Actual trajectory. Desired trajectory. Actual trajectory z [m] 0.1. z [m] 0.1. Desired trajectory 0.

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1 EndoBot: a Robotic Assistant in Minimally Invasive Surgeries Hyosig Kang and John T. Wen Center for Automation Technologies Rensselaer Polytechnic Institute, Troy, NY 1218 fkang,weng@cat.rpi.edu Abstract This paper presents a new surgical robotic system called EndoBot for assisting surgeons in performing minimally invasive surgery(mis). The EndoBot is designed for collaborative operation between the surgeon and the robot. The demand on the surgeon is higher during suturing task which is the primary tissue approximation method and has been known as one of the most difficult tasks in MIS. Our work is the first effort in autonomous robotic suturing for MIS. In this paper, we show the motion controller design for autonomous and shared control mode and discuss autonomous robotic suturing algorithms. precision and mechanical stability of the operation. Various specialized robotic tools have also been proposed [18 2]. For example, additional joints (like fingers) may be added to the end of the endoscopic tool to enhance the tool dexterity without requiring the motion of the entire tool stem. This is particularly useful in cardiac operation where the motion of the tool stem is limited [1, 13, 2]. It is important to note that in the various robotic surgical assistant systems described above, the surgical procedures are still completely performed by the human surgeon. The human commands are then mimicked by the robotic device through computer control. 1 Introduction Minimally invasive surgery (MIS), of which laparoscopy is an example, is an attractive alternative to the open surgery whereby the same operations are performed using specialized instruments designed to fit into the body through several pencil-sized holes instead of one large incision. By eliminating the large incision, it has many advantages over conventional open surgery. It can minimize trauma and pain, and reduce the recovery time and so reduce the hospital stay and cost [1]. However, the surgeon faces with the challenge of limited and constrained motion as well as indirect visual feedback. As demonstrated in [2], time-motion studies of endoscopic surgeries have indicated that for operations such as suturing, knot tying, suture cutting, and tissue dissection, the operation time variation between surgeons can be as large as 5%. The continuing growth of MIS operations depends in a large part on the reduction of variability and increase of efficiency of the MIS procedures. Toward this goal, many robotic devices have been patented or proposed [3 1]. One class of surgical robotic devices that has been proposed to assist surgeons in endoscopic surgeries is based on the concept of teleoperation" [4,11,12]. In [4,13 15], the surgeon's view of the operation may be further enhanced by vision to create a virtual presence." Various robotic positioners and stabilizers have also been proposed where, similar to the teleoperation, arobothold- ing surgical tool is controlled to follow surgeon's command [8, 12, 16, 17]. The role of the robot is to filter out tremor and disturbance of surgeon's hands to enhance the Figure 1: EndoBots In this paper, we present a new surgical robot design for MIS operations; we call this robot the EndoBot( shown in Figure 1). The EndoBot is designed for collaborative operation between the surgeon and the robotic device. The surgeon can select the device to operate completely manually, collaboratively where motion of the robotic device in certain directions are under computer control and others under manual surgeon control, or autonomously where the complete device is under computer control and surgeon's supervision. In this paper, we will present the mechanical design, kinematics and dynamics, control architecture, and suturing and knot tying results related to EndoBots. 1

2 2 The Robot System The EndoBot is capable of four degree-of-freedom(4- DOF) motion and consists of two parts as shown in Figure 2: rotational stage and translational stage. The rotational stage creates the spherical motion based on a pair of motor-driven semicircular arches for yaw and pitch, and a sleeve that can generate rolling motion. The translational stage carries the specific tool which is actuated pneumatically and is translated along the tool z-axis. All four actuators are DC servo motors and linear motion for translational stage is converted by lead screws. All axes are back-drivable when the motors are not energized. The center of rotation of the archjoints is at the incision point of the patient's abdominal wall. Therefore, any motion of EndoBot will not cause any tearing of the incision point. 3.1 Manual Mode For the manual mode, the controller only provides gravity compensation, so even when the EndoBot is in a tilted position, it will not fall: fi = G(q)+N(_q): 3.2 Autonomous Mode For the autonomous mode, the desired Cartesian motion is converted to the joint motion through inverse kinematics. An proportional-derivative (PD) joint level controller with friction and gravity compensation is then applied to track the required motion [22]. The controller torque is of the following form: fi = K p (q k 1 (x T d ) K d (q J 1 (q) x_ T d )+G(q)+N(_q) (2) where x T d is the desired motion for the task coordinate x T and k 1 is the inverse kinematics function and J 1 is the inverse Jacobian matrix. Ignoring the Coriolis/centrifugal terms (due to small velocity), the closed loop system is of the form: Më + K d _e + K p e =: (3) Due to the high gear ratio, M is approximately constant and diagonal. The PD gains, K p and K d, are chosen to be diagonal and provide critical damping. We have found that friction compensation (especially the Coulomb friction) is of critical importance to tracking accuracy [21]. Figure 2: Mechanical overview of EndoBot The dynamics in the following general form: M(q) q + C(q; _q)_q + G(q)+N(_q) =fi (1) where M is the mass-inertia matrix, C the Coriolis and centrifugal forces, G the gravity load, N the friction, and fi the joint torque. Due to low speed operation, we will ignore C. The task coordinate is chosen to be the position of the end effector and the roll angle. We willdenotethe task coordinate by x T and the Jacobian by J(q) whereq is the joint coordinate parameterized by yaw angle, pitch angle, roll angle, and translation. A full description of the kinematics and dynamics of EndoBots, and the parameter identification result can be found in [21]. 3 Control Architecture The control architecture is designed to allow the surgeon and the robot to collaborate in a range of programmable modes: 3.3 Shared Control Mode Shared control, as the name implies, enables the human operator and computer control the manipulator in parallel. In other words, the surgeon control some axes while the computer concurrently control other axes by adding an artificial constraint to relieve the surgeon of some sub task that would be tiring the surgeon to concentrate on such as tool alignment. In the shared control mode, the surgeon specifies motion constraints (directions where there should be no motion) and the complementary free motion direction. We will consider both joint space and direct Cartesian space implementations. Let the motion constraint on the task coordinate x T be specified as x c = c(x T )= (4) where c is a constraint function. Let f( ) be the complement ofc so that d(x T )=» c(xt ) f(x T ) (5) is a diffeomorphism (i.e., d is one-to-one and onto, and d and d 1 are both continuously differentiable). For example, suppose that the tip is to follow a straight line (through the center of the spherical joint). Let the 2

