Abstract

The positioning accuracy of industrial robots has an important influence on the stability and accuracy of robotic motion, which is one of the important indexes to measure the performance of robots. At present, some probability theory based methods are used to evaluate the positioning accuracy reliability of industrial robots. In practical engineering, the precise probability distribution of some robot’s parameters cannot be obtained directly. This study first uses the aleatory-epistemic hybrid model to describe the uncertain parameters of industrial robots. Second, the uncertain parameters are considered to construct the kinematic equation of industrial robots. Third, a probability-evidence hybrid reliability analysis model of industrial robots is established. Finally, the reliability interval of industrial robots under different thresholds can be obtained. Compared with the traditional method, the reliability results of industrial robots obtained by this method is an interval, which can more objectively evaluate the kinematics reliability of industrial robots. In the example, the effectiveness of the proposed method is verified by a six degrees of freedom (6-DoF) industrial robot.

Issue Section:
Design Automation
Keywords:
industrial robot, kinematics reliability analysis, positioning accuracy, reliability in design, probability, evidence theory
Topics:
Probability, Reliability, Robots, Kinematics, Event history analysis

References

1.
Vukobratović
,
M.
, and
Borovac
,
B.
,
1995
, “
Accuracy of the Robot Positioning and Orientation Assessed via Its Manufacturing Tolerances
,”
Mech. Mach. Theory
,
30
(
1
), pp.
11
–
32
. 10.1016/0094-114X(93)E0014-W
2.
Wu
,
J.
,
Zhang
,
D.
,
Liu
,
J.
, and
Han
,
X.
,
2019
, “
A Moment Approach to Positioning Accuracy Reliability Analysis for Industrial Robots
,”
IEEE Trans. Reliab.
,
69
(
2
), pp.
699
–
714
.
3.
Zhang
,
D.
, and
Han
,
X.
,
2020
, “
Kinematic Reliability Analysis of Robotic Manipulator
,”
ASME J. Mech. Des.
,
142
(
4
), p.
044502
. 10.1115/1.4044436
4.
Wu
,
J.
,
Zhang
,
D.
,
Liu
,
J.
,
Jia
,
X.
, and
Han
,
X.
,
2020
, “
A Computational Framework of Kinematic Accuracy Reliability Analysis for Industrial Robots
,”
Appl. Math. Model.
,
82
, pp.
189
–
216
. 10.1016/j.apm.2020.01.005
5.
Zhang
,
D.
,
Han
,
X.
,
Jiang
,
C.
,
Liu
,
J.
, and
Li
,
Q.
,
2017
, “
Time-dependent Reliability Analysis Through Response Surface Method
,”
ASME J. Mech. Des.
,
139
(
4
), p.
041404
. 10.1115/1.4035860
6.
Wang
,
Z.
,
Wang
,
Z.
,
Yu
,
S.
, and
Zhang
,
K.
,
2019
, “
Time-dependent Mechanism Reliability Analysis Based on Envelope Function and Vine-Copula Function
,”
Mech. Mach. Theory
,
134
, pp.
667
–
684
. 10.1016/j.mechmachtheory.2019.01.008
7.
Jiang
,
C.
,
Qiu
,
H.
,
Gao
,
L.
,
Wang
,
D.
,
Yang
,
Z.
, and
Chen
,
L.
,
2020
, “
Real-time Estimation Error-Guided Active Learning Kriging Method for Time-Dependent Reliability Analysis
,”
Appl. Math. Model.
,
77
, pp.
82
–
98
. 10.1016/j.apm.2019.06.035
8.
Zadeh
,
L. A.
,
1978
, “
Fuzzy Sets as a Basis for a Theory of Possibility
,”
Fuzzy Sets Syst.
,
1
(
1
), pp.
3
–
28
. 10.1016/0165-0114(78)90029-5
9.
Mandal
,
P.
, and
Ranadive
,
A.
,
2019
, “
Multi-granulation Fuzzy Decision-Theoretic Rough Sets and Bipolar-Valued Fuzzy Decision-Theoretic Rough Sets and Their Applications
,”
Granular Comput.
,
4
(
3
), pp.
483
–
509
. 10.1007/s41066-018-0111-8
10.
Meng
,
Z.
,
Pang
,
Y.
,
Pu
,
Y.
, and
Wang
,
X.
,
2020
, “
New Hybrid Reliability-Based Topology Optimization Method Combining Fuzzy and Probabilistic Models for Handling Epistemic and Aleatory Uncertainties
,”
Comput. Methods Appl. Mech. Eng.
,
363
, p.
112886
. 10.1016/j.cma.2020.112886
11.
Simon
,
C.
,
Weber
,
P.
