Abstract—Mandible reconstruction surgery is an extremely complex and high-risk surgical surgery. The aim of the project is to import the robotics technology into mandible reconstruction surgery, which can reduce the workload for doctors, decrease the difficulty of operation and improve the accuracy and quality of surgery. The development of Mandible Reconstruction Surgery Robotic System (MRSRS) provides a solution by integrating pre-operative 3D reconstruction and surgery design, optical navigation system, and intro-operative robot-assisted operation. In this paper, the whole robotic system was introduced firstly. Secondly, a novel Mandible Reconstruction Surgery Multi-arm Robot (MRSMR) and its optical navigation system were developed to assist surgeons. The navigation method of MRSMR was highlighted. At last, the accuracy test of the medical robot was conducted. The skull model experiment is finished to evaluate the robotic system.

I. INTRODUCTION ANDIBLE, which is a pivotal part of oral and maxillofacial region, plays an important role in the

maintenance of facial figure, chewing, language, swallowing, facial expressions and other functions. Mandible defects are the most common oral and maxillofacial hard tissue defects [1].

Mandible defects not only destroy the appearance of patients, but also result in structural damage or loss of the surrounding important tissues and organs, which seriously affects facial functions. In recent years, with the development of relative techniques, such as navigation technology and medical image positioning technology, the complex surgical procedures of mandible reconstruction surgery, including drilling, bone positioning and orienting, bone graft, fixing bones with screws and plates and so on, have been implemented by surgeons manually. However, the surgical procedures still have many difficulties [2-3]. First of all, the produces is a complex and high technical operation, relating to the brain, eyes and other important organs. In surgery, the structure of anatomic areas is intricacy, the shape extremely irregular, personalized feature evident, and the artificial operation cannot effectively ensure the quality of surgery and treatment. Secondly, the mandible reconstruction surgery is extremely high risk and difficult to implement because of the

Manuscript received November 5, 2013. This work was supported by the

National High Technology Research and Development program of CHINA (Grant No. 2012AA041606), the National Natural Science Foundation of China (Grant No. 61375106) and the Beijing Natural Science Foundation (Grant No. 7132132).

Xiangzhan Kong is with the Beijing Institute of Technology, Beijing, 100081 China (e-mail: ailiyakong@126.com).

Xingguang Duan* is the corresponding author, with Beijing Institute of Technology, Beijing, 100081 China (Tel & Fax: +8601068915920; E-mail:duanstar@126.com).

limitation of surgical field and instrument. Even though computer-assisted navigation and three-dimension reconstruction technology gradually walk into operation room, some difficulties, such as how to achieve the desired position in bone precisely by manually operation, are still the obstacle of mandible reconstruction surgery. Furthermore, it’s easy to spend more than 8 hours, or even longer, throwing the surgeon into fatigue [4]. Once the surgery failures, a serious consequence will be brought to the patient. So it is very difficult to attain the good result of mandible surgery.

Positioning accurately and moving stably are the characteristics of robot. As a result, many robots have been drawn into the surgery in order to assist the surgeon in fulfilling the entire operation procedures, such as the orthopaedic robot RoboDoc designed by America, the robot system ZEUS assisted minimally invasive surgery [5-7]. Medical robot assisted mandible reconstruction surgery has being pushed, resulting from the application of three-dimension image process, navigation technology and the robot technology in the medical field. The following lists some advantages concerning medical robot assisted mandible reconstruction surgery [8-10]. (1) The robot positions accurately, avoiding injuring important vessels and nerves to reduce surgical risk. In addition, it could grip the bone with the certain orientation for a long time in order to surgeon’s operation. (2) The system executed precisely preoperative virtual design and conducted interaction with the surgeon. (3) By establishing independent and safe monitoring platform of more information fusion, the reliable manual intervention measures would be taken to ensure safe operation.

Based on the above advantages, the medical robot assisted mandible reconstruction surgery could be appropriate for defusing the difficulties during the operation. By integrating preoperative 3D reconstruction module and relative patient information, Mandible Reconstruction Surgery Multi-arm Robot (MRSMR) could carry out accurately and stably by surgeon.

II. THE NAVIGATION METHOD OF THE ROBOTIC SYSTEM

A. The Integrated System The current system (Fig. 1) consists of the following major

components: a Mandible Reconstruction Surgery Multi-arm Robot (MRSMR); NDI optical navigation system; a workstation running the 3D Mandible Reconstruction Surgery Design Software (MRSDS); and main workstation running the application logic and high-level robot control.

