Abstract
Due to the flexibility and high degrees-of-freedom of flexible cables, their dynamic modeling and precise control are challenging. In this paper, the dynamic modeling and control of flexible cables with human-like dual manipulators are studied to deploy them on a plane and form the desired shapes automatically. First, we establish a dynamic model of flexible cables based on a discrete elastic rod model. This model can simulate their stretching, bending, and twisting deformations. Then, we consider the collisions, contacts, and frictions between the flexible cables and the plane, add kinematic constraints to the model, and finally obtain an implementable dynamic solution of the model. Next, we propose dynamic control schemes including parallel dual-arm control and coordinated dual-arm control to deploy the flexible cables on a plane and form the desired shapes for dual-arm controls. Finally, experimental and simulation studies are carried out to illustrate the effectiveness of the dynamic model and the validity of the control schemes. The results show that the model can successfully demonstrate the deformations of flexible cables, and the proposed control schemes can successfully manipulate flexible cables in different tasks.
Issue Section:
Research Papers
References
1.
Roussel
,
O.
,
Taïx
,
M.
, and
Bretl
,
T.
, 2014
, “
Motion Planning for a Deformable Linear Object
,” European Workshop on Deformable Object Manipulation
, Lyon, France, Mar. 25, pp. 153
–158
.2.
Provot
,
X.
, 1995
, “
Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior
,” Proceedings of the Graphics Interface Conference
, Quebec, QC, Canada
, May 17–19, pp. 147
–154
.https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.84.1732&rep=rep1&type=pdf3.
Loock
,
A.
,
Schömer
,
E.
, and
Stadtwald
,
I.
, 2001
, “
A Virtual Environment for Interactive Assembly Simulation: From Rigid Bodies to Deformable Cables
,” Fifth World Multiconference on Systemics, Cybernetics and Informatics (SCI)
, Orlando, FL, July 22–25, pp. 325
–332
.4.
Lv
,
N.
,
Liu
,
J.
,
Ding
,
X.
,
Liu
,
J.
,
Lin
,
H.
, and
Ma
,
J.
, 2017
, “
Physically Based Real-Time Interactive Assembly Simulation of Cable Harness
,” J. Manuf. Syst.
,
43
, pp. 385
–399
.10.1016/j.jmsy.2017.02.0015.
Hergenröther
,
E.
, and
Dähne
,
P.
, 2000
, “
Real-Time Virtual Cables Based on Kinematic Simulation
,” Proceedings of WSCG
,
Plzen, Czech Republic
, Feb. 7–10, pp. 402
–409
.http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=A838598A3C6826E3DFDB57F0EF134EBD?doi=10.1.1.142.334&rep=rep1&type=pdf6.
Servin
,
M.
, and
Lacoursiere
,
C.
, 2008
, “
Rigid Body Cable for Virtual Environments
,” IEEE Trans. Visualization Comput. Graphics
,
14
(4
), pp. 783
–796
.10.1109/TVCG.2007.706297.
Hadap
,
S.
, and
Magnenat-Thalmann
,
N.
, 2001
, “
Modeling Dynamic Hair as a Continuum
,” Comput. Graphics Forum
,
20
(3
), pp. 329
–338
.10.1111/1467-8659.005258.
Redon
,
S.
,
Galoppo
,
N.
, and
Lin
,
M. C.
, 2005
, “
Adaptive Dynamics of Articulated Bodies
,” ACM Trans. Graphics
,
24
(3
), pp. 936
–945
.10.1145/1073204.10732949.
Choe
,
B.
,
Choi
,
M. G.
, and
Ko
,
H.-S.
, 2005
, “
Simulating Complex Hair With Robust Collision Handling
,” Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
, Los Angeles, CA
, July 29–31, pp. 153
–160
. http://graphics.snu.ac.kr/publications/conference_proceedings/2005%20Choe%20SCA.pdf10.
Terzopoulos
,
D.
, and
Qin
,
H.
, 1994
, “
Dynamic NURBS With Geometric Constraints for Interactive Sculpting
,” ACM Trans. Graphics
,
13
(2
), pp. 103
–136
.10.1145/176579.17658011.
Nocent
,
O.
, and
Remion
,
Y.
, 2001
, “
Continuous Deformation Energy for Dynamic Material Splines Subject to Finite Displacements
,” Eurographic Workshop on Computer Animation and Simulation
, Manchester, UK, Sept. 2–3, pp. 88
–97
.12.
Lenoir
,
J.
,
Cotin
,
S.
