Graphical Abstract Figure
Abstract
Fast inverse kinematics (IK) algorithm is significant for real-time precise motion control for continuum and soft manipulators. In this paper, we studied an explicit expression of a two-segment continuum manipulator based on constant curvature assumptions and discussed the existence of the IK solutions. Utilizing the pseudo-rigid-body method, we contrast this model with the traditional six-axis rigid industrial robot arm, revealing that two-segment extensible continuum manipulators exhibit limited rotation angles around the directional vector of their tips, thereby showcasing reduced dexterity. By pre-constraining five degrees-of-freedom (DOF) and addressing the definition of the remaining DOF, we streamline the IK-solving process, resulting in minimal computational overhead suitable for a wide range of applications. This model promises a robust and real-time approach for controlling two-segment extensible continuum manipulators, enhancing their operational efficiency and effectiveness.
References
1.
Kim
, Y.-J.
, Cheng
, S.
, Kim
, S.
, and Iagnemma
, K.
, 2014
, “A Stiffness-Adjustable Hyperredundant Manipulator Using a Variable Neutral-Line Mechanism for Minimally Invasive Surgery
,” IEEE Trans. Rob.
, 30
(2
), pp. 382
–395
. 2.
Burgner-Kahrs
, J.
, Rucker
, D. C.
, and Choset
, H.
, 2015
, “Continuum Robots for Medical Applications: A Survey
,” IEEE Trans. Rob.
, 31
(6
), pp. 1261
–1280
. 3.
Frazelle
, C. G.
, Kapadia
, A. D.
, and Walker
, I. D.
, 2020
, “A Haptic Continuum Interface for the Teleoperation of Extensible Continuum Manipulators
,” IEEE Robot. Autom. Lett.
, 5
(2
), pp. 1875
–1882
. 4.
Dong
, X.
, Wang
, M.
, Mohammad
, A.
, Ba
, W.
, Russo
, M.
, Norton
, A.
, Kell
, J.
, Axinte
, D.
, and Axinte
, D.
, 2022
, “Continuum Robots Collaborate for Safe Manipulation of High-Temperature Flame to Enable Repairs in Challenging Environments
,” IEEE/ASME Trans. Mechatron.
, 27
(5
), pp. 1
–4
. 5.
Tiefeng
, S.
, Mingyu
, D.
, Guanjun
, B.
, Libin
, Z.
, and Qinghua
, Y.
, 2015
, “Fruit Harvesting Continuum Manipulator Inspired by Elephant Trunk
,” Int. J. Agric. Biol. Eng.
, 8
(1
), pp. 57
–63
. http:/dx.doi.org/10.3965/j.ijabe.20150801.0086.
Webster
, R. J.
, and Jones
, B. A.
, 2010
, “Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
,” Int. J. Rob. Res.
, 29
(13
), pp. 1661
–1683
. 7.
Rao
, P.
, Peyron
, Q.
, Lilge
, S.
, and Burgner-Kahrs
, J.
, 2020
, “How to Model Tendon-Driven Continuum Robots and Benchmark Modelling Performance
,” Front. Rob. AI
, 7
, p. 630245
. 8.
George Thuruthel
, T.
, Falotico
, E.
, Manti
, M.
, Pratesi
, A.
, Cianchetti
, M.
, and Laschi
, C.
, 2017
, “Learning Closed Loop Kinematic Controllers for Continuum Manipulators in Unstructured Environments
,” Soft Rob.
, 4
(3
), pp. 285
–296
. 9.
Frazelle
, C.
, Walker
, I.
, AlAttar
, A.
, and Kormushev
, P.
, 2021
, “Kinematic-Model-Free Control for Space Operations With Continuum Manipulators
,” 2021 IEEE Aerospace Conference (50100)
, Big Sky, MT
, pp. 1
–11
.10.
Wang
, X.
, Li
, Y.
, and Kwok
, K.-W.
, 2021
, “A Survey for Machine Learning-Based Control of Continuum Robots
,” Front. Rob. AI
, 8
, p. 730330
. 11.
Barrientos-Diez
, J.
, Dong
, X.
, Axinte
, D.
, and Kell
, J.
, 2021
, “Real-Time Kinematics of Continuum Robots: Modelling and Validation
,” Rob. Comput. Integr. Manuf.
, 67
, p. 102019
. 12.
Amanov
, E.
, Nguyen
, T.-D.
, and Burgner-Kahrs
, J.
, 2021
, “Tendon-Driven Continuum Robots With Extensible Sections—A Model-Based Evaluation of Path-Following Motions
,” Int. J. Rob. Res.
, 40
(1
), pp. 7
–23
. 13.
Chikhaoui
, M. T.
, Lilge
, S.
, Kleinschmidt
, S.
, and Burgner-Kahrs
, J.
, 2019
, “Comparison of Modeling Approaches for a Tendon Actuated Continuum Robot With Three Extensible Segments
,” IEEE Robot. Autom. Lett.
, 4
(2
), pp. 989
–996
. 14.
Mahl
, T.
, Hildebrandt
, A.
, and Sawodny
, O.
, 2014
, “A Variable Curvature Continuum Kinematics for Kinematic Control of the Bionic Handling Assistant
,” IEEE Trans. Rob.
, 30
(4
), pp. 935
–949
. 15.
Garriga-Casanovas
, A.
, and Rodriguez y Baena
, F.
, 2019
, “Kinematics of Continuum Robots With Constant Curvature Bending and Extension Capabilities
,” ASME J. Mech. Rob.
, 11
(1
), p. 011010
. 16.
Wang
, Y.
, Wu
, Z.
