IROS2019国际学术会议论文集 2231

Abstract Robot assisted laparoscopic minimally invasive surgery has gained significant attentions due to its enhanced dexterity improved precision natural eye hand coordination etc In these procedures stick like surgical tools with distal wrists are usually maneuvered by multiple patient side manipulators to perform an operation These patient side manipulators shall realize remote center of motion movements and are subject to risks of mutual collisions during motion On the other hand the continuum surgical manipulators often with multiple segments usually have several degrees of freedom DoFs for the movements in a patient s cavity and only need a lockable bedside stand rather than a manipulator However the continuum segments inherently have limited bending curvature such that large orientation changes of the surgical end effector around confined anatomical features can be challenging This paper hence proposes a modular continuum articulated laparoscopic robotic tool design with simple and decoupled kinematics An inverted dual continuum mechanism is used in the tool to realize pure translations while a 2 DoF cable driven distal wrist is incorporated for orientations The utilized dual continuum mechanism maintains a constant length across its entire cross section to significantly facilitate maintaining tensions for the actuation cables of the distal wrist Design concept kinematics system descriptions actuation calibration and experimental characterizations are reported demonstrating effectiveness of the proposed idea I INTRODUCTION Laparoscopic MIS Minimally Invasive Surgery robotic systems benefit both patients and doctors owning to the higher dexterity better precision intuitive eye hand coordination etc 1 2 In these systems 3 10 stick like surgical tools with distal articulated or continuum wrists are usually maneuvered by multiple patient side manipulators with serial or parallel structures to perform surgical tasks These bedside manipulators shall realize RCM Remote Center of Motion movements and are subject to risks of mutual collisions during a procedure This work was supported in part by the National Natural Science Foundation of China Grant No 51722507 Grant No 51435010 and Grant No 91648103 and in part by the National Key R e mails liqi362202 and k xu Jiangran Zhao is with Beijing Surgerii Technology Co Ltd Beijing China e mail jiangran zhao Jiangping Gao is with the Urology Department the First Affiliated Hospital of PLA General Hospital Beijing China e mail jpgao Alternatively continuum manipulators have been more widely applied in surgical applications 11 These continuum surgical manipulators often with multiple segments usually have several distal DoFs Degrees of Freedom for 6D movements in a patient s abdomen or other organ cavities 12 17 Then lockable bedside stands rather than active extracorporeal manipulators are enough to hold these continuum manipulators to the entry ports of patients cavities However bending curvature of a continuum segment is inherently limited Large orientation changes of the surgical end effector can be difficult to realize using a bending segment around confined anatomical structures A modular continuum articulated laparoscopic robotic tool design is hence proposed in this paper as shown in Fig 1 An inverted dual continuum mechanism IDCM is used to realize 2 DoF sideward translations while a cable driven distal wrist is integrated for orientations leading to simple and decoupled kinematics The IDCM is from the dual continuum mechanism that was proposed in 16 Its working principle is explained in Section II A da Vinci EndoWrist large needle driver is disassembled and attached on the top of the IDCM for orientations for proof of concept as shown in Fig 1 b Other Figure 1 a The modular continuum articulated laparoscopic robotic tool is mounted on an actuation unit that is translated by a linear actuator on a lockable stand b An inverted dual continuum mechanism IDCM is used for 2 DoF sideward translations while a cable driven distal wrist a da Vinci EndoWrist large needle driver is integrated for distal dexterity Design of a Modular Continuum Articulated Laparoscopic Robotic Tool with Decoupled Kinematics Zhonghao Wu Student Member IEEE Qi Li Jiangran Zhao Jiangping Gao and Kai Xu Member IEEE a Modular Continuum Articulated Laparoscopic Robotic Tool Sterile barrier Actuation unit Trocar Linear actuator Lockable stand b Articulated distal wrist 2 DoF