Navigation Method for Mandible Reconstruction Surgery Robot Xiangzhan Kong, Xingguang Duan*, Yonggui Wang, Meng Li, Yang Yang, Amjad Ali Syed, Chang Li

M

978-1-4799-2744-9/13/$31.00 ©2013 IEEE

Proceeding of the IEEEInternational Conference on Robotics and Biomimetics (ROBIO)

Shenzhen, China, December 2013

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Fig. 1 Overview of the Mandible Reconstruction Surgery Robotic System

B. The Mandible Reconstruction Surgery Multi-arm Robot (MRSMR) The MRSMR was designed with three arms, and each arm

consists of six active DOFs and one passive DOF. The first three DOFs (joint 1-3), which compose robot arm, realize positioning within the operating space, the other three DOFs, which compose robot wrist, realize orientation adjustment, the passive DOF is redundant in order to assist orientation adjustment by surgeons. The holding arm needs to arrive near of the mandibular ramus, and then adjust and hold them in the appropriate position and orientation. Fig. 2 shows the DOFs configuration of the right arm.

Fig. 2 DOFs Configuration of the right arm

The first DOF of each arm is used to accomplish vertical movement, the joint 2-3 DOF of each arm rotate in the level plane. The first three DOFs decide the position of end-effectors. The last three DOFs consist of the robot’s wrist, which can control the required orientation of end-effectors. The joint 7 of holding arm is a passive sphere joint to assist surgeons holding mandibular ramus. Fig. 3 shows the assembled mechanism and prototype of the MRSMR.

Fig. 3 The assembled mechanism and prototype of the MRSMR

The safety and robustness are of great importance for the

MRSMR. Therefore, distributed control structure based on CAN-bus is selected. The advantages of CAN-bus such as strong real-time communication, long distance transmission, anti-electromagnetic interference capability and maximum of 127 CAN devices allowed, that are the requirements of MRSMR. What’s more, the only one trunk reduces the number of cables which also leads to easier wiring. The whole control system structure is shown in Fig. 4.

Fig. 4 The distributed control system of the MRSMR

C. NDI Navigation System Optical tracking system (NDI) was used as 3D coordinate

measurement system for real model of patient and robot, as shown in Fig. 5.

In the optical tracking system, passive probe and passive rigid body were used for coordinate measurement. The optical tracker was used to position robot and locate the position and orientation of end-effectors. Also, optical tracker control was accomplished by PC-based workstation .The optical navigation method for the 3D reconstructed model, real patient model and robot were developed, so that the robot can be guided through coordinate transformation with target position input. The registration between 3D reconstructed image and skull model utilizes point to point matching.

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Optical tracker is used for position calibration of robot by a passive rigid body attached to the robot

Fig. 5 Optical Tracking System

D. Navigation System Components According to the main function of the components, the

navigation system contains surgery design subsystem, robot subsystem, optical measurement subsystem and patient subsystem.

Patient subsystem

Optical measurement subsystem

Surgery design subsystem

Robot subsystem

Fig.6 The four coordinate spaces of navigation system

Corresponding to these four subsystems, the four relative

spaces are generated, respectively being three-dimensional image space, robot space, optical measurement space and patient space. In pre-operation, medical positioning markers (titanium screws) were implanted into skull and the three-dimensional model of patients was reconstructed through CT scan, to get the three-dimensional image space. Passive rigid body was fixed in the robot body, to obtain the robot space. During operation, passive rigid body was fixed in the skull, to receive the patient space. In addition, optical tracking system, which could position and track the passive rigid body and probe, has optical measurement space.

E. System Workflow of Navigation System The navigation system workflow of the medical robot

based on the optical tracker system is as follows. (1) In pre-operation, three medical positioning markers

recognized by the CT scan are implanted into the skull. Through the CT scan, reconstruct the three-dimensional model and get the three-dimensional image space. So the coordinates of markers in the image space are obtained.

(2) Fixed the passive rigid body in the robot body. By the registration algorithm, complete the registration between robot and optical locator, to determine the mapping relationship of robot space and optical measurement space.

(3) During operation, construct the patient space by fixing the passive rigid body on the patient’s skull to receive the mapping relationship of patient space and optical measurement space. Combined with the step 1, the mapping relationship of image space and optical measurement space could be calculated.

(4) During operation, use the passive probe in optical measurement space to get the marked point coordinates in the target fibular implant which is clamped by the middle arm of the surgical robot. Combined with the step 2, get the marked point coordinates of the target fibular implant in the robot space to complete the registration of the clamped target fibular implant.

