Optimizing Robot-Assisted Surgery Suture Plans to Avoid Joint Limits and Singularities Brijen Thananjeyan 1 , Ajay Tanwani 1 , Jessica Ji, 1 , Danyal Fer 2 , Vatsal Patel 1 , Sanjay Krishnan 3 , Ken Goldberg 1 Abstract—Laparoscopic robots such as the da Vinci Research Kit encounter joint limits and singularities during procedures, leading to errors and prolonged operating times. We propose the Circle Suture Placement Problem to optimize the location and direction of four evenly-spaced stay sutures on surgical mesh for robot-assisted hernia surgery. We present an algorithm for this problem that runs in 0.4 seconds on a desktop equipped with commodity hardware. Simulated results integrating data from expert surgeon demonstrations suggest that optimizing over both suture position and direction increases dexterity reward by 11%- 57% over baseline algorithms that optimize over either suture position or direction only. I. I NTRODUCTION Limited autonomy has been studied for robotic surgical procedures and has the potential to reduce surgeon fatigue, improve precision, and facilitate long-range tele-operation [1–6]. We investigate suture placement planning to avoid joint limits and singularities for robot-assisted hernia surgery on the da Vinci Research Kit (dVRK) [7]. Robot-assisted hernia surgery, in which a surgical mesh is placed over an abdominal wall defect using a robot, is in- creasingly common and particularly challenging to perform [8]. The success of the repair depends on the mesh being placed tightly enough to restrain the protrusion but loosely enough to ensure healing. The challenging aspect of the procedure is using an articulated robotic wrist, without haptic feedback, to perform a number of precision suturing motions: a set of "stay sutures" are placed to ensure the mesh remains flat and then a running suture to place the mesh. We assume stay sutures are performed on a circle centered on the protrusion in a direction tangent to its boundary. Suturing motions constrained by joint limits and singularities can result in errors and are difficult to predict by a human or semi-autonomous controller before execution of a suture. This limits the ability of the robot to avoid these configurations during needle insertion, which can prevent the needle from following the desired trajectory. In this paper, we explore how the positions and directions of sutures can be optimally planned to avoid areas of the configuration space that are close to joint limits and singularities. Prior work on autonomous suturing uses self-righting needle fixtures to maintain a consistent and known needle pose during autonomous needle insertion, so we assume the pose Authors are affiliated with: 1 AUTOLAB at UC Berkeley; @berkeley.edu 2 UC San Francisco East Bay; @ucsf.edu 3 University of Chicago; @cs.chicago.edu {bthananjeyan, ajay.tanwani, jji, danyal.fer, vatsal.patel, goldberg} 978-1-5386-7825-1/19/$31.00 ©2019 IEEE Figure 1: The Circle Suture Plan Optimizer outputs position and orientation for suture throws on the boundary of a given circle with fixed radius centered around the herniated tissue with respect to a dexterity reward defined in Section III-D3 that penalizes motions that are close to joint limits and singularities. The suturing arm is mounted below and to the left of the tissue phantom. We display the optimal directions for evenly-spaced sutures with different initial suture locations and observe that the direction varies in different locations on the phantom. The bottom right image depicts the sequence of sutures that maximizes a weighted combination of joint margin and manipulability rewards by optimizing both suture positions and directions. of the needle relative to the gripper is fixed [1, 5]. Simulated experiments suggest that optimizing over suture position and direction enables the robot to avoid motions constrained by joint limits and singularities. In data collected from an expert surgeon on training tissue phantoms obtained from Intuitive Surgical, we observe that the robot encounters variation in manipulability and configurations near joint singularities during placement of the sutures, resulting in unpredictable motions and errors during teleoperation. A dataset containing kinematic data for 16 physically-performed sutures is used to estimate a reward function for sutures that avoid joint singularities. We compare the ability of an algorithm that optimizes both position and direction of evenly- spaced sutures to avoid joint limits and singularities to baseline alternatives that optimize either position or direction only in simulated experiments. Results suggest that optimizing both the position and direction of evenly spaced sutures perform