Abstract

The flexible or continuum manipulators present excellent dexterity in confined space, which is beneficial to wide application prospects in many fields. In this paper, we establish the kinematic model and propose a trajectory planning algorithm for multi-segment continuum manipulators. The multi-level mapping from the actuator variables to the manipulator tip is described. A novel modal kinematic method is proposed to overcome the singularity problem generated by the piecewise constant curvature kinematics modeling method. Then, the improved particle swarm optimization algorithm is proposed to solve the problem of redundant inverse kinematics and realize the trajectory tracking of the manipulator tip. In addition, the configuration parameters are restricted by the constraint functions, so that the precise shape of the multi-segment manipulator can be controlled. Finally, a series of numerical simulations are conducted to implement the investigation. Simulation results demonstrate that the proposed modal kinematic method and the trajectory planning algorithm are effective for multi-segment continuum manipulator.

References

1.
Laschi
,
C.
,
Cianchetti
,
M.
,
Mazzolai
,
B.
,
Margheri
,
L.
,
Follador
,
M.
, and
Dario
,
P.
,
2012
, “
Soft Robot Arm Inspired by the Octopus
,”
Adv. Robot.
,
26
(
7
), pp.
709
727
.
2.
Qin
,
G.
,
Ji
,
A.
,
Cheng
,
Y.
,
Zhao
,
W.
,
Pan
,
H.
,
Shi
,
S.
, and
Song
,
Y.
,
2022
, “
A Snake-Inspired Layer-Driven Continuum Robot
,”
Soft Rob.
,
9
(
4
), pp.
788
797
.
3.
Hopkins
,
J. K.
, and
Gupta
,
S. K.
,
2014
, “
Design and Modeling of a New Drive System and Exaggerated Rectilinear-Gait for a Snake-Inspired Robot
,”
ASME J. Mech. Rob.
,
6
(
2
), p.
021001
.
4.
Hannan
,
M. W.
, and
Walker
,
I. D.
,
2003
, “
Kinematics and the Implementation of an Elephant’s Trunk Manipulator and Other Continuum Style Robots
,”
J. Robot. Syst.
,
20
(
2
), pp.
45
63
.
5.
Jones
,
B. A.
, and
Walker
,
I. D.
,
2006
, “
Kinematics for Multisection Continuum Robots
,”
IEEE Trans. Robot.
,
22
(
1
), pp.
43
55
.
6.
Mu
,
Z.
,
Yuan
,
H.
,
Xu
,
W.
,
Liu
,
T.
, and
Liang
,
B.
,
2020
, “
A Segmented Geometry Method for Kinematics and Configuration Planning of Spatial Hyper-Redundant Manipulators
,”
IEEE Trans. Syst. Man Cybern. Syst.
,
50
(
5
), pp.
1746
1756
.
7.
Dai
,
Y.
,
Li
,
Z.
,
Chen
,
X.
,
Wang
,
X.
, and
Yuan
,
H.
,
2023
, “
A Novel Space Robot With Triple Cable-Driven Continuum Arms for Space Grasping
,”
Micromachines
,
14
(
2
), p.
416
.
8.
Han
,
S.
,
Chon
,
S.
,
Kim
,
J.
,
Seo
,
J.
,
Shin
,
D. G.
,
Park
,
S.
,
Kim
,
J. T.
,
Kim
,
J.
,
Jin
,
M.
, and
Cho
,
J.
,
2022
, “
Snake Robot Gripper Module for Search and Rescue in Narrow Spaces
,”
IEEE Robot. Autom. Lett.
,
7
(
2
), pp.
1667
1673
.
9.
Kwok
,
K.-W.
,
Hung Tsoi
,
K.
,
Vitiello
,
V.
,
Clark
,
J.
,
Chow
,
G. C. T.
,
Luk
,
W.
, and
Yang
,
G.-Z.
,
2013
, “
Dimensionality Reduction in Controlling Articulated Snake Robot for Endoscopy Under Dynamic Active Constraints
,”
IEEE Trans. Robot.
,
29
(
1
), pp.
15
31
.
10.
Hao
,
J.
,
Zhang
,
K.
,
Zhang
,
Z.
,
Wang
,
S.
, and
Shi
,
C.
,
2023
, “
An Online Model-Free Adaptive Tracking Controller for Cable-Driven Medical Continuum Manipulators
,”
IEEE Trans. Med. Robot. Bionics
,
5
(
3
), pp.
623
635
.
11.
