Analytic Description of Medical Robot Needles’ Collision-free Reachable Workspace Boundary
LIU Shaoli1, YANG Xiangdong1,2, XU Jing1,2, CHEN Ken1,2
1. Department of Precision Instruments and Mechanology, Tsinghua University.Beijing 100084, China; 2. The State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
Abstract:A surgical planning scheme for robot-assisted celiac interventional therapy system is proposed.Through analyzing the surgical procedure,a physical model is presented to simplify the needle into an operation arm with a single globe hinge joint.The nonlinear equations with parameter are adopted to obtain the analytic description of the needle's workspace based on the study on the analytic description of the arm's collision-free reachable workspace boundary in robotics.The ribs and blood vessels in the abdominal cavity are described with third-order continuous differentiable super quadric surface equation.With numerical iterative continuation method,the unidimensional manifold of needle's collision-free reachable workspace boundary is solved,and the three-dimensional models are displayed with the Matlab toolbox.For the case that ribs and vessels exist in the abdominal cavity,the workspace boundary of the needle is successfully obtained.According to simulation results,the needle-insertion path will not collide with fraises such as ribs and vessels if the entry point is selected within the needle's workspace boundary.This paper provides an effective means for doctors to make successful surgery operation planning,solves the problem that the current system determines the entry point by doctors' own surgical experiences, and improves the efficiency and success rate of surgery.
[1] Xu J,Jia Z Z,Song Z J,et al.Three-dimensional ultrasound image-guided robotic system for accurate microwave coagulation of malignant liver tumours[J].The International Journal of Medical Robotics and Computer Assisted Surgery,2010,6(3):256-268.
[2] 刘少丽,杨向东,陈恳.基于分割MC算法的超声影像三维重建方法[J].清华大学学报:自然科学版,2010,50(8):1214-1218.Liu S L,Yang X D,Chen K.Segmentation MC algorithm-based method for ultrasound image 3-D reconstruction[J].Journal of Tsinghua University:Science and Technology,2010,50(8):1214-1218.
[3] 刘少丽,杨向东,冯涛,等.三维超声影像导航机器人系统的临床应用[J].中国生物医学工程学报,2009,28(6):878-884.Liu S L,Yang X D,Feng T,et al.The clinical application of a 3D ultrasound-guided robot system[J].Chinese Joumal of Biomedical Engineering,2009,28(6):878-884.
[4] Coste-Maniere E,Adhami L,Severac-Bastide R,et al.Optimized port placement for the totally endoscopic coronary artery bypass grafting using the da Vinci robotic system[C]//International Symposium on Experimental Robotics.Berlin,Germany:Springer-Verlag,2000:199-208.
[5] Shevchenko N,Seidl B,Schwaiger J,et al.MiMed liver:A planning system for liver surgery[C]//32nd Annual International Conference of the IEEE Engineering-in-Medicine-andBiology-Society.Piscataway,NJ,USA:IEEE,2010: 1882-1885.
[6] Schwaiger J,Markert M,Seidl B,et al.Risk analysis for intraoperative liver surgery[C]//32nd Annual International Conference of the IEEE Engineering-in-Medicine-and-BiologySociety.Piscataway,NJ,USA:IEEE,2010:410-413.
[7] Anon.3D Slicer[EB/OL].(2008-10-24)[2011-06-18].http://www.slicer.org/.
[8] Renishaw.Surgical planning software[EB/OL].(2007-09-13)[2011-06-18].http://www.renishaw.com/en/surgical-planningsoftware--8244.
[9] Park S,Howe R D,Torchiana D F.Virtual fixtures for robotic cardiac surgery[C]//4th International Conference on Medical Image Computing and Computer-Assisted Intervention.London,UK:Springer-Verlag,2001:1419-1420.
[10] 徐静.基于超声影像导航的肝癌消融机器人系统精度研究[D].北京:清华大学精密仪器与机械学系,2007.Xu J.Research on the system accuracy of the ultrasound-guided robot for liver cancer coagulation therapy[D].Beijing:Department of Precision Instruments and Mechanology,Tsinghua University,2007.
[11] Kumar A,Waldron K J.The workspaces of a mechanical manipulator[J].ASME Journal of Mechanical Design,1981,103(3):665-672.
[12] Freudenstein F,Primrose E J F.On the analysis and synthesis of the workspace of a three-link,turning-pair connected robot arm[J].ASME Journal of Mechanisms,Transmissions,and Automation in Design,1984,106(3):365-370.
[13] Litvin F L.Application of theorem of implicit function system existence for analysis and synthesis of linkages[J].Mechanism and Machine Theory,1980,15(2):115-125.
[14] Yang X D,Wang H B,Zhang C Q,et al.A method for mapping the boundaries of collision-free reachable workspaces[J].Mechanism and Machine Theory,2010,45(7):1024-1033.
[15] Haug E J,Wang J Y,Wu J K.Dexterous workspaces of manipulators,Part 1:Analytical criteria[J].Mechanics of Structures and Machines,1992,20(3):321-361.
[16] Haug E J,Luh C M,Adkins F A,et al.Numerical algorithms for mapping boundaries of manipulator workspaces[J].ASME Journal of Mechanical Design,1996,118(2):228-234.
[17] Wang J Y,Wu J K.Dexterous workspaces of manipulators,Part 2:Computational methods[J].Mechanics of Structures and Machines,1993,21(4):471-506.
[18] Qiu C X C,Luh C M,Haug E J.Dexterous workspaces of manipulators,Part 3:Calculation of continuation curves at bifurcation points[J].Mechanics of Structures and Machines,1995,23(1):115-130.
[19] Luh C M,Adkins F A,Haug E J,et al.Working capability analysis of Stewart platforms[J].ASME Journal of Mechanical Design,1996,118(2):220-227.
[20] Rheinboldt W C.Numerical analysis of parameterized nonlinear equations[M].New York,USA:John Wiley & Sons,1986.
[21] Chakraborty N,Peng J F,Akella S,et al.Proximity queries between convex objects:An interior point approach for implicit surfaces[J].IEEE Transactions on Robotics,2008,24(1):211-220.
[22] Hanson A J.Hyperquadrics:Smoothly deformable shapes with convex polyhedral bounds[J].Computer Vision,Graphics,and Image Processing,1988,44(2):191-210.