Abstract

This paper presents the kinematic calibration of a four-degrees-of-freedom (4DOF) high-speed parallel robot. In order to improve the calibration effect by decreasing the influence of the unobservable disturbance variables introduced by error measurement, a measurement configuration optimization method is proposed. Configurations are iteratively selected inside the workspace by a searching algorithm, then the selection results are evaluated through an index associated with the condition number of the identification Jacobian matrix; finally, the number of optimized configurations is determined. Since the selection algorithm has been shown to be sensitive to local minima, a meta-heuristic method has been applied to decrease this sensibility. To verify the effectiveness of the algorithm and kinematic calibration, computation validations, pose error estimations, and experiments are performed. The results show that the identification accuracy and calibration effect can be significantly improved by using the optimized configurations.

References

1.
Corbel
,
D.
,
Gouttefarde
,
M.
,
Company
,
O.
, and
Pierrot
,
F.
,
2010
, “
Actuation Redundancy as a Way to Improve the Acceleration Capabilities of 3 T and 3T1R Pick-and-Place Parallel Manipulators
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041002
.
2.
Coste
,
M.
, and
Mady Demdah
,
K.
,
2015
, “
Extra Modes of Operation and Self-motions in Manipulators Designed for Schoenflies Motion
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041020
.
3.
Di Gregorio
,
R.
,
Cattai
,
M.
, and
Simas
,
H.
,
2018
, “
Performance-Based Design of the CRS-RRC Schoenflies-Motion Generator
,”
Robotics
,
7
(
3
), p.
55
.
4.
Chen
,
Y. Z.
,
Xie
,
F. G.
,
Liu
,
X. J.
, and
Zhou
,
Y. H.
,
2014
, “
Error Modeling and Sensitivity Analysis of a Parallel Robot With SCARA (Selective Compliance Assembly Robot Arm) Motions
,”
Chin. J. Mech. Eng.
,
27
(
4
), pp.
693
702
.
5.
Liu
,
X. J.
,
Yu
,
J. J.
,
Wang
,
G. B.
,
Lai
,
Y. N.
, and
He
,
B. Y.
,
2016
, “
Research Trend and Scientific Challenge of Robotics
,”
Bull. Natl. Nat. Sci. Found. Chin.
,
30
(
5
), pp.
426
431
.
6.
Pierrot
,
F.
,
Nabat
,
V.
,
Company
,
O.
,
Krut
,
S.
, and
Poignet
,
P.
,
2009
, “
Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry
,”
IEEE Trans. Rob.
,
25
(
2
), pp.
213
224
.
7.
Xie
,
F. G.
, and
Liu
,
X. J.
,
2015
, “
Design and Development of a High-Speed and High-Rotation Robot With Four Identical Arms and a Single Platform
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041015
.
8.
Xie
,
F. G.
, and
Liu
,
X. J.
,
2016
, “
Analysis of the Kinematic Characteristics of a High-Speed Parallel Robot With Schönflies Motion: Mobility, Kinematics, and Singularity
,”
Front. Mech. Eng.
,
11
(
2
), pp.
135
143
.
9.
Mekid
,
S.
, and
Ogedengbe
,
T.
,
2010
, “
A Review of Machine Tool Accuracy Enhancement Through Error Compensation in Serial and Parallel Kinematic Machines
,”
Int. J. Precis. Technol.
,
1
(
3/4
), pp.
251
286
.
10.
Weck
,
M.
, and
Staimer
,
D.
,
2002
, “
Accuracy Issues of Parallel Kinematic Machine Tools
,”
Proc. Inst. Mech. Eng. K: J. Multi-body Dyn.
,
216
(
1
), pp.
51
57
.
11.
Simas
,
H.
, and
Di Gregorio
,
R.
,
2016
, “
Geometric Error Effects on Manipulators’ Positioning Precision: A General Analysis and Evaluation Method
,”
ASME J. Mech. Rob.
,
8
(
6
), p.
061016
.
12.
Liu
,
X. J.
,
Han
,
G.
,
Xie
,
F. G.
,
Meng
,
Q. Z.
, and
Zhang
,
S.
,
2018
, “
A Novel Parameter Optimization Method for the Driving System of High-Speed Parallel Robots
,”
ASME J. Mech. Rob.
,
10
(
4
), p.
041010
.
13.
Meng
,
Q. Z.
,
Xie
,
F. G.
,
Liu
,
X. J.
, and
Takeda
,
Y.
,
2020
, “
An Evaluation Approach for Motion-Force Interaction Performance of Parallel Manipulators With Closed-Loop Passive Limbs