Qin
,
G.
,
Cheng
,
Y.
,
Pan
,
H.
,
Zhao
,
W.
,
Shi
,
S.
,
Ji
,
A.
, and
Wu
,
H.
,
2022
, “
Systematic Design of Snake Arm Maintainer in Nuclear Industry
,”
Fusion Eng. Des.
,
176
, p.
113049
.
12.
Wang
,
P.
,
Deng
,
B.
,
He
,
Z.
,
Liu
,
Y.
,
Xing
,
Z.
, and
Zhao
,
J.
,
2023
, “
Extensible Continuum Manipulator Toward In-Situ Explosive Ordnance Disposal
,”
ASME J. Mech. Rob.
,
15
(
5
), p.
051013
.
13.
Liu
,
B.
,
Liu
,
M.
,
Liu
,
X.
,
Tuo
,
X.
,
Wang
,
X.
,
Zhao
,
S.
, and
Xiao
,
T.
,
2019
, “
Design and Realize a Snake-Like Robot in Complex Environment
,”
J. Rob.
,
2019
, pp.
1
9
.
14.
Palmer
,
D.
,
Cobos-Guzman
,
S.
, and
Axinte
,
D.
,
2014
, “
Real-Time Method for Tip Following Navigation of Continuum Snake Arm Robots
,”
Rob. Auton. Syst.
,
62
(
10
), pp.
1478
1485
.
15.
Chen
,
Y.
,
Wu
,
B.
,
Jin
,
J.
, and
Xu
,
K.
,
2021
, “
A Variable Curvature Model for Multi-backbone Continuum Robots to Account for Inter-Segment Coupling and External Disturbance
,”
IEEE Robot. Autom. Lett.
,
6
(
2
), pp.
1590
1597
.
16.
Li
,
Y.
,
Myszka
,
D. H.
, and
Murray
,
A.
,
2023
, “
The Kinematics of Constant Curvature Continuum Robots Through Three Segments
,”
IEEE Robot. Autom. Lett.
,
8
(
11
), pp.
7631
7638
.
17.
Garriga-Casanovas
,
A.
,
Rodriguez
,
Y.
, and
Baena
,
F.
,
2019
, “
Kinematics of Continuum Robots With Constant Curvature Bending and Extension Capabilities
,”
ASME J. Mech. Rob.
,
11
(
1
), p.
011010
.
18.
Li
,
Z.
,
Wu
,
L.
,
Ren
,
H.
, and
Yu
,
H.
,
2017
, “
Kinematic Comparison of Surgical Tendon-Driven Manipulators and Concentric Tube Manipulators
,”
Mech. Mach. Theory
,
107
, pp.
148
165
.
19.
Renda
,
F.
,
Armanini
,
C.
,
Lebastard
,
V.
,
Candelier
,
F.
, and
Boyer
,
F.
,
2020
, “
A Geometric Variable-Strain Approach for Static Modeling of Soft Manipulators With Tendon and Fluidic Actuation
,”
IEEE Robot. Autom. Lett.
,
5
(
3
), pp.
4006
4013
.
20.
Xu
,
W.
,
Liu
,
T.
, and
Li
,
Y.
,
2018
, “
Kinematics, Dynamics, and Control of a Cable-Driven Hyper-Redundant Manipulator
,”
IEEE/ASME Trans. Mechatron.
,
23
(
4
), pp.
1693
1704
.
21.
Mahl
,
T.
,
Hildebrandt
,
A.
, and
Sawodny
,
O.
,
2014
, “
A Variable Curvature Continuum Kinematics for Kinematic Control of the Bionic Handling Assistant
,”
IEEE Trans. Robot.
,
30
(
4
), pp.
935
949
.
22.
Chawla
,
A.
,
Frazelle
,
C.
, and
Walker
,
I.
,
2018
, “
A Comparison of Constant Curvature Forward Kinematics for Multisection Continuum Manipulators
,”
2018 Second IEEE International Conference on Robotic Computing (IRC)
,
Laguna Hills, CA
,
Jan. 31–Feb. 2
, IEEE, pp.
217
223
.
23.
Pourafzal
,
M.
,
Talebi
,
H. A.
, and
Rabenorosoa
,
K.
,
2021
, “
Piecewise Constant Strain Kinematic Model of Externally Loaded Concentric Tube Robots
,”
Mechatronics
,
74
, p.
102502
.
24.
Du
,
Z.
,
Yang
,
W.
, and
Dong
,
W.