(5) Combined with step 3 and 4, the mapping relationship of 3D image space and robot space could be calculated, which used to control the robot by solving the ideal position of each joint.

(6) The optical tracker is real-time tracking the position and orientation of the end-effectors of robot, so as to achieve closed-loop control and security monitoring for the robot, real-time tracking display of the end-effectors, and navigation for the three-arm surgical robot assisted mandible surgery.

(7) After the target fibular implant operated by robot arrives to the target position and orientation, the surgeons fulfill the fixed connection between fibular implant and patient skull with robot-assisted positioning.

F. Space Registration based on improved ICP algorithm To satisfy the real-time and accuracy requirements, the 3D

reconstructed image space, robot space, optical measurement space and patient space need to be mapped to realize the space registration in the pre-operation surgery design. In fact, the space registration is to calculate the transformation matrix among the 3D Image coordinate system, patient coordinate system, robot coordinate system and optical measurement coordinate system.

When the number of point set is few, classical ICP algorithm couldn’t get the accurate and stable results, which need to iteratively solve the corresponding relation between two point sets. In order to reduce patient suffering caused by placing the titanium screws, the registration process couldn’t provide enough marker points. So the classical ICP algorithm would be improved to calculate transformation matrixes. In the improved ICP algorithm, the corresponding relation of points between two known point sets would be seen the initial condition to avoid the iterative solution process between two unknown point sets. Then solve the mapping relationship by

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the least squares method and calculate iteratively the transformation matrixes based on the result error, until the accuracy is higher than the certain safety threshold.

Fig.7 The transformation relationship between coordinate systems

The navigation space registration based on the improved

ICP algorithm is illustrated as follows. (1) O

PT , which is the transformation matrix of from patient space to optical measurement space, can be obtained by using optical tracker and passive rigid body on patient skull.

(2) ROT , which is the transformation matrix from optical

measurement space to robotic space, can be obtained by using optical tracker and passive rigid body on robot.

If, locationO is the coordinate matrix of passive rigid body on robot in optical measurement space, locationO can be obtained

directly with optical tracker. locationR is the coordinate matrix

of passive rigid body on robot in robotic space. locationR can be obtained with robotic kinematics in the process of robot design.

Then, from Rlocation O locationR T O= , we can get

( ) 1RO location locationT O R−= .

(3) PVT , which is the transformation matrix from 3D

reconstructed image space to patient space, can be obtained by using passive rigid body on patient and medical markers on patient skull.

If, markV is the coordinate matrix of markers in 3D

reconstructed image space, markV can be obtained through 3D

image reconstruction. markO is the coordinate matrix of corresponding markers of patient skull in optical measurement space. markO can be obtained with optical

tracker and passive probe. markP is the coordinate matrix of

corresponding markers in patient space. markP can be obtained with passive rigid body fixed on patient and passive probe, which can be measured by optical tracker.

Then, from Pmark V markP T V= and ( ) 1O

mark P markP T O−

= .

Where, OPT has been obtained in the first step.

We can get ( ) ( ) ( )11 1P OV mark mark P mark markT P V T O V

−− −= = .

(4) RVT , is the transformation matrix from 3D reconstructed

image space to robotic space. To sum up the above steps, we can get, R R O P

V O P VT T T T= . (1) In robot-assisted surgery, the target position and

orientation matrix targetV , which is planned by surgery design

system in pre-operation, can be obtained in 3D reconstructed image space. The target matrix targetR in robotic space which

corresponds to the target matrix targetV can be obtained.

According to the above matrix transformation, we can get, R

target V targetR T V= (2)

Therefore, targetR can be calculated with RVT , then the robot

could move accordingly to target position with right orientation.

III. EXPERIMENTS AND RESULTS

A. Accuracy of Robot As is shown in Fig. 8, the Polaris family of optical tracking

system (NDI) is used as a measuring tool in this experiment. At the same time, the rigid body marker is fixed on a suitable location whose distance with the end point of surgery tool is relatively rigid.

