“On the Kinematics of Robotic-assisted Minimally Invasive Surgery”

Authors: Pål J. From,
Affiliation: Norwegian University of Life Sciences
Reference: 2013, Vol 34, No 2, pp. 69-82.

Keywords: Minimally Invasive Surgery, Robotic-assisted Minimally Invasive Surgery, Robot Kinematics, Constrained Jacobian Matrices, Remote Center of Motion

Abstract: Minimally invasive surgery is characterized by the insertion of the surgical instruments into the human body through small insertion points called trocars, as opposed to open surgery which requires substantial cutting of skin and tissue to give the surgeon direct access to the operating area. To avoid damage to the skin and tissue, zero lateral velocity at the insertion point is crucial. Entering the human body through trocars in this way thus adds constraints to the robot kinematics and the end-effector velocities cannot be found from the joint velocities using the simple relation given by the standard Jacobian matrix. We therefore derive a new Jacobian matrix which gives the relation between the joint variables and the end-effector velocities and at the same time guarantees that the velocity constraints at the insertion point are always satisfied. We denote this new Jacobian the Remote Center of Motion Jacobian Matrix (RCM Jacobian). The main contribution of this paper is that we address the problem at a kinematic level and that we through the RCM Jacobian can guarantee that the insertion point constraints are satisfied which again allows for the controller to be implemented in the end-effector workspace. By eliminating the kinematic constraints from the control loop we can derive the control law in the end-effector space and we are therefore able to apply Cartesian control schemes such as compliant or hybrid control.

