Forward solution algorithm of Fracture reduction robots based on Newton-Genetic algorithm

Abstract

The Fracture Reduction Robot (FRR) is a crucial component of robot-assisted fracture correction technology. However, long-term clinical experiments have identified significant challenges with the forward kinematics of the parallel FRR, notably slow computation speeds and low precision. To address these issues, this paper proposes a hybrid algorithm that integrates the Newton method with a genetic algorithm. This approach harnesses the rapid computation and high precision of the Newton method alongside the strong global convergence capabilities of the genetic algorithm. To comprehensively evaluate the performance of the proposed algorithm, comparisons are made against the analytical method and the Additional Sensor Algorithm (ASA) using identical computational examples. Additionally, iterative comparisons of iteration counts and precision are conducted between traditional numerical methods and the Newton-Genetic algorithm. Experimental results show that the Newton-Genetic algorithm achieves a balance between computation speed and precision, with an accuracy reaching the 10−4mm order of magnitude, effectively meeting the clinical requirements for fracture reduction robots in medical correction.

Keywords

Fracture reduction robot / Newton method / Genetic algorithm / Forward kinematics / Medical application

CRediT authorship contribution statement

Jian Li: Writing - original draft, Methodology, Conceptualization. Xiangyan Zhang: Visualization, Formal analysis, Data curation. Yadong Mo: Validation, Software, Investigation. Guang Yang: Supervision, Resources, Project administration. Yun Dai: Writing - review & editing. Chengyu Lv: Visualization, Resources, Methodology. Ying Zhang: Validation, Supervision, Software. Shimin Wei: Writing - review & editing, Validation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This research work is supported by the National Natural Science Foundation of China (52005120), the interdisciplinary Team of Intelligent Elderly Care and Rehabilitation in the “Double first-class” Construction of Beijing University of Posts and Telecommunications in 2023 (2023SYLTD04), the BUPT innovation and entrepreneurship support program (2024-YC-T038), the BUPT Excellent Ph.D. Students Foundation (CX2023315).

References

[1] H.Q. Yang, L. Qu, Ilizarov bone transport technique, Zhongguo Gu Shang 35 (10) (2022) 903-907.

[2] V.P. Giannoudis, E. Ewins, D.M. Taylor, P. Foster, P. Harwood, Clinical and functional outcomes in patients with distal tibial fracture treated by circular external fixation: A retrospective cohort study, Strat. Trauma Limb Reconstr. 16 (2) (2021) 86-95.

[3] M.J. Moses, N. Tejwani, The role of external fixation in the management of upper extremity fractures, J. Am. Acad. Orthop. Surg. 31 (2023) 860-870.

[4] J. Meng, T. Sun, F. Zhang, et al., Deep surgical site infection after ankle fractures treated by open reduction and internal fixation in adults: A retrospective case-control study, Int. Wound J. 15 (6) (2018) 971-977.

[5] G.A. Hosny, Limb lengthening history, evolution, complications, and current concepts, J. Orthop. Traumatol. 21 (2020) 3.

[6] H. Zhang, F. Sun, Y. Li, Application of smart healthcare in comparative analysis of effect of early external fixator and plate internal fixation treat-ment on postoperative complications and lower limb function recovery of patients with unstable pelvic fracture, Front. Public Heal. 10 (2022) 887123.

[7] J. Lei, G. Song, Six-dimensional constraints and force feedback for robot-assisted teleoperated fracture reduction, Robot. 42 (7) (2024) 2328-2344.

[8] S. Lu, W. Yan, Z. Xu, T. Cheng, A framework of robot skill learning from complex and long-horizon tasks, IEEE Trans. Autom. Sci. Eng. 19 (4) (2021) 3628-3638.

[9] J. Lei, Z. Wang, Force/position tracking control of fracture reduction robot based on nonlinear disturbance observer and neural network, Int. J. Med. Robot. (2024).

[10] Z. Wu, Y. Dai, Y. Zeng, Intelligent robot-assisted fracture reduction system for the treatment of unstable pelvic fractures, J. Orthop. Surg. Res. 19 (1)(2024).