,
Duriez
,
C.
, and
Neumann
,
P.
, 2006
, “
Interactive Physically-Based Simulation of Catheter and Guidewire
,” Comput. Graphics
,
30
(3
), pp. 416
–422
.10.1016/j.cag.2006.02.01313.
Theetten
,
A.
,
Grisoni
,
L.
,
Andriot
,
C.
, and
Barsky
,
B.
, 2008
, “
Geometrically Exact Dynamic Splines
,” Comput. Aided Des.
,
40
(1
), pp. 35
–48
.10.1016/j.cad.2007.05.00814.
Echegoyen
,
Z.
,
Villaverde
,
I.
,
Moreno
,
R.
,
Graña
,
M.
, and
D'Anjou
,
A.
, 2010
, “
Linked Multi-Component Mobile Robots: Modeling, Simulation and Control
,” Rob. Auton. Syst.
,
58
(12
), pp. 1292
–1305
.10.1016/j.robot.2010.08.00815.
Valentini
,
P. P.
, and
Pennestrì
,
E.
, 2011
, “
Modeling Elastic Beams Using Dynamic Splines
,” Multibody Syst. Dyn.
,
25
(3
), pp. 271
–284
.10.1007/s11044-010-9232-916.
Driscoll
,
F.
,
Lueck
,
R.
, and
Nahon
,
M.
, 2000
, “
Development and Validation of a Lumped-Mass Dynamics Model of a Deep-Sea ROV System
,” Appl. Ocean Res.
,
22
(3
), pp. 169
–182
.10.1016/S0141-1187(00)00002-X17.
Kaufmann
,
P.
,
Martin
,
S.
,
Botsch
,
M.
, and
Gross
,
M.
, 2009
, “
Flexible Simulation of Deformable Models Using Discontinuous Galerkin FEM
,” Graphical Models
,
71
(4
), pp. 153
–167
.10.1016/j.gmod.2009.02.00218.
Wang
,
Q.
,
Fang
,
H.
,
Li
,
N.
,
Weggel
,
D. C.
, and
Wen
,
G.
, 2013
, “
An Efficient FE Model of Slender Members for Crash Analysis of Cable Barriers
,” Eng. Struct.
,
52
(9
), pp. 240
–256
.10.1016/j.engstruct.2013.02.02719.
Buckham
,
B.
,
Driscoll
,
F. R.
, and
Nahon
,
M.
, 2004
, “
Development of a Finite Element Cable Model for Use in Low-Tension Dynamics Simulation
,” ASME J. Appl. Mech.
,
71
(4
), pp. 476
–485
.10.1115/1.175569120.
Pai
,
D. K.
, 2002
, “
STRANDS: Interactive Simulation of Thin Solids Using Cosserat Models
,” Comput. Graphics Forum
,
21
(3
), pp. 347
–352
.10.1111/1467-8659.0059421.
Bertails
,
F.
,
Audoly
,
B.
,
Cani
,
M. P.
,
Querleux
,
B.
,
Leroy
,
F.
, and
Lévêque
,
J. L.
, 2006
, “
Super-Helices for Predicting the Dynamics of Natural Hair
,” ACM Trans. Graphics
,
25
(3
), pp. 1180
–1187
.10.1145/1141911.114201222.
Grégoire
,
M.
, and
Schömer
,
E.
, 2007
, “
Interactive Simulation of One-Dimensional Flexible Parts
,” Comput. Aided Des.
,
39
(8
), pp. 694
–707
.10.1016/j.cad.2007.05.00523.
Spillmann
,
J.
, and
Teschner
,
M.
, 2007
, “
CORDE: Cosserat Rod Elements for the Dynamic Simulation of One-Dimensional Elastic Objects
,” Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
, San Diego, CA
, Aug. 3–4, pp. 63
–72
.24.
Bergou
,
M.
,
Wardetzky
,
M.
,
Robinson
,
S.
,
Audoly
,
B.
, and
Grinspun
,
E.
, 2008
, “
Discrete Elastic Rods
,” ACM Trans. Graphics
,
27
(3
), p. 63
.10.1145/1360612.136066225.
Bergou
,
M.
,
Audoly
,
B.
,
Vouga
,
E.
,
Wardetzky
,
M.
, and
Grinspun
,
E.
, 2010
, “
Discrete Viscous Threads
,” ACM Trans. Graphics
,
29
(4
), pp. 1
–10
.10.1145/1778765.177885326.
Lv
,
N.
,
Liu
,
J.
