Abstract

This paper presents the design, calibration, and development of a novel cable-driven planar parallel continuum robot (PCR). The PCR employs a novel drive unit, which is mainly composed of cables, guiding pulleys, and miniature linear actuators. The kinematic model of the PCR is derived based on the constant curvature assumption and the space vector method, and its workspace and singularity are analyzed. In addition, this paper adopts a novel compound kinematic calibration method, which includes the linear calibration method in the robot-specific model and the use of genetic algorithm (GA) in the robot-independent model. To verify the validity of the calibration method, the pose accuracy is assessed by providing positional points on the elliptical trajectory, and the trajectory tracking accuracy is evaluated by using circular and rectangular trajectories. The experimental results show that the static positioning accuracy is maintained at 1 mm; meanwhile, the trajectory tracking accuracy is controlled within the range of 0.9–1.4 mm. The PCR developed in this paper shows good comprehensive performance by employing the proposed novel compound kinematic calibration method.

Graphical Abstract Figure
Graphical Abstract Figure
Close modal

References

1.
Rivera
,
J. A.
, and
Kim
,
C. J.
,
2014
, “
Spatial Parallel Soft Robotic Architectures
,”
Proceedings of the 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Chicago, IL
,
Sept. 14–18
, pp.
548
553
.
2.
Böttcher
,
G.
,
Lilge
,
S.
, and
Burgner-Kahrs
,
J.
,
2021
, “
Design of a Reconfigurable Parallel Continuum Robot With Tendon-Actuated Kinematic Chains
,”
IEEE Rob. Autom. Lett.
,
6
(
2
), pp.
1272
1279
.
3.
Mahoney
,
A. W.
,
Anderson
,
P. L.
,
Swaney
,
P. J.
,
Maldonado
,
F.
, and
Webster
,
R. J.
,
2016
, “
Reconfigurable Parallel Continuum Robots for Incisionless Surgery
,”
Proceedings of the 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
,
Daejeon
,
South Korea, Oct. 9–14
, pp.
4330
4336
.
4.
Orekhov
,
A. L.
,
Black
,
C. B.
,
Till
,
J.
,
Chung
,
S.
, and
Rucker
,
D. C.
,
2016
, “
Analysis and Validation of a Teleoperated Surgical Parallel Continuum Manipulator
,”
IEEE Rob. Autom. Lett.
,
1
(
2
), pp.
828
835
.
5.
Young
,
E. M.
, and
Kuchenbecker
,
K. J.
,
2019
, “
Implementation of a 6-DOF Parallel Continuum Manipulator for Delivering Fingertip Tactile Cues
,”
IEEE Trans. Haptic.
,
12
(
3
), pp.
295
306
.
6.
Ghafoori
,
M.
, and
Khalaji
,
A. K.
,
2020
, “
Modeling and Experimental Analysis of a Multi-Rod Parallel Continuum Robot Using the Cosserat Theory
,”
Rob. Autom. Syst.
,
134
, p.
103650
.
7.
Mauzé
,
B.
,
Laurent
,
G. J.
,
Dahmouche
,
R.
, and
Clévy
,
C.
,
2021
, “
Micrometer Positioning Accuracy With a Planar Parallel Continuum Robot
,”
Front. Rob. AI
,
8
, p.
706070
.
8.
Jian
,
S.
,
Xiong
,
H.
,
Yang
,
X.
, and
Lou
,
Y.
,
2024
, “
Enhancing Kinematic Calibration Accuracy for Parallel Manipulators Based on Truncated Total Least-Square Regularization
,”
ASME J. Mech. Rob.
,
16
(
5
), p.
051013
.
9.
Wang
,
L.
, and
Simaan
,
N.
,
2019
, “
Geometric Calibration of Continuum Robots: Joint Space and Equilibrium Shape Deviations
,”
IEEE Trans. Rob.
,
35
(
2
), pp.
387
402
.
10.
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 Rob. Autom. Lett.
,
4
(
2
), pp.
989
996
.
11.
Zheng
,
T.
,
Yang
,
G.
,
Zhang
,
C.
,
Wang
,
Y.
,
Shen
,
W.