, and
Evsukoff
,
A.
,
2008
, “
Bayesian Networks Inference Algorithm to Implement Dempster Shafer Theory in Reliability Analysis
,”
Reliab. Eng. Syst. Saf.
,
93
(
7
), pp.
950
–
963
. 10.1016/j.ress.2007.03.012
12.
Yodo
,
N.
, and
Wang
,
P.
,
2016
, “
Resilience Modeling and Quantification for Engineered Systems Using Bayesian Networks
,”
ASME J. Mech. Des.
,
138
(
3
), p.
031404
. 10.1115/1.4032399
13.
Wang
,
C.
, and
Matthies
,
H. G.
,
2019
, “
Novel Model Calibration Method via Non-Probabilistic Interval Characterization and Bayesian Theory
,”
Reliab. Eng. Syst. Saf.
,
183
, pp.
84
–
92
. 10.1016/j.ress.2018.11.005
14.
Jiang
,
C.
,
Han
,
X.
, and
Liu
,
G.
,
2007
, “
Optimization of Structures With Uncertain Constraints Based on Convex Model and Satisfaction Degree of Interval
,”
Comput. Methods Appl. Mech. Eng.
,
196
(
49–52
), pp.
4791
–
4800
. 10.1016/j.cma.2007.03.024
15.
Jiang
,
C.
,
Han
,
X.
,
Lu
,
G.
,
Liu
,
J.
,
Zhang
,
Z.
, and
Bai
,
Y.
,
2011
, “
Correlation Analysis of Non-Probabilistic Convex Model and Corresponding Structural Reliability Technique
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
33–36
), pp.
2528
–
2546
. 10.1016/j.cma.2011.04.007
16.
Meng
,
Z.
,
Zhang
,
D.
,
Li
,
G.
, and
Yu
,
B.
,
2019
, “
An Importance Learning Method for Non-Probabilistic Reliability Analysis and Optimization
,”
Struct. Multidiscip. Optim.
,
59
(
4
), pp.
1255
–
1271
. 10.1007/s00158-018-2128-7
17.
Meng
,
Z.
,
Zhang
,
Z.
, and
Zhou
,
H.
,
2020
, “
A Novel Experimental Data-Driven Exponential Convex Model for Reliability Assessment With Uncertain-but-Bounded Parameters
,”
Appl. Math. Model.
,
77
, pp.
773
–
787
. 10.1016/j.apm.2019.08.010
18.
Hao
,
P.
,
Wang
,
Y.
,
Liu
,
C.
,
Wang
,
B.
, and
Wu
,
H.
,
2017
, “
A Novel Non-Probabilistic Reliability-Based Design Optimization Algorithm Using Enhanced Chaos Control Method
,”
Comput. Methods Appl. Mech. Eng.
,
318
, pp.
572
–
593
. 10.1016/j.cma.2017.01.037
19.
Du
,
X.
,
2006
, “
Uncertainty Analysis With Probability and Evidence Theories
,”
Proceedings of ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (DETC2006-99078)
,
Philadelphia, PA
,
Sept. 10–13
,
American Society of Mechanical Engineers Digital Collection
, pp.
1025
–
1038
.
20.
Zhang
,
Z.
,
Jiang
,
C.
,
Han
,
X.
,
Hu
,
D.
, and
Yu
,
S.
,
2014
, “
A Response Surface Approach for Structural Reliability Analysis Using Evidence Theory
,”
Adv. Eng. Software
,
69
, pp.
37
–
45
. 10.1016/j.advengsoft.2013.12.005
21.
Zhang
,
Z.
,
Jiang
,
C.
,
Wang
,
G.
, and
Han
,
X.
,
2015
, “
First and Second Order Approximate Reliability Analysis Methods Using Evidence Theory
,”
Reliab. Eng. Syst. Saf.
,
137
, pp.
40
–
49
. 10.1016/j.ress.2014.12.011
22.
Huang
,
Z.
,
Jiang
,
C.
,
Zhang
,
Z.
,
Fang
,
T.
, and
Han
,
X.
,
2017
, “
A Decoupling Approach for Evidence-Theory-Based Reliability Design Optimization
,”
Struct. Multidiscip. Optim.
,
56
(
3
), pp.
647
–
661
. 10.1007/s00158-017-1680-x
23.
Huang
,
Z.
,
Jiang
,
C.
,
Zhang
,
Z.
,
Zhang
,
W.
, and
Yang
,
T.
,
2019
, “
Evidence-theory-based Reliability Design Optimization With Parametric Correlations
,”
Struct. Multidiscip. Optim.
,
60
(
2
), pp.
565
–
580
. 10.1007/s00158-019-02225-7
24.
Wang
,
Z.