,
Ding
,
X.
, and
Lin
,
H.
, 2017
, “
Assembly Simulation of Multi-Branch Cables
,” J. Manuf. Syst.
,
45
, pp. 201
–211
.10.1016/j.jmsy.2017.09.00727.
Jawed
,
M. K.
,
Novelia
,
A.
, and
O'Reilly
,
O. M.
, 2018
, A Primer on the Kinematics of Discrete Elastic Rods
,
Springer
, Cham, Switzerland.28.
Grazioso
,
S.
,
Gironimo
,
G. D.
, and
Siciliano
,
B.
, 2019
, “
A Geometrically Exact Model for Soft Continuum Robots: The Finite Element Deformation Space Formulation
,” Soft Robot
,
6
(6
), pp. 790
–811
.10.1089/soro.2018.004729.
Grazioso
,
S.
,
Gironimo
,
G. D.
, and
Siciliano
,
B.
, 2018
, “
From Differential Geometry of Curves to Helical Kinematics of Continuum Robots Using Exponential Mapping
,” International Symposium on Advances in Robot Kinematics
, Bologna, Italy, July 1–5, pp. 319
–326
.https://www.researchgate.net/publication/325950738_From_Differential_Geometry_of_Curves_to_Helical_Kinematics_of_Continuum_Robots_Using_Exponential_Mapping30.
Godbole
,
H.
,
Caverly
,
R.
, and
Forbes
,
J.
, 2019
, “
Dynamic Modelling and Adaptive Control of a Single Degree-of-Freedom Flexible Cable-Driven Parallel Robot
,” ASME J. Dyn. Syst. Meas. Control
, 141(10), p. 101002
.10.1115/1.404342731.
Lamiraux
,
F.
, and
Kavraki
,
L. E.
, 2001
, “
Planning Paths for Elastic Objects Under Manipulation Constraints
,” Int. J. Robot. Res
,
20
(3
), pp. 188
–208
.10.1177/0278364012206735432.
Asano
,
Y.
,
Wakamatsu
,
H.
,
Morinaga
,
E.
,
Arai
,
E.
, and
Hirai
,
S.
, 2010
, “
Deformation Path Planning for Manipulation of Flexible Circuit Boards
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
, Taipei, Taiwan
, China, Oct. 18–22, pp. 5386
–5391
.33.
Moll
,
M.
, and
Kavraki
,
L. E.
, 2005
, “
Path Planning for Variable Resolution Minimal-Energy Curves of Constant Length
,” IEEE International Conference on Robotics and Automation
, Barcelona, Spain
, Apr. 18–22, pp. 2130
–2135
.10.1109/ROBOT.2005.157042834.
Moll
,
M.
, and
Kavraki
,
L. E.
, 2006
, “
Path Planning for Deformable Linear Objects
,” IEEE Trans. Robot
,
22
(4
), pp. 625
–636
.10.1109/TRO.2006.87893335.
Hermansson
,
T.
,
Bohlin
,
R.
,
Carlson
,
J. S.
, and
Soderberg
,
R.
, 2013
, “
Automatic Assembly Path Planning for Wiring Harness Installations
,” J. Manuf. Syst.
,
32
(3
), pp. 417
–422
.10.1016/j.jmsy.2013.04.00636.
Gayle
,
R.
,
Lin
,
M. C.
, and
Manocha
,
D.
, 2005
, “
Constraint-Based Motion Planning of Deformable Robots
,” IEEE International Conference on Robotics and Automation
, Barcelona, Spain, Apr. 18–22, pp. 1046
–1053
.10.1109/ROBOT.2005.157025437.
Gayle
,
R.
,
Redon
,
S.
,
Sud
,
A.
,
Lin
,
M. C.
, and
Manocha
,
D.
, 2007
, “
Efficient Motion Planning of Highly Articulated Chains Using Physics-Based Sampling
,” IEEE International Conference on Robotics and Automation
,
Rome, Italy
, Apr. 10–14, pp. 3319
–3326
.10.1109/ROBOT.2007.36398538.
Roussel
,
O.
,
Taïx
,
M.
, and
Bretl
,
T.
, 2014
, “
Efficient Motion Planning for Quasi-Static Elastic Rods Using Geometry Neighborhood Approximation
,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)
,
Besancon, France
, July 8–11, pp. 1024
–1029
.10.1109/AIM.2014.687821539.
Mahoney
,
A.
,
Bross
,
J.
, and
Johnson
,
D.
