and kinematic modeling of constant curvature continuum robots: a review. The International Journal of Robotics Research29(13): 1661–1683.
67.
WebsterRJOkamuraAMCowanNJ (2006) Toward Active Cannulas: Miniature Snake-like Surgical Robots. In: 2006 IEEE/RSJ international conference on intelligent robots and systems, Beijing, China, 15 October 2006.
68.
WebsterRJRomanoJMCowanNJ (2009) Mechanics of precurved-tube continuum robots. IEEE Transactions on Robotics25(1): 67–78.
69.
WuKWuLLimCM, et al. (2015) Model-free image guidance for intelligent tubular robots with pre-clinical feasibility study: towards minimally invasive trans-orifice surgery. IEEE international conference on information and automation, Lijiang, China, 8–10 August 2015.
70.
YangPSuY (2022) Proximate fixed-time prescribed performance tracking control of uncertain robot manipulators. IEEE/ASME Transactions on Mechatronics27(5): 3275–3285.
71.
YangYHanJLiuZ, et al. (2023) Modeling and adaptive neural network control for a soft robotic arm with prescribed motion constraints. IEEE/CAA Journal of Automatica Sinica10(2): 501–511.
72.
YipMCCamarilloDB (2014) Model-less feedback control of continuum manipulators in constrained environments. IEEE Transactions on Robotics30(4): 880–889.
73.
YipMCCamarilloDB (2016) Model-less hybrid position/force control: a minimalist approach for continuum manipulators in unknown, constrained environments. IEEE Robotics and Automation Letters1(2): 844–851.
74.
YuanHZhouLXuW (2019) A comprehensive static model of cable-driven multi-section continuum robots considering friction effect. Mechanism and Machine Theory135: 130–149.
75.
ZhangYGuoD (2015) Zhang Functions and Various Models. Berlin, Heidelberg: Springer.
76.
ZhangWYangZDongT, et al. (2018) FABRIKc: an efficient iterative inverse kinematics solver for continuum robots. IEEE/ASME international conference on advanced intelligent mechatronics, Auckland, New Zealand, 9–12 July 2018.
77.
ZhuangFQiZDuanK, et al. (2021) A comprehensive survey on transfer learning. Proceedings of the IEEE109(1): 43–76.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