, and
Wang
,
P.
,
2012
, “
A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
134
(
12
), p.
121007
. 10.1115/1.4007931
25.
Zhang
,
X.
, and
Pandey
,
M. D.
,
2013
, “
An Efficient Method for System Reliability Analysis of Planar Mechanisms
,”
Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
,
227
(
2
), pp.
373
–
386
. 10.1177/0954406212448341
26.
Wang
,
L.
,
Zhang
,
X.
, and
Zhou
,
Y.
,
2018
, “
An Effective Approach for Kinematic Reliability Analysis of Steering Mechanisms
,”
Reliab. Eng. Syst. Saf.
,
180
, pp.
62
–
76
. 10.1016/j.ress.2018.07.009
27.
Jiang
,
C.
,
Qiu
,
H.
,
Yang
,
Z.
,
Chen
,
L.
,
Gao
,
L.
, and
Li
,
P.
,
2019
, “
A General Failure-Pursuing Sampling Framework for Surrogate-Based Reliability Analysis
,”
Reliab. Eng. Syst. Saf.
,
183
, pp.
47
–
59
. 10.1016/j.ress.2018.11.002
28.
Li
,
F.
,
Liu
,
J.
,
Wen
,
G.
, and
Rong
,
J.
,
2019
, “
Extending SORA Method for Reliability-Based Design Optimization Using Probability and Convex Set Mixed Models
,”
Struct. Multidiscip. Optim.
,
59
(
4
), pp.
1163
–
1179
. 10.1007/s00158-018-2120-2
29.
Bae
,
S.
,
Kim
,
N. H.
, and
Jang
,
S. G.
,
2019
, “
System Reliability-Based Design Optimization Under Tradeoff Between Reduction of Sampling Uncertainty and Design Shift
,”
ASME J. Mech. Des.
,
141
(
4
), p.
041403
. 10.1115/1.4041859
30.
Moon
,
M.-Y.
,
Choi
,
K.
,
Gaul
,
N.
, and
Lamb
,
D.
,
2019
, “
Treating Epistemic Uncertainty Using Bootstrapping Selection of Input Distribution Model for Confidence-Based Reliability Assessment
,”
ASME J. Mech. Des.
,
141
(
3
), p.
031402
.
31.
Yang
,
M.
,
Zhang
,
D.
, and
Han
,
X.
,
2020
, “
New Efficient and Robust Method for Structural Reliability Analysis and Its Application in Reliability-Based Design Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
366
, p.
113018
. 10.1016/j.cma.2020.113018
32.
Zhang
,
X.
,
Pandey
,
M. D.
, and
Zhang
,
Y.
,
2014
, “
Computationally Efficient Reliability Analysis of Mechanisms Based on a Multiplicative Dimensional Reduction Method
,”
ASME J. Mech. Des.
,
136
(
6
), p.
061006
. 10.1115/1.4026270
33.
Jiang
,
C.
,
Han
,
X.
,
Li
,
W.
,
Liu
,
J.
, and
Zhang
,
Z.
,
2012
, “
A Hybrid Reliability Approach Based on Probability and Interval for Uncertain Structures
,”
ASME J. Mech. Des.
,
134
(
3
), p.
031001
. 10.1115/1.4005595
34.
Du
,
X.
,
2008
, “
Unified Uncertainty Analysis by the First Order Reliability Method
,”
ASME J. Mech. Des.
,
130
(
9
), p.
091401
. 10.1115/1.2943295
35.
Mourelatos
,
Z. P.
, and
Zhou
,
J.
,
2006
, “
A Design Optimization Method Using Evidence Theory
,”
ASME J. Mech. Des.
,
128
(
4
), p.
901
–
908
. 10.1115/1.2204970
36.
Liu
,
J.
,
Cao
,
L.
,
Jiang
,
C.
,
Ni
,
B.
, and
Zhang
,
D.
,
2020
, “
Parallelotope-formed Evidence Theory Model for Quantifying Uncertainties With Correlation
,”
Appl. Math. Model.
,
77
, pp.
32
–
48
. 10.1016/j.apm.2019.07.017
37.
Cao
,
L.
,
Liu
,
J.
,
Jiang
,
C.
,
Wu
,
Z.
, and
Zhang
,
Z.
,
2020
, “
Evidence-based Structural Uncertainty Quantification by Dimension Reduction Decomposition and Marginal Interval Analysis
,”
ASME J. Mech. Des.
,
142
(
5
), p.
051701
.0.1115/1.4044915
38.
Liu
,
T.
, and
Wang
,
J.
,
1994
, “
A Reliability Approach to Evaluating Robot Accuracy Performance
,”
Mech. Mach. Theory
,
29
(
1
), pp.
