Robust Robotic Arm Calibration combining Multi-Distance Optimization Approach with Lagrange Starfish Optimization Algorithm

Yongtao Qu; Zhiqiang Li; Long Liao; Xun Deng; Yuanchang Lin; Tinghui Chen; Linlin Chen; Jia Liu; Peiyang Wei; Jianhong Gan; ZhenZhen  Hu; Can Hu; Yonghong Deng; Wei Li; Zhibin Li

doi:10.4108/airo.9002

Authors

Yongtao Qu Chinese Academy of Sciences https://orcid.org/0009-0003-5169-6423
Zhiqiang Li Dongfang Electric Corporation (China)
Long Liao Dongfang Electric Corporation (China)
Xun Deng Sichuan Railway Vocational College
Yuanchang Lin Chinese Academy of Sciences
Tinghui Chen Chinese Academy of Sciences
Linlin Chen Chengdu University of Information Technology
Jia Liu Chengdu University of Information Technology
Peiyang Wei Chengdu University of Information Technology
Jianhong Gan Chengdu University of Information Technology
ZhenZhen Hu Chengdu University of Information Technology
Can Hu Chengdu University of Information Technology
Yonghong Deng Chengdu University of Information Technology
Wei Li Sichuan Railway Vocational College
Zhibin Li Chengdu University of Information Technology

DOI:

https://doi.org/10.4108/airo.9002

Keywords:

Lagrangian Starfish Optimization Algorithm, LSFA, Support Vector Machine, SVM, Multi-dimensional distance metrics, Robotic arm calibration, Dynamic parameter estimation, Intelligent optimization algorithm

Abstract

In response to the limitations of existing robotic parameter calibration methods in terms of computational complexity, convergence speed, data requirements, and accuracy, this study proposes an innovative calibration scheme that combines an improved Lagrangian Starfish Optimization Algorithm (LSFA) with a Support Vector Machine (SVM) algorithm. By incorporating Lagrange interpolation and a multi-dimensional distance metric model (including Mahalanobis distance, Manhattan distance, Chebyshev distance, cosine distance, standardized Euclidean distance, and Euclidean distance), the enhanced starfish optimization algorithm significantly improves global search capabilities and local search accuracy. This effectively addresses issues such as initial value sensitivity, noise, and outliers, with the algorithm specifically designed for kinematic parameter calibration of robotic arms. Furthermore, the improved local search mechanism optimizes the position update strategy of starfish through a weighted system, preventing the algorithm from becoming trapped in local optima. To further enhance the accuracy of dynamic parameter calibration, this study integrates the SVM algorithm into the LSFA framework, proposing the LSFA-SVM method specifically for dynamic parameter calibration of robotic arms. Experiments demonstrate a 38.59% reduction in error compared to traditional SVM. The results indicate that LSFA excels in kinematic calibration of robotic arms, achieving a root mean square error (RMSE) of 0.29 mm, a 29.27% improvement over the traditional Starfish Optimization Algorithm (SFOA). This study provides an efficient and precise solution for robotic parameter calibration in complex environments.

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References

[1]Guo Y, Gao X, Liang W, et al. Robot joint space grid error compensation based on three-dimensional discrete point space circular fitting[J]. CIRP Journal of Manufacturing Science and Technology, 2024, 50: 140-150.

[2]Li Z, Li S, Luo X. Efficient industrial robot calibration via a novel unscented Kalman filter-incorporated variable step-size Levenberg–Marquardt algorithm[J]. IEEE Transactions on Instrumentation and Measurement, 2023, 72: 1-12.

[3]Wu X, Zuo W, Lin L, et al. F-SVM: Combination of feature transformation and SVM learning via convex relaxation[J]. IEEE transactions on neural networks and learning systems, 2018, 29(11): 5185-5199.

