An Assistant Robot System for Sinus Surgery1

Abstract

Traditionally, sinus surgery is conducted by surgeons with their only one hand, because the other hand is used to hold the endoscope. This manner leads to a long surgery time, a bad surgery result, and a longer recover time for patients [1]. Many researchers try to employ a robot to replace the surgeon's left hand to hold the endoscope for sinus surgery. In Ref. [1], Zhang et al. have designed a passive endoscopic robot for sinus surgery and discussed the locking methods of the passive joints; in Ref. [2], Navarro-Alarcon et al. have designed a robotic endoscope holder and employed passivity-based control techniques to guarantee the stable manipulation; and in Ref. [3], Trevillot et al. have quantified the motion and force ranges and designed a compact endoscope positioner dedicated to sinonasal tract surgery.This paper introduces a seven degree-of-freedom (DOF) active sinus robot which can adjust position and orientation of the endoscope. The robot is also equipped with a force/torque sensor which would feedback the contact force information between patient and robot. This paper discusses the design and kinematic analysis of this robot, the prototype and primary experiment results, and the control logic of the whole system.The workspace requirement for the endoscope holder robot is first analyzed. Trevillot et al. have quantified the motion ranges based on the analysis of the surgeon's movements on sinonasal tracts of cadavers, and Table 1 shows the results [3].Based on the analysis above, a robot with 7DOFs is proposed. The first 3DOFs are used to adjust the global position of the robot, which employs a prismatic–revolute–revolute serial mechanism. The fourth and fifth joints correspond to the rotations in the axial plane and sagittal plane, and are used to adjust the orientation of the endoscope, which employs a remote-center-of-motion (RCM) structure based on parallelogram linkage, to avoid tearing of the endoscope entry point; the sixth joint is used to adjust the penetration of the endoscope, and the seventh joint corresponds to the rotation around the axis and is used to compensate the nonzero camera angle. Figure 1 shows the CAD model of this robot, with the link-frame assignments.Since the seventh joint is rotation around its own axis, it will not affect the end effector's posture. This joint is ignored in the kinematics analysis. With the modified Denavit–Hartenberg (D–H) method [4], the link frames of the robot have been built, as shown in Fig. 1. Table 2 shows the D–H parameters for each joint. The homogeneous transform matrix is(1)T60=T10T21T32T43T54T65=[r11r12r13pxr21r22r23pyr31r32r33pz0001]In which(2)r11=s4 s5 c3−2−c5 s3−2(3)r12=−c4c3−2(4)r13=−(s5s3−2+c5s4c3−2)(5)px=D4 s3−2−(s5s3−2+c5s4c3−2)d6+L2c2(6)r21=−(c5c3−2+s4s5s3−2)(7)r22=c4s3−2(8)r23=c5 s4s3−2−s5c3−2(9)py=D4c3−2−(s5c3−2−c5s4s3−2)d6+L2s2(10)r31=c4s5(11)r32=s4(12)r33=−c4c5(13)pz=D1−d1−c4c5d6The direct kinematics can be used to generate the workspace, with D1 = 115 mm, D4 = 313 mm, and L2 = 84 mm; the workspace is calculated and shown in Fig. 2. Since the motion ranges of the last four joints are larger than the requirement in Table 1, the workspace of robot can meet the requirement of sinus surgery. To control the robot to move to a desired position, the inverse kinematics is needed. With a known end effector posture Ttarget, the position of each joint can be calculated(14)d1=D1−pz+r33d6(15)θ2=a tan 2(±C2+D2−E2,E)−a tan 2(r13,r23)(16)θ3=θ2+a tan 2(r22,−r12)(17)θ4=a tan 2(r32,1−r322)(18)θ5=a tan 2(r31,r33)(19)d6=A⋅c2+B⋅s2c2⋅r13+s2⋅r23In which(20)A=px−D4s3−2(21)B=py−D4c3−2(22)C=r23L2(23)D=r13L2(24)E=r23 A−r13 BBased on the CAD model, a prototype has been fabricated (Fig. 3). To evaluate the accuracy of the RCM structure, an NDI Polaris optical tracking system (Northern Digital, Canada) is used to record the position the RCM center; let the fourth and fifth joints move to ten groups of different positions (keep other joints fixed) and record the position of t