3 Figure 3: Block diagram of joint space shared controller straight line be parameterized as x a 1 = y a 2 = z a 3 : Then the constraint function is c(x T )=» 1 a 1 1 a 2 1 a 1 1 a 3 x T : (6) The free motion function, f, may be chosen to be any function that is not linearly dependent onc. However, to avoid coupling, it is in general desirable to choose f to be orthogonal to c. In this case, we maychoose f to be» a1 a f(x T )= 2 a 3 : (7) 1 where d is from (5). The desired task space velocity may be found similarly:» Jc x_ T d = J f 1» J f J _q where J c J f x T d is found, the same joint space controller (2) may be used. Figure 4 and Figure 5 show the experimental results of constraining the EndoBot tool tip to a line and a circle, respectively, while the operator moves the instrument using the handle. It is important to tune the feedback gains (especially the proportional gain) for the operator to have the right feel (tight but no oscillation). (9) Actual trajectory.6.8 Actual trajectory Desired trajectory z [m].1.12 Desired trajectory z [m] y [m] x [m] y [m] x [m].5 Figure 4: Shared control experiment with constrained line If we use the same joint space controller as described earlier, shared control can be achieved by removing the free motion component in the desired task space trajectory. Specifically, let q be the measured joint angle. The desired free motion should be the same as the actual free motion, therefore, f(x T d )=f(k(q)). The constraint motion is required to be zero, therefore, c(x T d ) =. The desired task space set point can then be obtained from x T d = d 1» f(k(q)) (8) Figure 5: Shared control experiment with constrained circle It is also straightforward to implement shared control in Cartesian space [24]. 4 Ligation Algorithm From closing the wound with an ant's head in ancient time to today's laparoscopic stitching with absorbable material, suturing has a long history and is one of the most 3

