Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory
Abstract
:1. Introduction
1.1. Background and Significance of the Study
1.2. Related Work
2. Sensor Placement Method
2.1. Derivation of Forward Kinematics of Industrial Robots
- 1.
- Link length : along the axis, the distance from to ;
- 2.
- The torsion angle of the connecting rod: the angle from to around the axis;
- 3.
- Link offset : along the axis, the distance from to ;
- 4.
- Joint angle : the angle of rotation from to around the axis.
2.2. Numerical Method of Velocity
2.3. Simulation Analysis of Industrial Robot
2.4. Optimal Sensor Placement Based on Bayesian
2.4.1. Bayesian Estimation of Motion Joint Position
2.4.2. Optimal Sensor Placement for Industrial Robots Based on Information Gain
2.5. Constraint Equation
3. Experiment
3.1. Verification Method for Layout
- According to the given initial position, sensors are arranged in the corresponding position of the real industrial robot;
- Set the joint speed of the industrial robot as a fixed speed, make the industrial robot move accordingly, and collect the acceleration of sensor distribution in the process of motion;
- The acceleration signal is processed to get the velocity of each point, and the probability of motion from each joint is calculated by using the probability model;
- Compare the probability of each joint with the real motion joint to determine whether the maximum probability corresponds to the real motion joint. If so, it is considered that the sensor layout can obtain the whole machine state.
Algorithm 1: Optimal sensor placement based on Bayesian and Constraint equation | |
Input: the measured velocity and the predicted velocity of the sensor. | |
Output: optimal sensor placement s_best. | |
1 | rn = 3; |
2 | if sn = 1 do |
3 | for i = 1 to rn do |
4 | for j = 1 to le do |
5 | compute p(i,j);//according to Equation (16). |
6 | end |
7 | end |
8 | for i = 1 to rn do |
9 | for j = 1 to le do |
10 | compute U(i,j);//according to Equation (19) |
11 | end |
12 | end |
13 | for i = 1 to rn do |
14 | compute Us(i);//sum U(i,j) |
15 | end |
16 | s_best = s(max(Us)); |
17 | else |
18 | sn = sn + 1; |
19 | for i = 1 to rn do |
20 | for j = 1 to le do |
21 | compute p(i,j);//according to Equation (16) |
22 | end |
23 | end |
24 | for i = 1 to rn do |
25 | for j = 1 to le do |
26 | compute U(i,j);//according to Equation (19) |
27 | end |
28 | end |
29 | for i = 1 to rn do |
30 | compute Us(i);//sum U(i,j) |
31 | end |
32 | s_best = snew(max(Us)); |
33 | for i = 1 to rn do |
34 | compute n_best;//according to Equation (21) |
35 | end |
36 | s_best = s_best(n_best);//optimal sensor placement |
37 | end |
38 | //rn—number of joints; |
39 | //s—initial Sensor placement; |
40 | //sn—number of sensors currently optimized; |
41 | //le—number of sensors in the initial layout; |
42 | //p(i j)—the likelihood function; |
43 | //U(i,j)—the sensor placement evaluation function according to Equation (19); |
44 | //Us(i)—sum of regression values of each sensor coordinate; |
45 | //snew—the new sensor placement based on heuristic sequential sensor placement; |
46 | //n_best—the optimal number of sensors according to the change of the objective function; |
3.2. Verification of Optimal Sensor Placement for Industrial Robots Based on the Simulation Model
3.3. Optimal Sensor Placement Method and Verification of Industrial Robots without Simulation Models
3.4. Result
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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When the axis of joint intersects with the axis of joint , the intersection point is taken | Coincides with the axis of joint | If the joint axis intersects , it is perpendicular to the plane where the joint axis and are located | Determined by the right-hand rule |
When the axis of joint is out of plane with the axis of joint , take the intersection of the common perpendicular of the two axes and the axis of joint | On the common perpendicular of the links and , its direction is from to | ||
When the axis of joint is parallel to the axis of joint , take the intersection of the common perpendicular of the axis of joint and the axis of joint with the axis of joint |
Link\Parameters | ||||
---|---|---|---|---|
1 | 0 | 0 | 0 | |
2 | 0 | |||
3 | 0 | 0 | ||
4 | 0 | |||
5 | 0 | 0 | ||
6 | 0 |
Project | Type | Number of Axes | Driving Mode | Repeat Positioning Accuracy | Range of Motion |
---|---|---|---|---|---|
Parameter | RB13 | 6 | AC servo | 0.07 mm | R499~R1404 mm |
Order | 1 | 2 | 3 | 4 | 5 | 6 |
Natural frequency/Hz | 12.6 | 20.0 | 30.0 | 70.3 | 116.7 | 338.3 |
Maximum relative amplitude/m | 0.11 | 0.09 | 0.10 | 0.12 | 0.15 | 0.14 |
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Hu, Q.; Zhang, Y.; Xie, X.; Su, W.; Li, Y.; Shan, L.; Yu, X. Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory. Appl. Sci. 2022, 12, 6086. https://doi.org/10.3390/app12126086
Hu Q, Zhang Y, Xie X, Su W, Li Y, Shan L, Yu X. Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory. Applied Sciences. 2022; 12(12):6086. https://doi.org/10.3390/app12126086
Chicago/Turabian StyleHu, Qiao, Yangkun Zhang, Xingju Xie, Wenbin Su, Yangyang Li, Liuhao Shan, and Xiaojie Yu. 2022. "Optimal Placement of Vibration Sensors for Industrial Robots Based on Bayesian Theory" Applied Sciences 12, no. 12: 6086. https://doi.org/10.3390/app12126086