,
2015
, “
Kinematics Modeling of a Notched Continuum Manipulator
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041017
.
25.
Sekiguchi
,
M.
, and
Takesue
,
N.
,
2020
, “
Fast and Robust Numerical Method for Inverse Kinematics With Prioritized Multiple Targets for Redundant Robots
,”
Adv. Rob.
,
34
(
16
), pp.
1068
1078
.
26.
Fahimi
,
F.
,
Ashrafiuon
,
H.
, and
Nataraj
,
C.
,
2002
, “
An Improved Inverse Kinematic and Velocity Solution for Spatial Hyper-Redundant Robots
,”
IEEE Trans. Robot. Automat.
,
18
(
1
), pp.
103
107
.
27.
Neppalli
,
S.
,
Csencsits
,
M. A.
,
Jones
,
B. A.
, and
Walker
,
I. D.
,
2009
, “
Closed-Form Inverse Kinematics for Continuum Manipulators
,”
Adv. Rob.
,
23
(
15
), pp.
2077
2091
.
28.
Amouri
,
A.
,
Mahfoudi
,
C.
,
Zaatri
,
A.
,
Lakhal
,
O.
, and
Merzouki
,
R.
,
2017
, “
A Metaheuristic Approach to Solve Inverse Kinematics of Continuum Manipulators
,”
Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng.
,
231
(
5
), pp.
380
394
.
29.
Amouri
,
A.
,
Mahfoudi
,
C.
,
Zaatri
,
A.
, and
Merabti
,
H.
,
2014
, “
A New Approach to Solve Inverse Kinematics of a Planar Flexible Continuum Robot
,”
AIP Conf. Proc.
,
1618
(
1
), pp.
643
646
.
30.
Godage
,
I. S.
, and
Walker
,
I. D.
,
2015
, “
Dual Quaternion Based Modal Kinematics for Multisection Continuum Arms
,”
2015 IEEE International Conference on Robotics and Automation (ICRA)
,
Seattle, WA
,
May 26–30
, IEEE, pp.
1416
1422
.
31.
Yang
,
J.
,
Peng
,
H.
,
Zhou
,
W.
, and
Wu
,
Z.
,
2022
, “
Integrated Control of Continuum-Manipulator Space Robots With Actuator Saturation and Disturbances
,”
J. Guid. Control Dyn.
,
45
(
12
), pp.
2379
2388
.
32.
Boyer
,
F.
,
Lebastard
,
V.
,
Candelier
,
F.
,
Renda
,
F.
, and
Alamir
,
M.
,
2023
, “
Statics and Dynamics of Continuum Robots Based on Cosserat Rods and Optimal Control Theories
,”
IEEE Trans. Robot.
,
39
(
2
), pp.
1544
1562
.
33.
Hao
,
J.
,
Duan
,
J.
,
Wang
,
K.
,
Hu
,
C.
, and
Shi
,
C.
,
2023
, “
Inverse Kinematic Modeling of the Tendon-Actuated Medical Continuum Manipulator Based on a Lightweight Timing Input Neural Network
,”
IEEE Trans. Med. Robot. Bionics
,
5
(
4
), pp.
916
928
.
34.
Li
,
J.
, and
Xiao
,
J.
,
2016
, “
An Efficient Algorithm for Real Time Collision Detection Involving a Continuum Manipulator With Multiple Uniform-Curvature Sections
,”
Robotica
,
34
(
7
), pp.
1566
1586
.
35.
Chen
,
G.
,
Liu
,
D.
,
Wang
,
Y.
,
Jia
,
Q.
, and
Zhang
,
X.
,
2018
, “
Path Planning Method With Obstacle Avoidance for Manipulators in Dynamic Environment
,”
Int. J. Adv. Rob. Syst.
,
15
(
6
), p.
172988141882022
.
36.
Gang
,
L.
, and
Wang
,
J.
,
2015
, “
PRM Path Planning Optimization Algorithm Research
,”
WSEAS Trans. Syst. Control
,
10
(
11
), pp.
81
86
.
37.
Karaman
,
S.
, and
Frazzoli
,
E.
,
2010
, “Incremental Sampling-Based Algorithms for Optimal Motion Planning.” http://arxiv.org/abs/1005.0416. Accessed March 05, 2024.
38.
Meng
,
B. H.
,
Godage
,
I. S.
, and
Kanj
,
I.
,
2022
, “
RRT*-Based Path Planning for Continuum Arms
,”
IEEE Robot. Autom. Lett.