,
Fang
,
Z.
, and
Ye
,
G.
,
2018
, “
Self-Calibration of Cable Driven Continuum Robot
,”
Proceedings of the 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO)
,
Kuala Lumpur
,
Dec. 12–15
, pp.
2496
2501
.
12.
Joubair
,
A.
,
Slamani
,
M.
, and
Bonev
,
I. A.
,
2012
, “
Kinematic Calibration of a 3-DOF Planar Parallel Robot
,”
Ind. Rob.
,
39
(
4
), pp.
392
400
.
13.
Wang
,
Z.
,
Bao
,
S.
,
Wang
,
D.
,
Qian
,
S.
,
Zhang
,
J.
, and
Hai
,
M.
,
2023
, “
Design of a Novel Flexible Robotic Laparoscope Using a Two Degrees-of-Freedom Cable-Driven Continuum Mechanism With Major Arc Notches
,”
ASME J. Mech. Rob.
,
15
(
6
), p.
064502
.
14.
Wang
,
Z.
,
Bao
,
S.
,
Zi
,
B.
,
Jia
,
Z.
, and
Yu
,
X.
,
2024
, “
Development of a Novel 4-DOF Flexible Endoscopic Robot Using Cable-Driven Multisegment Continuum Mechanisms
,”
ASME J. Mech. Rob.
,
16
(
3
), p.
031011
.
15.
Palacín
,
J.
,
Rubies
,
E.
,
Bitrià
,
R.
, and
Clotet
,
E.
,
2023
, “
Non-Parametric Calibration of the Inverse Kinematic Matrix of a Three-Wheeled Omnidirectional Mobile Robot Based on Genetic Algorithms
,”
Appl. Sci.
,
13
(
2
), p.
1053
.
16.
Zhao
,
X.
,
Wang
,
J.
,
Zhao
,
L.
,
Li
,
B.
, and
Zhou
,
H.
,
2021
, “
Fast Error Calibration of Flexible Measuring Arm Based on an Adaptive Genetic Algorithm
,”
Meas. Control
,
54
(
7–8
), pp.
1259
1269
.
17.
Yan
,
Y.
,
2020
, “
Error Recognition of Robot Kinematics Parameters Based on Genetic Algorithms
,”
J. Amb. Intel. Hum. Comp.
,
11
(
12
), pp.
6167
6176
.
18.
Fan
,
C.
,
Zhao
,
G.
,
Zhao
,
J.
,
Zhang
,
L.
, and
Sun
,
L.
,
2015
, “
Calibration of a Parallel Mechanism in a Serial-Parallel Polishing Machine Tool Based on Genetic Algorithm
,”
Int. J. Adv. Manuf. Technol.
,
81
(
1–4
), pp.
27
37
.
19.
Nuelle
,
K.
,
Sterneck
,
T.
,
Lilge
,
S.
,
Xiong
,
D.
,
Burgner-Kahrs
,
J.
, and
Ortmaier
,
T.
,
2020
, “
Modeling, Calibration, and Evaluation of a Tendon-Actuated Planar Parallel Continuum Robot
,”
IEEE Rob. Autom. Lett.
,
5
(
4
), pp.
5811
5818
.
20.
Song
,
Y.
,
Wang
,
S.
,
Luo
,
X.
, and
Shi
,
C.
,
2022
, “
Design and Optimization of a 3D Printed Distal Flexible Joint for Endoscopic Surgery
,”
IEEE Trans. Med. Rob. Bionics
,
4
(
1
), pp.
38
49
.
21.
Zhang
,
J.
,
Fang
,
Q.
,
Xiang
,
P.
,
Sun
,
D.
,
Xue
,
Y.
,
Jin
,
R.
,
Qiu
,
K.
,
Xiong
,
R.
,
Wang
,
Y.
, and
Lu
,
H.
,
2022
, “
A Survey on Design, Actuation, Modeling, and Control of Continuum Robot
,”
Cyborg Bionic Syst.
,
2022
, p.
9754697
.
22.
Webster
R. J.
III
, 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
.
23.
Lilge
,
S.
,
Nuelle
,
K.
,
Boettcher
,
G.
,
Spindeldreier
,
S.