sideward translations are realized using an inverted dual continuum mechanism IDCM IEEE Robotics and Automation Letters RAL paper presented at the 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 Copyright 2019 IEEE cable driven articulated wrists can certainly be used More importantly constant length of the IDCM across the entire cross section greatly facilitates maintaining the tensions on the actuation cables of the distal wrist The entire continuum articulated laparoscopic robotic tool is assembled onto an actuation unit as shown in Fig 1 a The actuation unit can provide a rotation around the tool s axis as well as be translated by a linear actuator The linear actuator is positioned by a lockable stand The main contribution of this paper is the proposal of this new continuum articulated tool structure with the following nice features The IDCM provides pure sideward translation to generate simple and decoupled kinematics The distal wrist can change the orientation of the surgical end effector in a confined surgical site The IDCM has a constant length across the entire cross section for easily maintaining the tensions of the wrist s actuation cables The IDCM supports redundant placement of its structural backbones for enhanced rigidity and payload capability The remainder of this paper is organized as follows Section II explains the design concept of the proposed modular continuum articulated laparoscopic robotic tool Kinematics is derived in Section III while the system descriptions are presented in Section IV Experimental characterizations are reported in Section V with the conclusions summarized in Section VI II DESIGN CONCEPT Design concept of the proposed continuum articulated laparoscopic robotic tool is shown in Fig 2 The tool includes i a rigid stem ii an IDCM iii a distal wrist The tool also includes a transmission assembly as shown in Fig 5 Since the transmission assembly is not the contribution of this paper it will be briefly introduced in the Section IV A The IDCM realizes translations of the distal wrist It consists of a proximal segment PS a multi lumen block MLB and a distal segment DS The PS and the DS are identical Each segment consists of several backbones an end disk and several spacer disks The backbones are made of super elastic nitinol nickel titanium alloy and can undertake both compressive and stretching loads There are passive and active backbones in the IDCM Passive backbones are routed through the DS the MLB and the PS with both ends attached to the end disks of the DS and the PS The actuation backbones are connected to the MLB and routed to the transmission assembly through the rigid stem When the actuation backbones are pulled and pushed by the transmission assembly shown in Fig 5 the PS will be bent Then the lengths of the passive backbones in the PS will be changed so as to change the lengths of the DS s passive backbones because the total lengths of the passive backbones will remain constant This leads to the identical bending angle of the DS in the opposite direction making the DS s end disk parallel to that of the PS Sideward translations of the distal wrist are hence realized The spacer disks prevent the backbones from buckling under compressive loads Figure 2 Design concept of the proposed continuum articulated tool a the structure and b a planar schematic The IDCM is from the dual continuum mechanism firstly proposed in 16 where the MLB is grounded In this inverted form the PS s end disk is grounded The distal wrist is cable actuated for orienting the surgical end effector in confined surgical sites For proof of concept a da Vinci EndoWrist large needle driver is disassembled from a da Vinci instrument and attached to the end disk of the IDCM s DS Other cable driven articulated wrists can certainly be used The actuation cables of the distal wrist are inside the guiding tubes passing through the DS the MLB the PS and the rigid stem The IDCM has particular advantages while integrated with a cable driven mechanism Because the IDCM s passive backbones all have the same and constant lengths lengths of the guiding tubes as well as the actuation cables inside the guiding tubes will remain constant no matter how the IDCM is bent This feature greatly helps maintain the tensions on the actuation cables If a single segment is used the segment s bending will cause the guiding tubes to be shortened on one side and lengthened on the other side the tension keeping then has to