83
–
94
. 10.1016/0094-114X(94)90022-1
39.
Zhang
,
D.
, and
Lei
,
J.
,
2011
, “
Kinematic Analysis of a Novel 3-DOF Actuation Redundant Parallel Manipulator Using Artificial Intelligence Approach
,”
Rob. Comput.-Integr. Manuf.
,
27
(
1
), pp.
157
–
163
. 10.1016/j.rcim.2010.07.003
40.
Wei
,
P.
,
Song
,
J.
,
Lu
,
Z.
, and
Yue
,
Z.
,
2016
, “
Time-dependent Reliability Sensitivity Analysis of Motion Mechanisms
,”
Reliab. Eng. Syst. Saf.
,
149
, pp.
107
–
120
. 10.1016/j.ress.2015.12.019
41.
Zhu
,
J.
, and
Ting
,
K.-L.
,
2000
, “
Uncertainty Analysis of Planar and Spatial Robots With Joint Clearances
,”
Mech. Mach. Theory
,
35
(
9
), pp.
1239
–
1256
. 10.1016/S0094-114X(99)00076-2
42.
Rao
,
S. S.
, and
Bhatti
,
P.
,
2001
, “
Probabilistic Approach to Manipulator Kinematics and Dynamics
,”
Reliab. Eng. Syst. Saf.
,
72
(
1
), pp.
47
–
58
. 10.1016/S0951-8320(00)00106-X
43.
Kim
,
J.
,
Song
,
W.-J.
, and
Kang
,
B.-S.
,
2010
, “
Stochastic Approach to Kinematic Reliability of Open-Loop Mechanism With Dimensional Tolerance
,”
Appl. Math. Model.
,
34
(
5
), pp.
1225
–
1237
. 10.1016/j.apm.2009.08.009
44.
Pandey
,
M. D.
, and
Zhang
,
X.
,
2012
, “
System Reliability Analysis of the Robotic Manipulator With Random Joint Clearances
,”
Mech. Mach. Theory
,
58
, pp.
137
–
152
. 10.1016/j.mechmachtheory.2012.08.009
45.
Rocha
,
C.
,
Tonetto
,
C.
, and
Dias
,
A.
,
2011
, “
A Comparison Between the Denavit–Hartenberg and the Screw-Based Methods Used in Kinematic Modeling of Robot Manipulators
,”
Rob. Comput.-Integr. Manuf.
,
27
(
4
), pp.
723
–
728
. 10.1016/j.rcim.2010.12.009
46.
Alici
,
G.
, and
Shirinzadeh
,
B.
,
2005
, “
A Systematic Technique to Estimate Positioning Errors for Robot Accuracy Improvement Using Laser Interferometry Based Sensing
,”
Mech. Mach. Theory
,
40
(
8
), pp.
879
–
906
. 10.1016/j.mechmachtheory.2004.12.012
47.
Yager
,
R. R.
,
1983
, “
Entropy and Specificity in a Mathematical Theory of Evidence
,”
Int. J. Gen. Syst.
,
9
(
4
), pp.
249
–
260
. 10.1080/03081078308960825
48.
Xiao
,
Q.
,
2014
, “
Evaluating Correlation Coefficient for Nataf Transformation
,”
Probab. Eng. Mech.
,
37
, pp.
1
–
6
. 10.1016/j.probengmech.2014.03.010
49.
Li
,
G.
,
Lu
,
Z.
,
Li
,
L.
, and
Ren
,
B.
,
2016
, “
Aleatory and Epistemic Uncertainties Analysis Based on Non-Probabilistic Reliability and Its Kriging Solution
,”
Appl. Math. Model.
,
40
(
9–10
), pp.
5703
–
5716
. 10.1016/j.apm.2016.01.017
50.
Dong
,
W.
, and
Shah
,
H. C.
,
1987
, “
Vertex Method for Computing Functions of Fuzzy Variables
,”
Fuzzy Sets Syst.
,
24
(
1
), pp.
65
–
78
. 10.1016/0165-0114(87)90114-X
51.
Du
,
X.
,
2007
, “
Interval Reliability Analysis
,”
Proceedings of ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (DETC2007-34582)
,
Las Vegas, NV
,
Sept. 4–7
,
American Society of Mechanical Engineers Digital Collection
, pp.
1103
–
1109
.
52.
Zhang
,
Y.
, and
Der Kiureghian
,
A.
,
1995
, “Two Improved Algorithms for Reliability Analysis,”
Reliability and Optimization of Structural Systems
,
R.
Rüdiger
,
A.
Guiliano
, and
B.
Antonio
, eds.,
Springer
,
New York
, pp.
297
–
304
.
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