, Wang
, L.
, Feng
, B.
, and Xu
, K.
, 2022
, “IK and Dexterous Workspace Formulation for 2-Segment Continuum Robots With Inextensible Segments
,” IEEE Robot. Autom. Lett.
, 7
(1
), pp. 510
–517
. 17.
Zhang
, W.
, Yang
, Z.
, Dong
, T.
, and Xu
, K.
, 2018
, “FABRIKC: An Efficient Iterative IK Solver for Continuum Robots
,” 2018 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)
, Auckland, New Zealand
, pp. 346
–352
.18.
Neppalli
, S.
, Csencsits
, M. A.
, Jones
, B. A.
, and Walker
, I. D.
, 2009
, “Closed-Form IK for Continuum Manipulators
,” Adv. Rob.
, 23
(15
), pp. 2077
–2091
. 19.
Neppalli
, S.
, Csencsits
, M. A.
, Jones
, B. A.
, and Walker
, I.
, 2008
, “A Geometrical Approach to IK for Continuum Manipulators
,” 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems
, Nice, France
, pp. 3565
–3570
.20.
Mbakop
, S.
, Tagne
, G.
, Drakunov
, S.
, and Merzouki
, R.
, 2022
, “Parametric PH Curves-Model Based Kinematic Control of the Shape of Mobile Soft-Manipulators in Unstructured Environment
,” IEEE Trans. Ind. Electron.
, 69
(10
), pp. 10292
–10300
. 21.
Godage
, I. S.
, Guglielmino
, E.
, Branson
, D. T.
, Medrano-Cerda
, G. A.
, and Caldwell
, D. G.
, 2011
, “Novel Modal Approach for Kinematics of Multisection Continuum Arms
,” 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems
, San Francisco, CA
, pp. 1093
–1098
.22.
Chen
, Y.
, Wang
, L.
, Galloway
, K.
, Godage
, I.
, Simaan
, N.
, and Barth
, E.
, 2021
, “Modal-Based Kinematics and Contact Detection of Soft Robots
,” Soft Rob.
, 8
(3
), pp. 298
–309
. 23.
Chen
, X.
, Zhang
, X.
, Huang
, Y.
, Cao
, L.
, and Liu
, J.
, 2022
, “A Review of Soft Manipulator Research, Applications, and Opportunities
,” J. Field Rob.
, 39
(3
), pp. 281
–311
. 24.
Li
, J.
, Chen
, X.
, Su
, Y.
, Wang
, W.
, Lam
, J.
, and Wang
, Z.
, 2022
, “Kinematic Analysis of Soft Continuum Manipulators Based on Sparse Workspace Mapping
,” IEEE Robot. Autom. Lett.
, 7
(2
), pp. 5055
–5062
. 25.
Peng
, J.
, Xu
, W.
, Liu
, T.
, Yuan
, H.
, and Liang
, B.
, 2021
, “End-Effector Pose and Arm-Shape Synchronous Planning Methods of a Hyper-Redundant Manipulator for Spacecraft Repairing
,” Mech. Mach. Theory
, 155
, p. 104062
. 26.
Kapadia
, A.
, and Walker
, I. D.
, 2011
, “Task-Space Control of Extensible Continuum Manipulators
,” 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems
, San Francisco, CA
, Sept. 2011
, pp. 1087
–1092
.27.
Garriga-Casanovas
, A.
, and Rodriguez y Baena
, F.
, 2018
, “Complete Follow-the-Leader Kinematics Using Concentric Tube Robots
,” Int. J. Rob. Res.
, 37
(1
), pp. 197
–222
. 28.
Chikhaoui
, M. T.
, Granna
, J.
, Starke
, J.
, and Burgner-Kahrs
, J.
, 2018
, “Toward Motion Coordination Control and Design Optimization for Dual-Arm Concentric Tube Continuum Robots
,” IEEE Robot. Autom. Lett.
, 3
(3
), pp. 1793
–1800
. 29.
Nguyen
, T.-D.
, and Burgner-Kahrs
, J.
, 2015
, “A Tendon-Driven Continuum Robot With Extensible Sections
,” 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, Hamburg, Germany
, pp. 2130
–2135
.30.
Xu
, Y.
, Peyron
, Q.
, Kim
, J.
, and Burgner-Kahrs
, J.
, 2021
, “Design of Lightweight and Extensible Tendon-Driven Continuum Robots Using Origami Patterns
,” 2021 IEEE 4th International Conference on Soft Robotics (RoboSoft)
, New Haven, CT
, pp. 308
–314
.31.
Chiang
, S.-S.
, Yang
, H.
, Skorina
, E.
, and Onal
, C. D.
, 2021
, “SLInKi: State Lattice Based Inverse Kinematics—A Fast, Accurate, and Flexible IK Solver for Soft Continuum Robot Manipulators
,” 2021 IEEE 17th International Conference on Automation Science and Engineering (CASE)
, Lyon, Spain
, Oct. 1–5
.32.
Zhang
, H. J.
, Giamou
, M.
, Marić
, F.
, Kelly
, J.
, and Burgner-Kahrs
, J.
, 2023
, “CIDGIKC: Distance-Geometric Inverse Kinematics for Continuum Robots
,” IEEE Robot. Autom. Lett.
, 8
(11
), pp. 7679
–7686
. 33.
Grassmann
, R. M.
, Modes
, V.
, and Burgner-Kahrs
, J.
, 2018
, “Learning the Forward and Inverse Kinematics of a 6-DOF Concentric Tube Continuum Robot in SE(3)
,” 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, Madrid, Spain, pp. 5125–5132
.
