The kinematics of the octopus’s arm is studied from the point of view of robotics. A continuum three-dimensional kinematic model of the arm, based on a nonlinear rod theory, is proposed. The model enables the calculation of the strains in various muscle fibers that are required in order to produce a given configuration of the arm—a solution to the inverse kinematics problem. The analysis of the forward kinematics problem shows that the strains in the muscle fibers at two distinct points belonging to a cross section of the arm determine the curvature and the twist of the arm at that cross section. The octopus’s arm lacks a rigid skeleton and the role of material incompressibility in enabling the configuration control is studied.
Issue Section:
Research Papers
1.
Levinson
, Y.
, 2008, “On the Kinematics of the Octopus’s Arm
,” MS thesis, Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, Israel.2.
Fahimi
, F.
, Ashrafiuon
, H.
, and Nataraj
, C.
, 2002, “An Improved Inverse Kinematic and Velocity Solution for Spatial Hyper-Redundant Robots
,” IEEE Trans. Rob. Autom.
1042-296X, 18
(1
), pp. 103
–107
.3.
Sujan
, V. A.
, and Dubowsky
, S.
, 2004, “Design of a Lightweight Hyper-Redundant Deployable Binary Manipulator
,” ASME J. Mech. Des.
0161-8458, 126
, pp. 29
–39
.4.
Yamada
, H.
, and Hirose
, S.
, 2006, “Study on the 3D Shape of Active Cord Mechanism
,” Proceedings of the 2006 IEEE International Conference on Robotics and Automation (ICRA)
, pp. 2890
–2895
.5.
Gallardo
, J.
, Orozco
, H.
, Rico
, J. M.
, and Gonzalez-Galvan
, E. J.
, 2009, “A New Spatial Hyper-Redundant Manipulator
,” Rob. Comput.-Integr. Manufact.
0736-5845, 25
, pp. 703
–708
.6.
Chapelle
, F.
, and Bidaud
, Ph.
, 2006, “Evaluation Functions Synthesis for Optimal Design of Hyper-Redundant Robotic Systems
,” Mech. Mach. Theory
0094-114X, 41
, pp. 1196
–1212
.7.
Dasgupta
, B.
, Gupta
, A.
, and Gingla
, E.
, 2009, “A Variational Approach to Path Planning for Hyper-Redundant Manipulators
,” Rob. Auton. Syst.
0921-8890, 57
, pp. 194
–201
.8.
Trivedi
, D.
, Rahn
, C. D.
, Kier
, W. M.
, and Walker
, I. D.
, 2008, “Soft Robotics: Biological Inspiration, State of the Art and Future Research
,” Applied Bionics and Biomechanics
, 5
, pp. 99
–117
.9.
Jones
, B. A.
, and Walker
, I. D.
, 2006, “Kinematics for Multisection Continuum Robots
,” IEEE Trans. Robot.
, 22
, pp. 43
–55
.10.
Sugiyama
, Y.
, and Hirai
, Sh.
, 2006, “Crawling and Jumping by a Deformable Robots
,” Int. J. Robot. Res.
0278-3649, 25
, pp. 603
–620
.11.
Li
, C.
, and Rahn
, C. D.
, 2002, “Design of Continuous Backbone, Cable-Driven Robots
,” ASME J. Mech. Des.
0161-8458, 124
, pp. 265
–271
.12.
Wakamatsu
, H.
, Arai
, E.
, and Hirai
, Sh.
, 2006, “Knotting/Unknotting Manipulation of Deformable Linear Objects
,” Int. J. Robot. Res.
0278-3649, 25
, pp. 371
–395
.13.
Moll
, M.
, and Kavraki
, L. E.
, 2006, “Path Planning for Deformable Linear Objects
,” IEEE Trans. Robot.
, 22
, pp. 625
–636
.14.
Saha
, M.
, and Isto
, P.
, 2006, “Motion Planning for Robotic Manipulation of Deformable Linear Objects
,” Proceedings of the 2006 IEEE International Conference on Robotics and Automation (ICRA)
, pp. 2478
–2484
.15.
Theetten
, A.
, Grisoni
, L.
, Andriot
, C.
, and Barsky
, B.
, 2008, “Geometrically Exact Dynamic Splines
,” Comput.-Aided Des.
0010-4485, 40
, pp. 35
–48
.16.
Jingzhou
, Y.
, Jason
, P.
, and Abdel-Malek
, K.
, 2006, “A Hyper-Redundant Continuous Robot
,” Proceedings of the 2006 IEEE International Conference on Robotics and Automation (ICRA)
, pp. 1854
–1859
.17.
Yekutieli
, Y.
, Sagiv-Zohar
, R.
, Aharonov
, R.
, Engel
, Y.
, Hochner
, B.
, and Flash
, T.
, 2005, “Dynamic Model of the Octopus Arm I: Biomechanics of the Octopus Reaching Movement
,” J. Neurophysiol.
0022-3077, 94
, pp. 1443
–1458
.18.
Yekutieli
, Y.
, Sagiv-Zohar
, R.
, Hochner
, B.
, and Flash
, T.
, 2005, “Dynamic Model of the Octopus Arm II: Control of Reaching Movements
,” J. Neurophysiol.
0022-3077, 94
, pp. 1459
–1468
.19.
Chirikjian
, G. S.
, and Burdick
, J. W.
, 1995, “Kinematically Optimal Hyper-Redundant Manipulator Configurations
,” IEEE Trans. Rob. Autom.
1042-296X, 11
(6
), pp. 794
–806
.20.
Zanganeh
, K. E.
, and Angeles
, J.
, 1995, “Inverse Kinematics of Hyper-Redundant Manipulators Using Splines
,” Proceedings of the IEEE International Conference on Robotics and Automation
, Vol. 3
, URL http://dx.doi.org/10.1109/ROBOT.1995.525679http://dx.doi.org/10.1109/ROBOT.1995.525679.21.
Boyer
, F.
, Porez
, M.
, and Khalil
, W.
, 2006, “Macro-Continuous Computed Torque Algorithm for a Three-Dimensional Eel-Like Robot
,” IEEE Trans. Robot.
, 22
(4
), pp. 763
–775
.22.
Antman
, S. S.
, 2006, “A Priori Bounds on Spatial Motions of Incompressible Nonlinearly Elastic Rods
,” Journal of Hyperbolic Differential Equations
, 3
(3
), pp. 481
–504
.23.
Kier
, W. M.
, and Smith
, K. K.
, 1985, “Tongues, Tentacles and Trunks: The Biomechanics of Movement in Muscular-Hydrostats
,” Zool. J. Linn. Soc.
, 83
, pp. 307
–324
.24.
Kier
, W.
, and Stella
, M.
, 2007, “The Arrangement and Function of Octopus Arm Musculature and Connective Tissue
,” J. Morphol.
0362-2525, 268
, pp. 831
–843
.25.
Villaggio
, P.
, 1997, Mathematical Models for Elastic Structures
, Cambridge University Press
, Cambridge, England
.26.
Struik
, D.
, 1961, Lectures on Classical Differential Geometry
, Addison-Wesley
, Reading, MA
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.