PDF PDF (662 Kb)        DOI: 10.4173/mic.2013.2.3

DOI forward links to this article:
[1] Pal Johan From, Jang Ho Cho, Anders Robertsson, Tomohiro Nakano, Mahdi Ghazaei and Rolf Johansson (2014), doi:10.1109/BIOROB.2014.6913800
[2] Cong Dung Pham and Pal Johan From (2014), doi:10.1109/ROBIO.2014.7090632
[3] Huynh Nhat Trinh Phan and Pal Johan From (2014), doi:10.1109/ROBIO.2014.7090542
[4] Cong D. Pham, Fernando Coutinho, Antonio C. Leite, Fernando Lizarralde, Pal J. From and Rolf Johansson (2015), doi:10.1109/IROS.2015.7353557
[5] Cong Dung Pham, Fernando Coutinho, Fernando Lizarralde, Liu Hsu and Pål Johan From (2014), doi:10.3182/20140824-6-ZA-1003.00219
[6] Pål Johan From, Anders Robertsson and Rolf Johansson (2014), doi:10.3182/20140824-6-ZA-1003.02498
[7] Murilo M. Marinho, Mariana C. Bernardes and Antonio P. L. Bo (2016), doi:10.1142/S2424905X16500070
[8] Hamid Sadeghian, Fatemeh Zokaei and Shahram Hadian Jazi (2018), doi:10.1007/s10846-018-0927-0
[9] Ahmed R. J. Almusawi, L. C. Dülger and S. Kapucu (2019), doi:10.1007/978-3-030-20131-9_182
[10] Hang Su, Shuai Li, Jagadesh Manivannan, Luca Bascetta, Giancarlo Ferrigno and Elena De Momi (2019), doi:10.1109/ICRA.2019.8793676
[11] Bohan Yang, Wei Chen, Zerui Wang, Yiang Lu, Jiayue Mao, Hesheng Wang and Yun-Hui Liu (2019), doi:10.1109/TMRB.2019.2949881
[12] Hang Su, Yingbai Hu, Hamid Reza Karimi, Alois Knoll, Giancarlo Ferrigno and Elena De Momi (2020), doi:10.1016/j.neunet.2020.07.033
[13] Xiao Xiao and Hongliang Ren (2018), doi:10.1109/NEMS.2018.8556998
[14] Hang Su, Yunus Schmirander, Zhijun Li, Xuanyi Zhou, Giancarlo Ferrigno and Elena De Momi (2020), doi:10.1109/ICRA40945.2020.9197267
[15] Hang Su, Chenguang Yang, Jiehao Li, Yiming Jiang, Giancarlo Ferrigno and Elena De Momi (2020), doi:10.1109/ICHMS49158.2020.9209500
[16] Vincenzo Schettino, Mario D. Fiore, Claudia Pecorella, Fanny Ficuciello, Felix Allmendinger, Johannes Lachner, Stefano Stramigioli and Bruno Siciliano (2020), doi:10.1109/IROS45743.2020.9340690
[17] Hang Su, Yingbai Hu, Jiehao Li, Jing Guo, Yuan Liu, Mengyao Li, Alois Knoll, Giancarlo Ferrigno and Elena De Momi (2020), doi:10.1109/IROS45743.2020.9341302
[18] Hang Su, Wen Qi, Jiahao Chen and Dandan Zhang (2022), doi:10.1109/TFUZZ.2022.3157075
[19] Hang Su, Yunus Schmirander, Sarah Elena Valderrama-Hincapie, Wen Qi, Salih Ertug Ovur and Juan Sandoval (2022), doi:10.1017/S0263574722001679
[20] Fangxun Zhong and Yun-Hui Liu (2023), doi:10.1177/02783649231179753
[21] Wuxiang Zhang, Zhi Wang, Ke Ma, Fei Liu, Pengzhi Cheng and Xilun Ding (2024), doi:10.1007/s11465-024-0785-3
[1] Azimian, H. (2012). Preoperative Planning of Robotics-Assisted Minimally Invasive Cardiac Surgery Under Uncertainty, Ph.D. thesis, University of Western Ontario - Electronic Thesis and Dissertation Repository.
[2] Azimian, H., Patel, R., Naish, M. (2010). On constrained manipulation in robotics-assisted minimally invasive surgery, In Biomedical Robotics and Biomechatronics.BioRob, 3rd IEEE RAS and EMBS International Conference on. pp. 650--655 doi:10.1109/BIOROB.2010.5627985
[3] Cho, J.H., From, P.J., Annerstedt, M., Robertsson, A., Johansson, R. (2012). Design of an intermediate layer to enhance operator awareness and safety in telesurgical systems, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Vilamoura, Portugal doi:10.1109/IROS.2012.6386138
[4] Craig, J. Raibert, M. (1979). A systematic method of hybrid position/force control of a manipulator, In Computer Software and Applications Conference, Proceedings. COMPSAC 79. The IEEE Computer Society´s Third International. pages 446 -- 451 doi:10.1109/CMPSAC.1979.762539
[5] Deal, A., Chow, D.L., Newman, W. (2012). Hybrid natural admittance control for laparoscopic surgery, In Proceedings of the IEEE/RSJ International Conference on the Intelligent Robots and Systems doi:10.1109/IROS.2012.6385885
[6] From, P.J., Pettersen, K.Y., Gravdahl., J.T. (2013). Vehicle-manipulator systems - modeling for simulation, analysis, and control, Springer Verlag, London, UK.
[7] Funda, J., Taylor, R., Eldridge, B., Gomory, S., Gruben, K. (1996). Constrained cartesian motion control for teleoperated surgical robots, Robotics and Automation, IEEE Transactions on, 1.3:453--465 doi:10.1109/70.499826
[8] Hannaford, B., Rosen, J., Friedman, D., King, H., Roan, P., Cheng, L., Glozman, D., Ma, J., Kosari, S., White, L. (2013). Raven-ii: An open platform for surgical robotics research, Biomedical Engineering, IEEE Transactions on, 6.4:954--959 doi:10.1109/TBME.2012.2228858
[9] Lenarcic, J. Galletti, C. (2004). Kinematics and modelling of a system for robotic surgery, In On Advances in Robot Kinematics. Springer.
[10] Li, M., Kapoor, A., Taylor, R. (2005). A constrained optimization approach to virtual fixtures, In Intelligent Robots and Systems, IEEE/RSJ International Conference on. pp. 1408--1413 doi:10.1109/IROS.2005.1545420
[11] Locke, R. Patel, R. (2007). Optimal remote center-of-motion location for robotics-assisted minimally-invasive surgery, In Robotics and Automation, IEEE International Conference on. pp. 1900--1905 doi:10.1109/ROBOT.2007.363599
[12] Mason, M.T. (1981). Compliance and force control for computer controlled manipulators, Systems, Man and Cybernetics, IEEE Transactions on, 1.6:418 --432 doi:10.1109/TSMC.1981.4308708
[13] Nakamura, Y. (1991). Advanced robotics: redundancy and optimization, Addison-Wesley series in electrical and computer engineering: Control engineering. Addison-Wesley Longman, Incorporated, http://books.google.no/books?id=hp4QAQAAMAAJ.
[14] Natale, C. (2003). Interaction Control of Robot Manipulators: Six-degrees-of-freedom Tasks, Springer Tracts in Advanced Robotics. Springer, http://books.google.no/books?id=mSyqXs5ci4sC.
[15] Newman, W.S. Zhang, Y. (1994). Stable interaction control and coulomb friction compensation using natural admittance control, Journal of Robotic Systems, 1.1:3--11 doi:10.1002/rob.4620110103
[16] Ortmaier, T. Hirzinger, G. (2000). Cartesian control issues for minimally invasive robot surgery, In Intelligent Robots and Systems, Proc. IEEE/RSJ International Conference on, volume1. pp. 565--571 vol.1 doi:10.1109/IROS.2000.894664
[17] Sun, L. Yeung, C. (2007). Port placement and pose selection of the da vinci surgical system for collision-free intervention based on performance optimization, In Intelligent Robots and Systems, IEEE/RSJ International Conference on. pp. 1951--1956 doi:10.1109/IROS.2007.4399354

  title={{On the Kinematics of Robotic-assisted Minimally Invasive Surgery}},
  author={From, Pål J.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}