Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches...
Transcript of Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches...
![Page 1: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/1.jpg)
Probabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems
Qianli Ma, Zachariah Goh, Gregory S. Chirikjian Department of Mechanical Engineering,
Johns Hopkins University, Baltimore, MD, USA
Robotics: Science and Systems 2016
![Page 2: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/2.jpg)
The AX = XB and AX = YB Calibrations
AX = XB Robot Hand-Eye Calibration
![Page 3: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/3.jpg)
The AX = XB and AX = YB Calibrations
AX = XB Robot Hand-Eye Calibration AX = YB Hand-Eye and Robot-World Calibration
![Page 4: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/4.jpg)
The AXB = YCZ Calibration
Hand-Eye (X), Robot-Robot (Y) and Tool-Flange (Z) Calibrations of a Dual Arm System[1,2]
[1] Wang, Jiaole, et al. IROS 2014. [2] Wu, Liao, et al. T-RO 2016.
![Page 5: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/5.jpg)
The AXB = YCZ Calibration
[3] Yan, S.J., et al. Robotica 2015.
Flange-Base (Y), Camera-Base (Z) and Tool-Gripper (X) Calibrations of a Serial-Parallel Manipulator[3]
Hand-Eye (X), Robot-Robot (Y) and Tool-Flange (Z) Calibrations of a Dual Arm System[1,2]
[1] Wang, Jiaole, et al. IROS 2014. [2] Wu, Liao, et al. T-RO 2016.
![Page 6: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/6.jpg)
The AXB = YCZ Calibration
Triple Hand-Eye (X, Y, Z) Calibrations of a Multi-Robot System
![Page 7: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/7.jpg)
Mathematical Background
![Page 8: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/8.jpg)
Mathematical Background
![Page 9: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/9.jpg)
Mathematical Background
Mean Def.
Covariance Def.
![Page 10: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/10.jpg)
Mathematical Formulation
![Page 11: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/11.jpg)
Mathematical Formulation
Independent of correspondence
![Page 12: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/12.jpg)
Mathematical Formulation
(1) Mean Equation on
(2) Covariance Equation on
Independent of correspondence
![Page 13: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/13.jpg)
Mathematical Formulation
(1) Mean Equation on
(2) Covariance Equation on
Lost Y in the covariance equation
Independent of correspondence
![Page 14: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/14.jpg)
Case Study with Completely Scrambled Data
(1) (2)
![Page 15: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/15.jpg)
Case Study with Completely Scrambled Data
Mean Eq. (1)Covariance Eq. (1)
(1)
Mean Eq. (2) Covariance Eq. (2)
(2)
![Page 16: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/16.jpg)
Case Study with Completely Scrambled Data
Mean Eq. (1)Covariance Eq. (1)
(1)
Mean Eq. (2) Covariance Eq. (2)
(2)
![Page 17: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/17.jpg)
Case Study with Completely Scrambled Data
Mean Eq. (1)Covariance Eq. (1)
(1)
Mean Eq. (2) Covariance Eq. (2)
(2)
![Page 18: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/18.jpg)
Case Study with Completely Scrambled Data
Mean Eq. (1)Covariance Eq. (1)
(1)
Mean Eq. (2) Covariance Eq. (2)
(2)
![Page 19: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/19.jpg)
Case Study with Completely Scrambled Data
Mean Eq. (1)Covariance Eq. (1)
(1)
Mean Eq. (2) Covariance Eq. (2)
(2)
![Page 20: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/20.jpg)
Case Study with Completely Scrambled Data
Mean Eq. (1)Covariance Eq. (1)
(1)
Mean Eq. (2) Covariance Eq. (2)
(2)
![Page 21: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/21.jpg)
Comparison between Probabilistic Methods and Traditionals Methods
Prob1 and Prob2 are probabilistic methods; Wang, DK and PN are traditional methods
![Page 22: Probabilistic Approaches to the AXB = YCZ Calibration ... · PDF fileProbabilistic Approaches to the AXB = YCZ Calibration Problem in Multi-Robot Systems Qianli Ma, Zachariah Goh,](https://reader034.fdocuments.in/reader034/viewer/2022042801/5a7d00917f8b9a2e358d30b5/html5/thumbnails/22.jpg)
Acknowledgements
This work was supported by NSF Grant RI-Medium: 1162095.
Lab website : https://rpk.lcsr.jhu.edu/
Contact: [email protected]
Thank you for listening!