,”
Mech. Mach. Theory
,
149
, p.
103844
.
14.
Huang
,
T.
,
Bai
,
P. J.
,
Mei
,
J. P.
, and
Chetwynd
,
G. D.
,
2016
, “
Tolerance Design and Kinematic Calibration of a Four-Degrees-of-Freedom Pick-and-Place Parallel Robot
,”
ASME J. Mech. Rob.
,
8
(
6
), p.
061018
.
15.
Liu
,
X. J.
,
Chen
,
X.
, and
Nahon
,
M.
,
2014
, “
Motion/Force Constrainability Analysis of Lower-Mobility Parallel Manipulators
,”
ASME J. Mech. Rob.
,
6
(
3
), p.
031006
.
16.
Xie
,
H.
,
Li
,
W. L.
,
Zhu
,
D. H.
,
Yin
,
Z. P.
, and
Ding
,
H.
,
2020
, “
A Systematic Model of Machining Error Reduction in Robotic Grinding
,”
IEEE ASME Trans. Mechatron.
,
25
(
6
), pp.
2961
2972
.
17.
Menq
,
C. H.
,
Borm
,
J. H.
, and
Lai
,
J. Z.
,
1989
, “
Identification and Observability Measure of a Basis Set of Error Parameters in Robot Calibration
,”
ASME J. Mech. Des.
,
111
(
4
), pp.
513
518
.
18.
Driels
,
M. R.
, and
Pathre
,
U. S.
,
1990
, “
Significance of Observation Strategy on the Design of Robot Calibration Experiments
,”
J. Robot. Syst.
,
7
(
2
), pp.
197
223
.
19.
Nahvi
,
A.
,
Hollerbach
,
J. M.
, and
Hayward
,
V.
,
1994
, “
Calibration of a Parallel Robot Using Multiple Kinematic Closed Loops
,”
IEEE International Conference on Robotics and Automation
,
San Diego, CA
,
May 8–13
, pp.
407
412
.
20.
Nahvi
,
A.
, and
Hollerbach
,
J. M.
,
1996
, “
The Noise Amplification Index for Optimal Pose Selection in Robot Calibration
,”
IEEE International Conference on Robotics and Automation
,
Minneapolis, MN
,
Apr. 22–28
, pp.
647
654
.
21.
Borm
,
J. H.
, and
Menq
,
C. H.
,
1991
, “
Determination of Optimal Measurement Configurations for Robot Calibration Based on Observability Measure
,”
Int. J. Rob. Res.
,
10
(
1
), pp.
51
63
.
22.
Joubair
,
A.
, and
Bonev
,
I. A.
,
2013
, “
Comparison of the Efficiency of Five Observability Indices for Robot Calibration
,”
Mech. Mach. Theory
,
70
, pp.
254
265
.
23.
Joubair
,
A.
,
Nubiola
,
A.
, and
Bonev
,
I. A.
,
2013
, “
Calibration Efficiency Analysis Based on Five Observability Indices and Two Calibration Models for a Six-Axis Industrial Robot
,”
SAE Int. J. Aerosp.
,
6
(
1
), pp.
161
168
.
24.
Lintott
,
A. B.
, and
Dunlop
,
G. R.
,
1997
, “
Parallel Topology Robot Calibration
,”
Robotica
,
15
(
4
), pp.
395
398
.
25.
Daney
,
D.
,
Papegay
,
Y.
, and
Madeline
,
B.
,
2005
, “
Choosing Measurement Poses for Robot Calibration With the Local Convergence Method and Tabu Search
,”
Int. J. Rob. Res.
,
24
(
6
), pp.
501
518
.
26.
Mitchell
,
T. J.
,
1974
, “
An Algorithm for the Construction of ‘D-Optimal’ Experimental Designs
,”
Techometrics
,
42
(
1
), pp.
203
210
.
27.
Sun
,
Y.
, and
Hollerbach
,
J. M.
,
2008
, “
Active Robot Calibration Algorithm
,”
IEEE International Conference on Robotics and Automation
,
Pasadena, CA
,
May 19–23
, pp.
1276
1281
.
28.
Wang
,
H. B.
,
Gao
,
T. Q.
,
Kinugawa
,
J.
, and
Kosuge
,
K.
,
2017
, “
Finding Measurement Configurations for Accurate Robot Calibration: Validation With a Cable-Driven Robot
,”
IEEE Trans. Rob.
,
33
(
5
), pp.
1156
1169
.
29.
Han
,
C. Y.
,
Yu
,
Y.
,
Xu
,
Z. B.
,
Wang
,
X. M.
,
Yu
,
P.
, and
Zhou
,
X. Q.
,
2019
, “
Complete Kinematic Calibration of a 6-RRRPRR Parallel Kinematic Machine Based on the Optimal Measurement Configurations
,”
Proc. Inst. Mech. Eng., Part C
,
234
(
1
), pp.
121
136
.
30.
Huang
,
C. H.
,
Xie
,
F. G.
,
Liu
,
X. J.
, and
Meng
,
Q. Z.
,
2020
, “
Error Modeling and Sensitivity Analysis of a Parallel Robot With R-(SS)2 Branches
,”
Int. J. Intell. Robot. Appl.
,
4
(
4
), pp.
416
428
.
31.
Glover
,
F.
,
1986
, “
Future Paths for Integer Programming and Links to Artificial Intelligence
,”
Comput. Oper. Res.
,
13
(
5
), pp.
533
549
.
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