A Stylus-Based Calibration Method for Robotic Belt Grinding Tools
Abstract
1. Introduction
2. Calibration Principle
2.1. Definition of the Grinding Tool Coordinate System
2.2. Coarse Calibration of the Tool Matrix
2.2.1. Coarse Calibration of the TCP
2.2.2. Coarse Calibration of the TCF
2.3. Precise Calibration of Tool Matrix
2.3.1. Kinematic Modeling Based on the DH Method
2.3.2. Stylus Tip Localization and Transformation Relationship
2.3.3. Error Modeling and Identification for PSO
2.3.4. PSO-Based Parameter Optimization
Algorithm 1: Calibration Process using Particle Swarm Optimization (PSO) |
Require: |
1:: A set of measured end-effector poses. |
2:: Swarm size (number of particles). |
3:: Maximum number of iterations. |
4:: Error threshold for convergence. |
5:, , : Inertia weight and learning factors. 6: Parameter Range: Search space for DH parameters, TCP offset, and stylus tip position. |
Ensure: 7: BestParams: The optimal set of DH parameters, TCP offset, and stylus tip position. |
8: Initialize a swarm of M particles with random positions () and velocities (); set each particle’s best-known position ←. |
9: Calculate the fitness value f() for each particle (e.g., RMSE, see Equation (28)) and determine the global best position . |
10: for iteration = 1 to do |
11: for each particle p do // Update personal and global best |
12: if f()<f() then |
13: ← |
14: end if |
15: if f() < f() then |
16: ← |
17: end if |
18: end for |
19: for each particle p do //Update velocity and position |
20: Generate random numbers , ∼U(0,1) |
21: ←w⋅+ (−) + (−) |
22: ←+ |
23: Constrain to be within the defined Parameter Range. |
24: end for |
25: if f() ≤ ϵ then //Check for convergence |
26: break |
27: end if |
28: end for |
29: return |
3. Numerical Simulation
4. Experiments and Results
4.1. Calibration Experiment and Result Analysis
4.2. Grinding Experimental Verification and Accuracy Assessment
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Method | Principle | Cost | Accuracy | Environmental Robustness |
---|---|---|---|---|
Classical Multi-Point | Manual teaching of a fixed point | Low | Medium/Low, operator-dependent | Poor |
Vision-Based | Camera identifies tool features | High | High, but sensitive to lighting | Poor, unsuitable for dusty environments |
Template-Based | Contact with a calibration block of known geometry | Medium | High, dependent on template accuracy | Medium |
Proposed Method | Stylus contact + Global optimization | Low | High | High, unaffected by lighting/dust |
Parameter Category | Parameters to Be Optimized | Search Range |
---|---|---|
Robot Kinematic Errors | DH Parameter Errors ) | Lengths: ±5 mm, Angles: ±2° |
Tool Transformation Errors | Positional Errors ) | ±10 mm |
Orientational Errors ) | ±2° | |
Stylus Position Errors | Positional Errors ) | ±5 mm |
Parameter | Value |
---|---|
Swarm Size () | 200 |
Inertia Weight () | 0.8 |
Cognitive Factor () | 1.49 |
Social Factor () | 1.49 |
Maximum Iterations () | 500 |
Error Threshold () | 1 × 10−6 |
Joint Angle | ||||||
---|---|---|---|---|---|---|
1 | −0.068 8 | −1.664 1 | −1.741 7 | 0.000 0 | −2.874 4 | 0.313 8 |
2 | −0.226 4 | −1.670 4 | −1.616 0 | 0.000 0 | −2.997 8 | 1.012 8 |
3 | −0.258 6 | −1.683 0 | −1.533 2 | 0.000 1 | −3.062 7 | 1.242 3 |
4 | −0.277 7 | −1.745 0 | −1.271 9 | 0.000 0 | 3.018 1 | 1.737 9 |
5 | 0.022 4 | −1.772 4 | −1.525 5 | 0.013 8 | −2.737 0 | −0.009 0 |
6 | 0.019 4 | −1.912 7 | −1.183 0 | 0.020 9 | −2.599 5 | 0.001 7 |
… | … | … | … | … | … | … |
24 | −0.018 0 | −1.666 6 | −1.749 1 | 0.000 0 | −2.867 5 | 0.128 6 |