[4]Jiang Z, Zhou W, Li H, et al. A new kind of accurate calibration method for robotic kinematic parameters based on the extended Kalman and particle filter algorithm[J]. IEEE Transactions on Industrial Electronics, 2017, 65(4): 3337-3345.

[5]Cao H Q, Nguyen H X, Nguyen T T, et al. Robot calibration method based on extended Kalman filter–dual quantum behaved particle swarm optimization and adaptive neuro-fuzzy inference system[J]. IEEE Access, 2021, 9: 132558-132568.

[6]Chen T, Li S. Highly Accurate Robot Calibration Using Adaptive and Momental Bound with Decoupled Weight Decay[J]. arXiv preprint arXiv:2408.12087, 2024.

[7]Dzedzickis A, Subačiūtė-Žemaitienė J, Šutinys E, et al. Advanced applications of industrial robotics: New trends and possibilities[J]. Applied Sciences, 2021, 12(1): 135.

[8]Javaid M, Haleem A, Singh R P, et al. Substantial capabilities of robotics in enhancing industry 4.0 implementation[J]. Cognitive Robotics, 2021, 1: 58-75.

[9]Zhu D, Feng X, Xu X, et al. Robotic grinding of complex components: a step towards efficient and intelligent machining challenges, solutions, and applications[J]. Robotics and Computer-Integrated Manufacturing, 2020, 65: 101908.

[10]Branco, Mariana P., et al. "Encoding of kinetic and kinematic movement parameters in the sensorimotor cortex: A Brain‐Computer Interface perspective." European Journal of Neuroscience 50.5 (2019): 2755-2772.

[11]Jin T, Han X. Robotic arms in precision agriculture: A comprehensive review of the technologies, applications, challenges, and future prospects[J]. Computers and Electronics in Agriculture, 2024, 221: 108938.

[12]Van Toan N, Khoi P B. A svd-least-square algorithm for manipulator kinematic calibration based on the product of exponentials formula[J]. Journal of Mechanical Science and Technology, 2018, 32: 5401-5409.

[13]Miao L, Zhang Y, Song Z, et al. A two-step method for kinematic parameters calibration based on complete pose measurement—verification on a heavy-duty robot[J]. Robotics and Computer-Integrated Manufacturing, 2023, 83: 102550.

[14]Fan C, Zhao G, Zhao J, et al. Calibration of a parallel mechanism in a serial-parallel polishing machine tool based on genetic algorithm[J]. The International Journal of Advanced Manufacturing Technology, 2015, 81: 27-37.

[15]Li H, Hu X, Zhang X, et al. Kinematic parameters calibration of industrial robot based on RWS-PSO algorithm[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2023, 237(14): 3210-3220.

[16]Luo G, Zou L, Wang Z, et al. A novel kinematic parameters calibration method for industrial robot based on Levenberg-Marquardt and Differential Evolution hybrid algorithm[J]. Robotics and Computer-Integrated Manufacturing, 2021, 71: 102165.

[17]Liu, Yuzhe, et al. "Parameter identification algorithm of kinematic calibration in parallel manipulators." Advances in Mechanical Engineering 8.9 (2016):1687814016667908.

[18]Sun T, Lian B, Zhang J, et al. Kinematic calibration of a 2-DoF over-constrained parallel mechanism using real inverse kinematics[J]. IEEE Access, 2018, 6: 67752-67761.

[19]Kong Y, Yang L, Chen C, et al. Online kinematic calibration of robot manipulator based on neural network[J]. Measurement, 2024, 238: 115281.

[20]Le P N, Kang H J. A New Manipulator Calibration Method for the Identification of Kinematic and Compliance Errors Using Optimal Pose Selection[J]. Applied Sciences, 2022, 12(11): 5422.

[21]Luo X, Li Z, Yue W, et al. A Calibrator Fuzzy Ensemble for Highly-Accurate Robot Arm Calibration[J]. IEEE Transactions on Neural Networks and Learning Systems, 2024.