,
7
(
3
), pp.
6830
6837
.
39.
Kim
,
J.-J.
, and
Lee
,
J.-J.
,
2015
, “
Trajectory Optimization With Particle Swarm Optimization for Manipulator Motion Planning
,”
IEEE Trans. Ind. Inf.
,
11
(
3
), pp.
620
631
.
40.
Lalwani
,
S.
,
Singhal
,
S.
,
Kumar
,
R.
, and
Gupta
,
N.
,
2013
, “
A Comprehensive Survey: Applications of Multi-objective Particle Swarm Optimization (MOPSO) Algorithm
,”
Trans. Comb.
,
2
(
1
), pp.
39
101
.
41.
Chai
,
R.
,
Tsourdos
,
A.
,
Savvaris
,
A.
,
Chai
,
S.
, and
Xia
,
Y.
,
2021
, “
Solving Constrained Trajectory Planning Problems Using Biased Particle Swarm Optimization
,”
IEEE Trans. Aerosp. Electron. Syst.
,
57
(
3
), pp.
1685
1701
.
42.
Ekrem
,
Ö
, and
Aksoy
,
B.
,
2023
, “
Trajectory Planning for a 6-Axis Robotic Arm With Particle Swarm Optimization Algorithm
,”
Eng. Appl. Artif. Intell.
,
122
, p.
106099
.
43.
Seleem
,
I. A.
,
El-Hussieny
,
H.
,
Assal
,
S. F. M.
, and
Ishii
,
H.
,
2020
, “
Development and Stability Analysis of an Imitation Learning-Based Pose Planning Approach for Multi-section Continuum Robot
,”
IEEE Access
,
8
, pp.
99366
99379
.
44.
Li
,
X.
,
Lv
,
H.
,
Zeng
,
D.
, and
Zhang
,
Q.
,
2023
, “
An Improved Multi-objective Trajectory Planning Algorithm for Kiwifruit Harvesting Manipulator
,”
IEEE Access
,
11
, pp.
65689
65699
.
45.
Kabir
,
A. M.
,
Thakar
,
S.
,
Malhan
,
R. K.
,
Shembekar
,
A. V.
,
Shah
,
B. C.
, and
Gupta
,
S. K.
,
2021
, “
Generation of Synchronized Configuration Space Trajectories With Workspace Path Constraints for an Ensemble of Robots
,”
Int. J. Rob. Res.
,
40
(
2–3
), pp.
651
678
.
46.
Katzschmann
,
R. K.
,
Santina
,
C. D.
,
Toshimitsu
,
Y.
,
Bicchi
,
A.
, and
Rus
,
D.
,
2019
, “
Dynamic Motion Control of Multi-segment Soft Robots Using Piecewise Constant Curvature Matched With an Augmented Rigid Body Model
,”
2019 2nd IEEE International Conference on Soft Robotics (RoboSoft)
,
Seoul, South Korea
,
Apr. 14–18
, IEEE, pp.
454
461
.
47.
Della Santina
,
C.
,
Bicchi
,
A.
, and
Rus
,
D.
,
2020
, “
On an Improved State Parametrization for Soft Robots With Piecewise Constant Curvature and Its Use in Model Based Control
,”
IEEE Robot. Autom. Lett.
,
5
(
2
), pp.
1001
1008
.
48.
Tian
,
Y.
,
Yang
,
S.
,
Geng
,
H.
,
Wang
,
W.
, and
Li
,
L.
,
2016
, “
Kinematic Modeling of the Constant Curvature Continuum Line Drive Robot
,”
2016 IEEE International Conference on Robotics and Biomimetics (ROBIO)
,
Qingdao, China
,
Dec. 3–7
, IEEE, pp.
289
294
.
49.
Zhong
,
G.
,
Peng
,
B.
, and
Dou
,
W.
,
2022
, “
Kinematics Analysis and Trajectory Planning of a Continuum Manipulator
,”
Int. J. Mech. Sci.
,
222
, p.
107206
.
50.
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
.
51.
Wilkening
,
P.
,
Alambeigi
,
F.
,
Murphy
,
R. J.
,
Taylor
,
R. H.
, and
Armand
,
M.
,
2017
, “
Development and Experimental Evaluation of Concurrent Control of a Robotic Arm and Continuum Manipulator for Osteolytic Lesion Treatment
,”
IEEE Robot. Autom. Lett.
,
2
(
3
), pp.
1625
1631
.
You do not currently have access to this content.