Fig. 8 The Slave Side of Experiment

The first experiment was performed as follows. First, we

marked a point besides the arm’s guiding hole; then select randomly a preset point within the robot’s workspace and solve the joint angles with inverse kinematics; then manipulate the robot arm to the preset point and measure the real position of the marked point with coordinate measure machine after manipulation; finally calculate the error in Euclidian space with equation (3).

preset arrivedErr p p= − (3)

Link parameter errors, transmission error and zero position error of the medical robot contribute to the most influence on its accuracy. In order to improve the accuracy of the robot, this experiment studied the positioning accuracy and error compensation of our mandible reconstruction robot using

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NDI Polaris based on analysis of surgery procedure. The kinematic parameters are identified based on a revised D- H kinematic mode, taking small distortions of the joint axes and link parameter into consideration. Joint transmission error and the calibration error of joint angle’s zero point are compensated with experiments. Absolute positioning accuracy of the robot is measured using an accurate NDI Polaris measuring device according to the three models.

This experiment was repeated 12 times with 12 different preset points. Results show that the average error was descended from 7.81mm to 3.26 mm, 2.68 mm, 1.47 mm after D-H kinematic parameters were identified, Joint transmission error and the calibration error of joint angle’s zero point compensated. The result shows that the maximum value and the mean value of the robot absolute positioning accuracy are much better than the previous values after compensating the errors caused by link parameter, transmission and zero position. The robot can satisfy the requirements of mandible reconstruction surgical operations.

B. Skull Model Test of Integrated System This experiment was performed using a plastic skull model

that represents the target anatomy. The experiments verify the robotic-assisted surgical procedure and measure the accuracy and repeatability of the integrated system. The work flow is shown as Fig. 9.

Fig. 9 Skull Model Experiment.

The experiment was conducted to assist surgeons positioning and holding fibula reconstructed mandible defect implant. During experiment, surgeons operated robot and optical navigator with PC-based workstation, with which robot control software and reconstructed 3D model were shown on double displays. The work flow of skull model experiment is showed as follows.

(1) According to the actual patient’s condition, manufacture the mandibular defect skull model (a); (2) Titanium screws, used for registration between skull model and reconstructed 3D image, were fixed on skull model as marker points; (3) High-precision CT scan of skull model (b); (4) Based on the CT data, complete 3D skull model reconstruction and surgery design of fibular reconstruction mandibular defect (c); (5) Designing, modeling, and printing

the fibula implant, after that titanium screws were fixed on fibula implant in order to do its registration in robotic space (d); (6) Initialize navigation systems and robot. The rigid body was fixed on the skull as patient’s coordinate system (e); (7) By using probe to point to the titanium screws markers on the skull model, the registration between patient coordinate system and image coordinate system was finished (e); (8) The fibula implant was clamped by end-effectors of middle arm. Likewise by using probe to point to the titanium screws markers on the fibula implant, complete the registration of fibula implant in the robot coordinate system; (9) Based on the preoperative planning, the data of target position and orientation of fibula implant in image coordinate system were transferred to robot coordinate system; (10) After trajectory planning, control the end-effectors of middle arm with fibula implant to target position with certain orientation.; (11) At last, fibula implant was firmly held for surgeon operation.

Fig. 10 shows the result of skull model experiment. During experiment, with the help of navigation system, the fibula implant was adjusted to appropriate position and orientation by middle arm of robot according to the surgery design result. The robot ran stably. The positioning error in this model experiment was acceptable in clinical application. The error mainly comes from manufacturing and assembly error, 3D reconstruction error, registration error, robot initialization error, coordinate system mapping error, and so on. In future work, more model experiments should be conducted to test the error of whole robotic system.

Fig. 10 The Result of Skull Model Experiment

C. Conclusion and Discussion In robot assisted mandible reconstruction surgery, the

robot can quantify the movement of surgeon operation to achieve an accuracy surgery. The labor intensity of doctors can be reduced with short operation time. The optical navigation system can assist surgeons to carries out pre-operative design and ensures operation security. In this paper, we presented an integrated surgical robot system. Assembled mechanism, control system and optical navigation system of robot were introduced respectively. Finally, experiments were conducted to verify the feasibility of robot system.

Although results of these studies show the feasibility of robot system, there are still some shortcomings needed to be overcome, and designs needed to be improved and optimized.

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The wrist of each arm is not flexible enough, so the structure of robot needs to be optimized. The robot tools are still too clumsy to be used.

There are a lot of work to be done, and a lot of inadequacies to be improved. More experiments will be done to measure the error of whole robotic system and evaluate performance of the robotic system. The safety of robotic system should be improved and optimized. More flexible robot wrist and more easy-to-use end-effectors need to be designed according to clinical requirements. Future tests will be performed in more model experiments and animal experiments until the system proves to be safe enough to conduct a first simple operation on human.

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