[11] Q. Zha, Z. Xu, H. Yang, G. Zhang, X. Cai, W. Zhang, Y. Liu, X. Shen, Y. Li, Development of a robot-assisted reduction and rehabilitation system for distal radius fractures, Front. Bioeng. Biotechnol. 11 (2024) 1342229.

[12] F. Alruwaili, M.S. Saeedi-Hosseiny, L. Guzman, S. McMillan, I.I. Iordachita, M. H. Abedin-Nasab, A 3-armed 6-DOF parallel robot for femur fracture reduction: Trajectory and force testing, in: 2022 Int. Symp. Med. Robot., ISMR, GA, USA, 2022, pp. 1-6.

[13] H. Sheng, W. Xu, B. Xu, H. Song, D. Lu, W. Ding, M.H. Mildred, Application of intelligent computer-assisted taylor 3D external fixation in the treat-ment of tibiofibular fracture: Retrospective case study, JMIR Med. Inf. 9 (5) (2021) e21455.

[14] W. Kou, P. Zhou, J. Lin, S. Kuang, L. Sun, Technologies evolution in robot-assisted fracture reduction systems: a comprehensive review, Front. Robot. AI 10 (2023) 1315250.

[15] Z. He, Y. Song, B. Lian, T. Sun, Kinematic calibration of a 6-DoF parallel manipulator with random and less measurements, IEEE Trans. Instrum. Meas. 72 (2023) 1-12, http://dx.doi.org/10.1109/TIM.2022.3221149, Art. no. 7500912.

[16] M. Liu, Q. Gu, B. Yang, Z. Yin, S. Liu, L. Yin, W. Zheng, Kinematics model optimization algorithm for six degrees of freedom parallel platform, Appl. Sci. 13 (2023) 3082.

[17] C.C. Nguyen, Z.-L. Zhou, S.S. Antrazi, C.E. Campbell, Efficient computation of forward kinematics and Jacobian matrix of a Stewart platform-based manipulator, in: IEEE Proc. SOUTHEASTCON ’91, Williamsburg, VA, USA, 1991, pp. 869-874.

[18] K. Kiu, J.M. Fitzgerald, F.L. Lewis, Kinematic analysis of a Stewart platform manipulator, IEEE Trans. Ind. Electron. 40 (2) (1998) 282-293.

[19] Z. Zhou, C. Gosselin, Analysis and design of a novel compact three-degree-of-freedom parallel robot, J. Mech. Robotics: Trans. ASME 15 (5) (2023).

[20] S. Cheng, An analytical method for the forward kinematics analysis of 6-SPS parallel mechanisms, J. Mech. Eng. 46 (9) (2010) 75-80, http://dx.doi.org/10.3901/JME.2010.09.026.

[21] A. Mahmoodi, M. Sayadi, M.B. Menhaj, Solution of forward kinematics in Stewart platform using six rotary sensors on joints of three legs, Adv. Robot. 28 (1) (2014) 27-37.

[22] P. Wang, et al., Research of the forward kinematics of parallel robot using genetic algorithm, Mech. Sci. Technol. (2005).

[23] J. Zhao, et al., Evolution and current applications of robot-assisted fracture reduction: A comprehensive review, Ann. Biomed. Eng. 48 (1) (2020) 203-224.

[24] T. Liu, Y. Lu, C.Z. Wang, Study on orthopaedic path planning of Taylor spatial frame, Int. J. Med. Robot. Comput. Assist. Surg. 20 (1) (2024) e2606.

[25] J. Lei, J. Wang, Orientation workspace analysis and parameter optimization of 3-RRPS parallel robot for pelvic fracture reduction, J. Mech. Robot. Trans. ASME 15 (5) (2023).

[26] N. Petr, W. Dominik, Investigation of the Stewart platform workspace using MATLAB-simulink and simscape multibody library, in: 21st Int. Conf. Res. Educ. Mechatronics, REM, Cracow, Poland, 2020, pp. 1-5.