4 difficult tasks and uses a significant percentage of operating time in MIS. However, laparoscopic suturing task demands high level of skill and endurance on the surgeon. Despite the needs to be performed autonomously, no research effort has been published. It is worthwhile to decompose the suturing task into subtask and figure out what challenge is encountered with each subtask. The most common knotting technique used in surgery is a square knot and it is preferable because of requiring fewer steps than a surgeon's knot [23]. For this reason, only the square knot technique has been considered for analysis. Based on the observation of the manual suturing operation, the suturing task can be broken down into the following four subtasks: Stitching The stitching subtask is involved in entrance and exit bites, extracting the needle, and pulling the suture. The challenge of this subtask lies in manipulating the curved needle between two graspers without slippage or dropping. Creating a suture loop In the subtask of loop forming, a wrapping motion is required to create a suture loop with long tail and this is difficult to perform autonomously because the trajectory of the suture is not predictable due to its flexibility. The surgeon creates the loop based on visual feedback. Developing a knot Once a suture loop is created, the needle or short tail needs to be passed through the loop to develop a knot. The challenge lies in grasping the short tail with one of the grasper and pulling the suture through the loop. Securing a knot Once the knot is formed, proper tension should be applied to secure the knot. With the long stems of laparoscopic instruments, it is difficult to apply the appropriate amount of tension so as not to tear off the soft tissue or loosen the knot. To summarize, the primary challenges are 1) manipulating the curved needle 2) dealing with flexible suture 3) applying proper tension. To address 1), we will consider ashuttle needle device. The basic idea is to transfer the needle between two jaws and lock the tapered tip of needle by oneofjaws. A disposable shuttle needle device is available on market by USSC (US Surgical Corp.). We have adopted this device as our suturing instrument and modified it to be operated by pneumatic power. To address 2), we will consider two algorithms of automatic ligation in this section. The first one uses a standard manual stitching tool instrumented for robotic operation. The second one modifies the grasping tool with a flexible hook to facilitate the knot tying process. 4.1 Algorithm 1 The key observation for tying a simple knot is that if the suture can be placed over the jaw carrying the needle, then a loop can be formed by passing the needle to the other jaw. For a human surgeon, this step is performed by putting the jaws over the thread and then pass the needle. This is not possible for the EndoBots since the thread is flexible and its position is not directly measured. Instead, we use the rigidity of the grasper to guarantee that the suture is placing over the jaw. Automatic tying a simple knot can then be accomplished through the following steps (shown schematically in Figure 6): 1. Make a single stitch near the wound and pull out the suture. The stitcher then retracts until a specified amount of suture has been pulled through the suturing point. 2. Grab the suture tail with the grasper tip. 3. Move the stitcher so that the open jaw(thejaw without the needle) touches the front of the grasper stem. Denote the point of contact between the stitcher jaw and grasper stem P. 4. Rotate the stitcher 18 ffi about the axis OP where O is the center of the spherical joint. At the completion of this step, the thread has to lay over the open jaw. 5. Move the stitcher towards the grasper until the grasper stem is within the open jaw of the stitcher. 6. Rotate the grasper so that its narrow side faces the jaw opening. The stitcher can now close and pass the needle to the other jaw. 7. Retract the stitcher to tighten the knot. Figure 6: Autonomous simple knot tying algorithm 1 The above procedure would create a simple knot. Two simple knots may be combined to form a square knot. However, the second simple knot must be the mirror image of the first, otherwise, the knot is known as the granny knot which is not secure. 4

5 The above procedure works well most of the time in the laboratory, but has the following drawbacks: ffl In the Step 4 above, a large angle is required between the two instruments. For knots near the center of the workspace, this may not be feasible. ffl Because of errors in positioning, the thin suture thread could fall between the open jaw and the grasper stem. ffl During retraction stage, the thread could get tangled. 4.2 Ligation Algorithm 2 The first algorithm is a step toward automatic laparoscopic suturing and knotting, but suffers several drawbacks as to render the procedure less than robust. To address these issues, we made a small modification of the conventional grasping instrument. The key observation is that if we can hold on to any part of the suture at a known position, the rotation of the stitcher would be unnecessary. To achieve this, we added a reciprocating actuator connected to a flexible hook over the grasper hinge so that it can be extended or extracted as needed (see Figure 7). Figure 8: Autonomous simple knot tying algorithm 2 Figure 7: Flexible hook for catching the suture The simple knot algorithm is now modified as described below (shown schematically in Figure 8 and pictures from the experiment in Figure 9): 1. Perform Steps 1 2 in Algorithm Extend the flexible hook. Move the stitcher over the hook from the front toback so that the suture hangs over the hook. 3. Perform Steps 5 6 in Algorithm Retract the flexible hook. 5. Retract the stitcher to tighten the knot. Again, a mirror image of the first simple knot needs to be performed to ensure a secured square knot. It is done by replacing the motion over the hook to back to front (instead of front to back). This algorithm does not have the angle limitation as in Algorithm 1. The motion over the hook can be designed so the thread is always snared by the hook, so the positioning requirement is not as tight as before. Finally, since the hook is close to the grasper tip, the grasper could retract by a small amount as to avoid thread tangling. Figure 9: Implementation of simple knot tying algorithm 2 5

6 5 Conclusion This paper has presented the mechanical design, control architecture, experimental results, and algorithmic implementation of a robotic system assisting endoscopic surgeries. Innovations in this system include mechanical design consistent with natural kinematics constraint (at the incision point), interchangeable tools, variable level of autonomy in shared surgeon/robot control, and novel algorithms for ligation. For successful clinical deployment, many other issues would need to be addressed. Foremost is the safety issue. All fault scenarios and contingency would need to be considered, e.g., power failure, computer malfunction, work space variation for different patients, etc. Another important issue is the design of man-machine interface. In order for surgeons to gain comfort and trust of such a system, the mechanical interface such asthetypeofhan- dle, placement ofcontrol buttons, and electrical interface such as specification of different commands would need to carefully developed with strong input from surgeons. In terms of further technical development, we are focusing on making the autonomous surgical procedures more robust. Careful modeling and control of the thread tension is critical in avoiding tissue tearing and yanking the needle from the stitcher or the holder. Ensuring knot tightness is needed to prevent leakage at the suture. Finally, the impact of different work volume (due to variation between patients) is also under investigation. References [1] L.W. Way, S.Bhoyrul, and T.Mori. Fundamentals of laparobotic surgery. Churchill Livingstone, [2] C. Cao, C. MacKenzie, and S. Payandeh. 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