accommodate these length changes When large tensions are applied on the cables to increase the wrist s payload capability the passive backbones all collaboratively undertake the compressions from the cable tensions The cable tensions will not increase the buckling risks of the actuation backbones Redundant passive backbones can be arranged for increased tool rigidity and strength This feature is inherited DS distal segment PS proximal segment MLB multi lumen block Rigid stem Distal wrist Actuation backbone of the PS Actuation cable Intra abdominal Extra abdominal Guiding tube Rigid stem DS DS s end disk PS s end disk b 1 2 3 4 ra PS Spacer disks Spacer disks MLB multi lumen block a Passive backbone DS s end disk PS s end disk Actuation backbone arrangement in the MLB from the dual continuum mechanism and has been practiced for stiffness adjustments as in 18 19 Since the articulated wrist orients the surgical end effector translation of the wrist is realized by the continuum segments If the IDCM is not used two coordinately controlled bending segments shall be used to realize a pure translation Then the 2 DoF sideward translation is realized by four actuators since each continuum segment is bent by two actuators This is an inefficient use of the actuators If only one bending segment is used the lengths of the wrist s actuation cables through the continuum segment will change during a bending movement Furthermore the bending segment translates the wrist with a parasite orientation change leading to possible reduction of the useful portion of the orientation workspace The use of the IDCM is indeed advantageous The rigid stem can be fed along and rotated about its axis Then the proposed continuum articulated laparoscopic robotic tool has 6 DoFs excluding the actuation of the end effector the IDCM realizes 2 DoF sideward translation while the wrist realizes 2 DoF orientation III KINEMATICS Nomenclature and coordinates are defined in Section III A The forward and inverse kinematics is derived in Section III B and Section III C respectively The actuation kinematics is introduced in Section III D A Nomenclature and Coordinates Nomenclature is defined in Table I and the coordinates are defined as follows referring to Fig 3 TABLE I NOMENCLATURE USED IN THE KINEMATICS MODELING Symbol Representation L0 Feeding length of the rigid stem defined as the distance from the origin of the World Coordinate to PS s end disk center Right handed rotation of the rigid stem Bending angle of the PS and DS Rotation angle of the bending plane from 1y to bx Rotation angle of the wrist joint from ax to wx Rotation angle from wx to j y about jz Configuration vector defined as L0 T L1 L2 Lengths of the PS and the DS respectively Lr Length of the MLB which is between the PS and the DS Lm Offset between the DS s end disk and the wrist joint axis a k a the distance between az and wz g1 Offset between the wrist joint axis and the jaw joint axis a k a the distance between wz and jz g2 The length of each jaw ra Radius of the pitch circle defining the positions of the actuation backbones in the PS r1 r2 Pulley radii for the wrist actuation cables in the wrist joint and the jaw joint respectively rg Radius of the guiding pulleys in the distal wrist aR b Coordinate transformation of frame b with respect to frame a ap b Position vector of the origin of frame b with respect to the origin of frame a in the view of coordinate a Figure 3 Nomenclature and coordinates of the laparoscopic robotic tool World Coordinate oooo O xyz is located at the skin incision point Base Disk Coordinate bbbb O xyz is obtained by a translation L0 and a rotation along and around oz Bending Plane Coordinate 1 1111 O x yz share the same origin with b O 1x is aligned with bz such that the PS bends in the XY plane of 1 O Bending Plane Coordinate 2 2222 O xyz has the origin at the DS s end disk center translated from 1 O End Disk Coordinate eeee O xyz shares the origin with 2 O and ez is aligned with 2x Since the PS and DS undergo identical bending e O is translated from b O Auxiliary Coordinate aaaa O xyz is under a permutation transformation 20 from e O where azis aligned with ey and axis aligned with ez a O is introduced for the Denavit Hartenberg representation of the distal wrist Wrist Joint Coordinate wwww O xyz has its origin translated from that of a O along ax by a length of Lm wz coincides with the axis of the wrist joint and wx points from the wrist joint to the jaw joint