, and
Burgner-Kahrs
,
J.
,
2021
, “
Tendon Actuated Continuous Structures in Planar Parallel Robots: A Kinematic Analysis
,”
ASME J. Mech. Rob.
,
13
(
1
), p.
011025
.
24.
Merlet
,
J. P.
,
2019
, “
Singularity of Cable-Driven Parallel Robot With Sagging Cables: Preliminary Investigation
,”
Proceedings of the 2019 International Conference on Robotics and Automation (ICRA)
,
Montreal, QC
,
May 20–24
, pp.
504
509
.
25.
Su
,
Z.
,
Lamantia
,
M. D.
, and
Chen
,
P.
,
2023
, “
Social-Aware Long-Distance Trip Planner for Electric Vehicles Using Genetic Algorithm
,”
ASME Lett. Dyn. Syst. Control
,
3
(
2
), p.
021011
.
26.
Gutierrez
,
M. K.
,
Choi
,
D. M.
, and
Jula
,
H.
,
2020
, “
Using Genetic Algorithms to Optimize Control of a Ball-and-Beam System
,”
Proceedings of the 2020 IEEE Green Energy and Smart Systems Conference (IGESSC)
,
Long Beach, CA
,
Nov. 3–4
, pp.
1
6
.
27.
Yongbin
,
Y. U.
,
Chenyu
,
Y. A. N. G.
,
Quanxin
,
D. E. N. G.
,
Tashi
,
N.
,
Shouyi
,
L.
, and
Chen
,
Z.
,
2021
, “
Memristive Network-Based Genetic Algorithm and Its Application to Image Edge Detection
,”
J. Syst. Eng. Electron.
,
32
(
5
), pp.
1062
1070
.
28.
Lee
,
C. K. H.
,
2018
, “
A Review of Applications of Genetic Algorithms in Operations Management
,”
Eng. Appl. Artif. Intell.
,
76
, pp.
1
12
.
29.
Vieira
,
R.
,
Argento
,
E.
, and
Revoredo
,
T.
,
2021
, “
Trajectory Planning for Car-Like Robots Through Curve Parametrization and Genetic Algorithm Optimization With Applications to Autonomous Parking
,”
IEEE Lat. Am. Trans.
,
20
(
2
), pp.
309
316
.
30.
Fan
,
Q.
,
Wu
,
S.
,
Zhou
,
X.
,
Li
,
L.
, and
Wang
,
Z.
,
2020
, “
A Genetic Algorithm Based on Auxiliary-Individual-Directed Crossover for Internet-of-Things Applications
,”
IEEE Internet Things J.
,
8
(
7
), pp.
5518
5530
.
31.
Lambora
,
A.
,
Gupta
,
K.
, and
Chopra
,
K.
,
2019
, “
Genetic Algorithm—A Literature Review
,”
Proceedings of the 2019 International Conference on Machine Learning, Big Data, Cloud and Parallel Computing (COMITCon)
,
Faridabad
,
Feb. 14–16
, pp.
380
384
.
32.
Dahiya
,
A.
, and
Sangwan
,
S.
,
2018
, “
Literature Review on Genetic Algorithm
,”
Int. J. Res.
,
5
(
16
), p.
1142
.
33.
Abdulal
,
W.
, and
Ramachandram
,
S.
,
2011
, “
Reliability-Aware Genetic Scheduling Algorithm in Grid Environment
,”
Proceedings of the 2011 International Conference on Communication Systems and Network Technologies (CSNT)
,
Katra
,
June 3–5
, pp.
673
677
.
34.
Toathom
,
T.
, and
Champrasert
,
P.
,
2022
, “
The Complete Subtour Order Crossover in Genetic Algorithms for Traveling Salesman Problem Solving
,”
Proceedings of the 37th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC)
,
Phuket
,
July 5–8
, pp.
904
907
.
35.
Katoch
,
S.
,
Chauhan
,
S. S.
, and
Kumar
,
V.
,
2021
, “
A Review on Genetic Algorithm: Past, Present, and Future
,”
Multimed. Tools Appl.
,
80
(
5
), pp.
8091
8126
.
You do not currently have access to this content.