, 2010
, “
Deformable Robot Motion Planning in a Reduced-Dimension Configuration Space
,” IEEE International Conference on Robotics and Automation
, Anchorage, AK, May 3–7, pp. 5133
–5138
.10.1109/ROBOT.2010.550964940.
Bretl
,
T.
, and
McCarthy
,
Z.
, 2014
, “
Quasi-Static Manipulation of a Kirchhoff Elastic Rod Based on a Geometric Analysis of Equilibrium Configurations
,” Int. J. Robot. Res
,
33
(1
), pp. 48
–68
.10.1177/027836491247316941.
Roussel
,
O.
,
Borum
,
A.
,
Taix
,
M.
, and
Bretl
.,
T.
, 2015
, “
Manipulation Planning With Contacts for an Extensible Elastic Rod by Sampling on the Submanifold of Static Equilibrium Configurations
,” IEEE International Conference on Robotics and Automation
, Seattle, WA, May 26–30, pp. 3116
–3121
. 10.1109/ICRA.2015.713962742.
Mukadam
,
M.
,
Borum
,
A.
, and
Bretl
,
T.
, 2014
, “
Quasi-Static Manipulation of a Planar Elastic Rod Using Multiple Robotic Grippers
,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS
),
Chicago, IL, Sept. 14–18, pp.
55
–60
. 10.1109/IROS.2014.694254043.
Mikchevitch
,
A.
,
Léon
,
J.-C.
, and
Gouskov
,
A.
, 2004
, “
Flexible Beam Part Manipulation for Assembly Operation Simulation in a Virtual Reality Environment
,” ASME J. Comput. Inf. Sci. Eng.
,
4
(2
), pp. 114
–123
.10.1115/1.173668744.
Matthews
,
D.
, and
Bretl
,
T.
, 2012
, “
Experiments in Quasi-Static Manipulation of a Planar Elastic Rod
,” 25th IEEE/RSJ International Conference on Robotics and Intelligent Systems
,
Vilamoura-Algarve, Portugal
, Oct. 7–12, pp. 5420
–5427
. 10.1109/IROS.2012.638587645.
Borum
,
A.
, and
Bretl
,
T.
, 2015
, “
The Free Configuration Space of a Kirchhoff Elastic Rod is Path-Connected
,” IEEE International Conference on Robotics and Automation,
Seattle, WA, May 26–30, pp. 2958
–2964
.10.1109/ICRA.2015.713960446.
Tuan
,
L. A.
,
Joo
,
Y. H.
,
Duong
,
P. X.
, and
Tien
,
L. Q.
, 2017
, “
Parameter Estimator Integrated-Sliding Mode Control of Dual Arm Robots
,” Int. J. Control Autom. Syst.
,
15
(6
), pp. 2754
–2763
.10.1007/s12555-017-0018-147.
Tuan
,
L. A.
,
Joo
,
Y. H.
,
Tien
,
L. Q.
, and
Duong
,
P. X.
, 2017
, “
Adaptive Neural Network Second-Order Sliding Mode Control of Dual Arm Robots
,” Int. J. Control Autom. Syst.
,
15
(6
), pp. 1
–9
.10.1007/s12555-017-0026-148.
Lv
,
N.
,
Liu
,
J.
,
Xia
,
H.
, and
Jia
,
Y.
, 2019
, “
Dynamic Modeling and Control of Flexible Cables for Shape Forming
,” ASME
Paper No. DSCC2019-9049
. 10.1115/DSCC2019-904949.
Audoly
,
B.
,
Clauvelin
,
N.
,
Brun
,
P. T.
,
Bergou
,
M.
,
Grinspun
,
E.
, and
Wardetzky
,
M.
, 2013
, “
A Discrete Geometric Approach for Simulating the Dynamics of Thin Viscous Threads
,” J. Comput. Phys.
,
253
(C
), pp. 18
–49
.10.1016/j.jcp.2013.06.03450.
ABB, “YuMi® - IRB 14000 | Collaborative Robot,” accessed Mar. 22, 2021, https://new.abb.com/products/robotics/industrial-robots/irb-14000-yumi
51.
JiaXi
,
Y.
,
Cheng
,
N. Y.
, and
Liang
,
S.
, 2014
, “
Coordinated Motion Control of a Nonholonomic Mobile Manipulator for Accurate Motion Tracking
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
, Chicago, IL, Sept. 14–18, pp. 1635
–1640
.10.1109/IROS.2014.6942774Copyright © 2021 by ASME
You do not currently have access to this content.