Jaw Joint Coordinate jjjj O xyz is attached to the jaw joint with j z aligned with the joint axis j O is obtained from w O by a translation of g1 along wx Tip of the gripper is at a distance of g2 along j y and the jaws open symmetrically with respect to j y oy 1 b zx bx ey by 2y 2z 2 e zx 1y 1z e a zy 2z wy wx wz j x ex oz ox j z 2y 0 L j y j z j x j y e a yx 2ae zxx B Forward Kinematics The homogeneous transformation from the World Coordinate to the Jaw Joint Coordinate is as follows 1 3 1 oo oobeawjj jbeawj Rp TTTTTT 0 1 Since the rigid stem can be fed and rotated oTb is obtained as follows 1 3 1 oo obb b Rp T 0 2 Where o b z RR and opb 0 0 L0 T z R is a basic rotation matrix about z for an angle of According to the widely accepted constant curvature bending assumption 21 22 the PS and the DS bend into circular arcs Since the Oe is purely translated from the Ob the upper left corner of bTe is an identity matrix 3 3 1 3 1 b b e e Ip T 0 3 The path along which the Oe is translated from the Ob in the bending plane is as follows i the PS s central axis a circular arc with length L1 and bending angle ii the MLB s central axis a distance of Lr and iii the DS s central axis a circular arc with length L2 and bending angle The direction of the bending plane is parameterized using Then the bpe is derived as follows cos1 coscossin sincos1sinsin sincos b12 er LL L p 4 When approaches zero bpe 0 0 L1 L2 Lr T The eTa is obtained via permutation transformation 20 3 1 1 3 1 e e a a R0 T 0 5 Where 2 2 e a xz RRR aT w and wT j can be directly obtained using the Denavit Hartenberg parameters as listed in Table II 1 1 1 2 ak wk wk jk k k TT TT 6 Where 11 1 1 kk kkk k Rp T 0 1 111 sincos T k kkkkkk dd p 7 1 111 111 cossin0 sincoscoscossin sinsincossincos kk k kkkkkk kkkkk R 8 TABLE II DENAVIT HARTENBERG PARAMETERS OF THE WRIST No ak 1 k 1 dk k k 1 Lm 0 0 k 2 g1 2 0 2 In this design the radius of the nitinol backbones is chosen as rNiTi 0 50 mm and the used elastic strain is 1 The constraints on the elastic strain are hence formulated NiTi1 NiTi2 rL rL 9 Maximal is preset as 60 L1 and L2 are set equal for simplicity The values of L1 and L2 are subject to 9 and hence rounded to 50 mm Certainly L1 L2 and Lr can be altered to realize different workspace for different surgical purposes The values of Lm g1 and g2 and the ranges of and are measured from the da Vinci EndoWrist large needle driver which is disassembled from a da Vinci instrument All structural parameters and variable ranges are listed in Table III The workspace of the continuum articulated laparoscopic robotic tool can be generated as illustrated in Fig 4 excluding the distal wrist The workspace has a cylindrical shape mainly because the IDCM realizes 2 DoF sideward translation The workspace has a shell shaped top because the IDCM s sideward translation is associated with a parasite retraction in the direction of the rigid stem referring to Fig 2 C Inverse Kinematics Since the IDCM only translates the orientation is purely determined by and Then the inverse kinematics will be solved for the three angles first From 1 the oRj is expanded as following o j c s ss cc s cs sc c s s sc cs s cc ss c c sc cs R 10 Where s and c denote sin and cos respectively TABLE III STRUCTURAL PARAMETERS AND VARIABLE RANGES L1 L2 Lr Lm g1 g2 50 mm 50 mm 40 mm 35 mm 9 mm 10 mm L0 0 150 mm 180 180 0 60 70 70 90 90 Figure 4 Workspace of the proposed laparoscopic robotic tool and can thus be derived as arcsin3 3 atan23 1 3 2 atan22 3 1 3 o j oo jj oo jj cc cc R RR RR 11 and will be bounded at their mechanically allowed joint limits if the solved values exceed the limits Equation 12 is rewritten from 1 oT obebeabeaw bjeaeaweawj oT ob bbe RpRpRRpRRRp Rpp 12 The left side of 12 can be calculated using the solved and values Then 12 becomes a set of three equations with three unknowns and L0 The and L0 are solved numerically D Actuation Kinematics Actuation kinematics describes how the actuation backbones of the IDCM and the cables of the distal wrist should be actuated according to the desired configuration variables As shown in Fig 2 a the division angle of the actuation backbones is 2 and the radius of the pitch circle for the actuation backbone distribution is ra The push pull actuation length qi is hence given by 13 cos1 2 ia qri 13 Where i 1 2 3 and 4 Since the lengths of the actuation cables are not affected by the IDCM the changes of the actuation lengths for the wrist are determined referring