[22]Moshayedi A J, Roy A S, Kolahdooz A, et al. Deep learning application pros and cons over algorithm[J]. EAI Endorsed Transactions on AI and Robotics, 2022, 1(1): e7.

[23]Zanfei A, Menapace A, Brentan B M, et al. Shall we always use hydraulic models? A graph neural network metamodel for water system calibration and uncertainty assessment[J]. Water Research, 2023, 242: 120264.

[24]Moshayedi A J, Roy A S, Sambo S K, et al. Review on: The service robot mathematical model[J]. EAI Endorsed Transactions on AI and Robotics, 2022, 1(1): 1-19.

[25]Wang Z, Cao B, Xie Z, et al. Kinematic Calibration of a Space Manipulator Based on Visual Measurement System with Extended Kalman Filter[J]. Machines, 2023, 11(3): 409.

[26]Bao W, Bi M, Xiao S, et al. Lagrange interpolation based extended Kalman filter for phase noise suppression in CO-OFDM system[J]. Optics Communications, 2019, 435: 221-226.

[27]Liu J, Huang Q, Ulishney C, et al. A support-vector machine model to predict the dynamic performance of a heavy-duty natural gas spark ignition engine[R]. SAE Technical Paper, 2021.

[28]Sarin K, Bardamova M, Svetlakov M, et al. A three-stage fuzzy classifier method for Parkinson’s disease diagnosis using dynamic handwriting analysis[J]. Decision Analytics Journal, 2023, 8: 100274.

[29]Qi J, Chen B, Zhang D. A calibration method for enhancing robot accuracy through integration of kinematic model and spatial interpolation algorithm[J]. Journal of Mechanisms and Robotics, 2021, 13(6): 061013.

[30]Lin X, Zhu H, Ennocent A F. Locomotion trajectory optimization for quadruped robots with kinematic parameter calibration and compensation[J]. Measurement, 2024: 115622.

[31]Yu D. Kinematic Parameter Identification for a Parallel Robot with an Improved Particle Swarm Optimization Algorithm[J]. Applied Sciences, 2024, 14(15): 6557.

[32]Gao G, Guo X, Li G, et al. Kinematic Parameter Identification and Error Compensation of Industrial Robots Based on Unscented Kalman Filter with Adaptive Process Noise Covariance[J]. Machines, 2024, 12(6): 406.

[33]Zhu Y, Yang C, Wei Q, et al. Human–robot shared control for humanoid manipulator trajectory planning[J]. Industrial Robot: the international journal of robotics research and application, 2020, 47(3): 395-407.

[34]Fan Y, Lv X, Lin J, et al. Autonomous operation method of multi-DOF robotic arm based on binocular vision[J]. Applied Sciences, 2019, 9(24): 5294.

[35]Woodside M R, Fischer J, Bazzoli P, et al. A kinematic error controller for real-time kinematic error correction of industrial robots[J]. Procedia Manufacturing, 2021, 53: 705-715.

[36]Lao D, Quan Y, Wang F, et al. Error Modeling and Parameter Calibration Method for Industrial Robots Based on 6-DOF Position and Orientation[J]. Applied Sciences, 2023, 13(19): 10901.

[37]Liu J, Yang Y, Xu B, et al. RSTC: Residual Swin Transformer Cascade to approximate Taylor expansion for image denoising[J]. Computer Vision and Image Understanding, 2024, 248: 104132.

[38]Bolin Liao, Jianfeng Li, Shuai Li, and Zhan Li. "Briefly Revisit Kinematic Control of Redundant Manipulators via Constrained Optimization." (2022).

[39]Gan Y, Duan J, Dai X. A calibration method of robot kinematic parameters by drawstring displacement sensor[J]. International Journal of Advanced Robotic Systems, 2019, 16(5): 1729881419883072.

