Abstract：A viscoelastic contact model between surgical instruments and ocular tissue is established on the basis of generalized Maxwell viscoelastic model, and the contact model parameters are identified through force relaxation experiment. On top of that, an admittance control method is developed. The contact force is controlled through adjusting the displacement of surgical instruments. In the proposed method, the traditional admittance controller is taken place by the proportionalintegral (PI) controller. In this way, the ideal differential element in viscoelastic contact model is replaced by the 1st order differential element. After replacement, the amplitude-frequency response at low frequency can be improved and kept stable, especially when the frequency approaches zero. The attenuation of contact force caused by low amplitude-frequency response can be avoided. Some force control experiments on in vitro pig eyes are carried out to prove the effectiveness of the proposed method. The experiment results show that the average error and response time of step force are 4.6% and 2.5 s respectively, no obvious overshot occurs, and the sinusoidal force with certain frequency can be output. The output accuracy of step force meets the requirements of robot-assisted ophthalmic surgery.
[1] 贺昌岩，杨洋，梁庆丰，等. 机器人在眼科手术中的应用及研究进展[J].机器人， 2019， 41(2)： 265-275.He C Y, Yang Y, Liang Q F, et al. Applications and research progress of robot assisted eye surgery[J]. Robot, 2019, 41(2): 265-275. [2] 肖晶晶，杨洋，沈丽君，等. 视网膜血管搭桥手术机器人系统的研究[J].机器人， 2014， 36(3)： 293-299. Xiao J J, Yang Y, Shen L J, et al. A robotic system for retinal vascular bypass surgery[J]. Robot, 2014, 36(3): 293-299. [3] He X C, Roppenecker D, Gierlach D, et al. Toward clinically applicable steady-hand eye robot for vitreretinal surgery[C]//ASME 2012 International Mechanical Engineering Congress and Exposition. New York, USA: ASME, 2012: 145-153. [4] Smits J, Ourak M, Gijbels A, et al. Development and experimental validation of a combined FBG force and OCT distance sensing needle for robot-assisted retinal vein cannulation[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2018: 129-134. [5] Gonenc B, Gehlbach P, Taylor R H, et al. Effects of microvibratory modulation during robot-assisted membrane peeling [C]//IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway, USA: IEEE, 2015: 3811-3816. [6] Ebrahimi A, He C Y, Roizenblatt M, et al. Real-time sclera force feedback for enabling safe robot assisted vitreoretinal surgery[C]//40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Piscataway, USA: IEEE, 2018: 3650-3655. [7] He C Y, Patel N, Shahbazi M, et al. Toward safe retinal microsurgery: Development and evaluation of an RNN-based active interventional control framework[J]. IEEE Transactions on Biomedical Engineering, 2020, 67(4): 966-977. [8] He C Y, Ebrahimi A, Yang E, et al. Towards bimanual vein cannulation: Preliminary study of a bimanual robotic system with a dual force constraint controller[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2020: 4441-4447. [9] Roy J, Whitcomb L L. Adaptive force control of position/ velocity controlled robots: Theory and experiment[J]. IEEE Transactions on Robotics and Automation, 2002, 18(2): 121- 137. [10] Ebrahimi A, Patel N, He C Y, et al. Adaptive control of sclera force and insertion depth for safe robot-assisted retinal surgery [C]//2019 International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2019: 9073-9079. [11] Fung Y C. Biomechanics: Mechanical properties of living tissue[M]. 2nd ed. New York, USA: Springer, 1993. [12] Su P, Yang Y, Xiao J J, et al. Corneal hyper-viscoelastic model: Derivations, experiments, and simulations[J]. Acta of Bioengineering and Biomechanics, 2015, 17(2): 73-84. [13] Karlmi A, Razaghi R, Navidbakhsh M, et al. Mechanical properties of the human sclera under various strain rates: Elastic, hyperelastic, and viscoelastic models[J]. Journal of Biomaterial and Tissue Engineering, 2017, 7(8): 686-695. [14] Burd H J. A structural constitutive model for the human lens capsule[J]. Biomechanics and Modeling in Mechanobiology, 2009, 8(3): 217-231. [15] Han S F, Yang Y. Influence of needling conditions on the corneal insertion force[J]. Computer Methods in Biomechanics and Biomedical Engineering, 2019, 22(16): 1239-1246. [16] Asadian A, Kermani M R, Patel R V. A novel force modeling scheme for needle insertion using multiple Kalman filters[J]. IEEE Transactions on Instrumentation and Measurement, 2012, 61(2): 429-438. [17] Moreira P, Zemiti N, Liu C, et al. Viscoelastic model based force control for soft tissue interaction and its application in physiological motion compensation[J]. Computer Methods and Programs in Biomedicine, 2014, 116(2): 52-67. [18] Ott C, Mukherjee R, Nakamura Y, Unified impedance and admittance control[C]//IEEE International Conference on Robotics and Automation. Piscataway, USA: IEEE, 2010: 554- 561. [19] 邬如靖，韩少峰，广晨汉，等. 具有微力感知的眼科手术器械的设计与实现[J].机械工程学报， 2020， 56(17)： 12-19. Wu R J, Han S F, Guang C H, et al. Design and implementation of a micro-force sensing instrument for ophthalmic surgery[J]. Journal of Mechanical Engineering, 2020, 56(17): 12-19.