[27] F. Tavassolian, et al., Forward kinematic analysis of spatial parallel robots using a parallel evolutionary neural networks, Iran J. Sci. Technol. Trans. Mech. Eng. 47 (2022) 1079-1092.

[28] T. Li, M. Gong, K. Hu, L. Zhao, B. Zhao, A novel 3-DOF translational parallel robot and its fuzzy controller design, J. Intell. Fuzzy Syst. 41 (2021) 4211-4224.

[29] H.-B. Q, W. Li-Hang, J. Xue, et al., Forward kinematics of Stewart parallel manipulator based on step-adjusting Newton method, Guangxue Jingmi Gongcheng/ Opt. Precis. Eng. 26 (12) (2018) 2982-2990.

[30] M. Geng, Direct position analysis of parallel mechanism based on quasi-Newton method, J. Mech. Eng. 51 (9) (2015).

[31] J. Tang, S. Wang, T. Bai, S. Lu, J. Xiong, Intelligent ATM replenishment optimization based on hybrid genetic algorithm, in: 24th Int. Conf. Adv. Commun. Technol., ICACT, PyeongChang, Korea, 2022, pp. 469-475.

[32] P. Ye, J. You, H. Shen, Shen, A novel semi-analytical algorithm for forward kinematics of 6-DOF parallel mechanisms, in: M. Okada (Ed.), Advances in Mechanism and Machine Science, IFToMM WC 2023, in: Mech. Mach. Sci., vol. 147, Springer, Cham.

[33] E.P. dos Santos, C.R. Xavier, P. Goldfeld, F. Dickstein, R. Weber dos Santos, Comparing genetic algorithms and Newton-like methods for the solution of the history matching problem, in: G. Allen, J. Nabrzyski, E. Seidel, G.D. van Albada, J. Dongarra, P.M.A. Sloot (Eds.), Computational Science - ICCS 2009, in: Lect. Notes Comput. Sci., vol. 5544, Springer, Berlin, Heidelberg, 2009, pp. 37-48.

[34] A.-D. Li, B. Xue, M. Zhang, Multi-objective feature selection using hy-bridization of a genetic algorithm and direct multisearch for key quality characteristic selection, Inform. Sci. 523 (2020) 245-265.

[35] M. Alshehri, P. Sharma, R. Sharma, O. Alfarraj, Motion-based activities monitoring through biometric sensors using genetic algorithm, Comput. Mater. Contin. 66 (3) (2020) 2525-2538.

[36] S. Harifi, R. Mohamaddoust, Zigzag mutation: a new mutation operator to improve the genetic algorithm, Multimedia Tools Appl. 82 (2023) 45411-45432.

[37] Huang, Forward kinematics analysis of the general 6-6 platform parallel mechanism based on algebraic elimination, Chin. J. Mech. Eng. 45 (2009) 56.

[38] H. Tian, et al., Influence of different position modal parameters on milling chatter stability of orthopedic surgery robots, Sci. Rep. 14 (2024) 10581.

[39] Z. Cao, et al., Robot-assisted internal fixation of calcaneal fractures versus conventional open reduction internal fixation: a systematic review and meta-analysis, J. Robot. Surg. 18 (1) (2024) 1-10.

[40] H. Du, et al., Experimental research based on robot-assisted surgery: Lower limb fracture reduction surgery planning navigation system, Heal. Sci. Rep. 7 (4) (2024).

[41] C. Li, et al., Advances of surgical robotics: image-guided classification and application, Natl. Sci. Rev. 9 (2024) 9.

[42] X. Long, et al., The current status and global trends of clinical trials related to robotic surgery: a bibliometric and visualized study, J. Robot. Surg. 18 (1) (2024).

[43] J. Wang, et al., Editorial for the special issue on design, sensing and control in medical robots, Biomim. Intell. Robot. 4 (3) (2024) 100177, http://dx.doi.org/10.1016/j.birob.2024.100177.

[44] L. Chen, et al., Adaptive patient-cooperative compliant control of lower limb rehabilitation robot, Biomim. Intell. Robot. 4 (2) (2024) 100155, http://dx.doi.org/10.1016/j.birob.2024.100155.