[40]Xu J, Liu X, Li P, et al. Calibration Method of Industrial Robot Kinematic Parameters Based on Improved SSA Algorithm[C]//2023 6th International Conference on Software Engineering and Computer Science (CSECS). IEEE, 2023: 1-7.

[41]Soleymani M, Kiani M. Planar soft space robotic manipulators: Dynamic modeling and control[J]. Advances in Space Research, 2024, 74(1): 384-402.

[42]Kana S, Gurnani J, Ramanathan V, et al. Fast kinematic re-calibration for industrial robot arms[J]. Sensors, 2022, 22(6): 2295.

[43]Xiang T, Jiang X, Qiao G, et al. Kinematics Parameter Calibration of Serial Industrial Robots Based on Partial Pose Measurement[J]. Mathematics, 2023, 11(23): 4802.

[44]Cheng B, Wang B, Chen S, et al. Investigation of axis-fitting-based measurement and identification techniques for kinematic parameters in multi-joint industrial robots[J]. Precision Engineering, 2024, 91: 1-13.

[45]Kang Z, Wang L, Sun A, et al. Two-step calibration of 6-DOF industrial robots by grouping kinematic parameters based on distance constraints[J]. Measurement, 2024, 235: 114906.

[46]Zhao C, Qian L, Wang S, et al. A closed-loop kinematic approach to Self-Calibration of joint offset for multi-branched robots[J]. Measurement, 2024, 238: 115237.

[47]Cao D, Liu W, Liu S, et al. Simultaneous calibration of hand-eye and kinematics for industrial robot using line-structured light sensor[J]. Measurement, 2023, 221: 113508.

[48]Feng X, Tian D, Wu H, et al. A matrix-solving hand-eye calibration method considering robot kinematic errors[J]. Journal of Manufacturing Processes, 2023, 99: 618-635.

[49]Song Y, Tian W, Tian Y, et al. An efficient calibration method for serial industrial robots based on kinematics decomposition and equivalent systems[J]. Robotics and Computer-Integrated Manufacturing, 2023, 84: 102607.

[50]Ma S, Deng K, Lu Y, et al. Error compensation method of industrial robots considering non-kinematic and weak rigid base errors[J]. Precision Engineering, 2023, 82: 304-315.

[51]Ahmad N S, Goh P. Material classification via embedded rf antenna array and machine learning for intelligent mobile robots[J]. Alexandria Engineering Journal, 2024, 106: 60-70.

[52]Liu J, Deng Y, Liu Y, et al. A logistic-tent chaotic mapping Levenberg Marquardt algorithm for improving positioning accuracy of grinding robot[J]. Scientific Reports, 2024, 14(1): 9649.

[53]Deng X, Ge L, Li R, et al. Research on the kinematic parameter calibration method of industrial robot based on LM and PF algorithm[C]//2020 Chinese Control and Decision Conference (CCDC). IEEE, 2020: 2198-2203.

[54]Wang Y, Chen Z, Zu H, et al. Improvement of Heavy Load Robot Positioning Accuracy by Combining a Model‐Based Identification for Geometric Parameters and an Optimized Neural Network for the Compensation of Nongeometric Errors[J]. Complexity, 2020, 2020(1): 5896813.

[55]Wang J, Chen H. BSAS: Beetle swarm antennae search algorithm for optimization problems[J]. arXiv preprint arXiv:1807.10470, 2018.

[56]Sun, Tao, et al. "Calibration for precision kinematic control of an articulated serial robot." IEEE Transactions on Industrial Electronics 68.7 (2020): 6000-6009.

[57]Fan, Cheng, et al. "Calibration of a parallel mechanism in a serial-parallel polishing machine tool based on genetic algorithm." The International Journal of Advanced Manufacturing Technology 81 (2015): 27-37.

[58]Deng, Xin, et al. "Research on the kinematic parameter calibration method of industrial robot based on LM and PF algorithm." 2020 Chinese Control and Decision Conference (CCDC). IEEE, 2020.