25 | 0.024 6 | −1.666 1 | −1.748 4 | 0.000 0 | −2.867 7 | −0.024 6 |
X-Axis Angle Difference/(°) | Y-Axis Angle Difference/(°) | Z-Axis Angle Difference/(°) | X-Axis Position Difference/(mm) | Y-Axis Position Difference/(mm) | Z-Axis Position Difference/(mm) |
---|---|---|---|---|---|
0.0000 | −0.0084 | 0.0005 | 0.0050 | 0.0000 | 0.0569 |
Link | ||||
---|---|---|---|---|
1 | 0 | 0 | 0 | 0 |
2 | 0.1 | 0.1 | 0.1 | 0.1 |
3 | 0.1 | 0.1 | 0.1 | 0.1 |
4 | 0.1 | 0.1 | 0.1 | 0.1 |
5 | 0.1 | 0.1 | 0.1 | 0.1 |
6 | 0.1 | 0.1 | 0.1 | 0.1 |
Link | ||||
---|---|---|---|---|
1 | 0 | 0 | 0 | 0 |
2 | −0.0998 | −0.0980 | −0.1200 | −0.0999 |
3 | −0.0982 | −0.0911 | −0.0930 | −0.1007 |
4 | −0.1004 | −0.0900 | −0.0900 | −0.0999 |
5 | −0.0967 | −0.0984 | −0.1200 | −0.0987 |
6 | −0.1048 | −0.0999 | −0.0900 | −0.1135 |
Outlier 0% | Outlier 2% | Outlier 5% | Outlier 10% | |
---|---|---|---|---|
Noise 0 mm | 3.2 × 10−8 | 1.4454 | 1.4538 | 2.6917 |
Noise 0.1 mm | 0.1004 | 0.9222 | 2.0352 | 2.3635 |
Noise 0.2 mm | 0.1965 | 1.5088 | 1.7198 | 3.0938 |
Noise 0.5 mm | 0.4949 | 1.0205 | 2.6622 | 3.0501 |
Link | ||||
---|---|---|---|---|
1 | 0 | 0 | 0 | 0 |
2 | 0.0018 | −0.0162 | −0.0993 | −0.0041 |
3 | −0.0014 | −0.0292 | −0.0291 | 0.0003 |
4 | 0.0022 | 0.0736 | −0.0186 | 0.0038 |
5 | −0.0034 | 0.0993 | −0.0957 | 0.0013 |
6 | −0.0020 | −0.0332 | −0.0991 | −0.0046 |
RMSE/mm | MAE/mm | Max Deviation/mm | |
---|---|---|---|
Before Optimization | 0.2932 | 0.2198 | 1.0071 |
After Optimization | 0.0952 | 0.0741 | 0.5157 |
RMSE/mm | MAE/mm | Max Deviation/mm | |
---|---|---|---|
Proposed method | 0.0952 | 0.0741 | 0.5157 |
Four-point method | 0.4213 | 0.3646 | 1.1281 |
Group 1 | Group 2 | Group 3 | Group 4 | Group 5 | Mean ± STD | |
---|---|---|---|---|---|---|
TCP-x (mm) | 128.135 | 128.102 | 128.128 | 128.117 | 128.124 | 128.121 ± 0.013 |
TCP-y (mm) | −6.352 | −6.379 | −6.365 | −6.370 | −6.360 | −6.365 ± 0.010 |
TCP-z (mm) | 35.305 | 35.281 | 35.298 | 35.287 | 35.296 | 35.293 ± 0.009 |
TCF-roll (°) | 0.182 | 0.119 | 0.144 | 0.164 | 0.135 | 0.149 ± 0.025 |
TCF-pitch (°) | −0.210 | −0.142 | −0.171 | −0.189 | −0.165 | −0.175 ± 0.026 |
TCF-yaw (°) | 0.992 | 0.931 | 0.959 | 0.972 | 0.948 | 0.960 ± 0.023 |
Needle-x (mm) | 449.820 | 449.789 | 449.815 | 449.802 | 449.809 | 449.807 ± 0.012 |
Needle-y (mm) | 1.752 | 1.739 | 1.747 | 1.741 | 1.744 | 1.745 ± 0.005 |
Needle-z (mm) | 44.538 | 44.508 | 44.523 | 44.532 | 44.519 | 44.524 ± 0.011 |
Setting | RMSE (mm) |
---|---|
DH-only | 0.210 ± 0.012 |
TCP-only | 0.120 ± 0.010 |
Stylus-only | 0.180 ± 0.015 |
DH + TCP+ Stylus | 0.095 ± 0.009 |
Ideal Grinding Circle | Before Optimization | After Optimization | |
---|---|---|---|
Position difference/mm | 0 | 0.815 | 0.096 |
Angle difference/° | 0 | 1.477 | 0.326 |
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Chang, D.; Wang, Y.; Chen, Y.; Zhang, L. A Stylus-Based Calibration Method for Robotic Belt Grinding Tools. Appl. Sci. 2025, 15, 10846. https://doi.org/10.3390/app151910846
Chang D, Wang Y, Chen Y, Zhang L. A Stylus-Based Calibration Method for Robotic Belt Grinding Tools. Applied Sciences. 2025; 15(19):10846. https://doi.org/10.3390/app151910846
Chicago/Turabian StyleChang, Di, Yichao Wang, Yi Chen, and Lieshan Zhang. 2025. "A Stylus-Based Calibration Method for Robotic Belt Grinding Tools" Applied Sciences 15, no. 19: 10846. https://doi.org/10.3390/app151910846
APA StyleChang, D., Wang, Y., Chen, Y., & Zhang, L. (2025). A Stylus-Based Calibration Method for Robotic Belt Grinding Tools. Applied Sciences, 15(19), 10846. https://doi.org/10.3390/app151910846