## 1 Introduction  
Minimally invasive surgery has been a continuing medical trend because it can reduce the pain and the recovery time of patients. Robotic surgery has emerged as a solution for minimally invasive surgery. Diverse continuum robot manipulators are being developed for laparoscopic or endoscopic surgery [1]. The most well-known surgical robot system is the da Vinci system (Intuitive Surgical Inc., CA), which has been successfully used in various surgeries in the past decade. Its efficiency has been verified in various ways [2]. The da Vinci Si and Xi have wire-driven robotic arms for multiport surgery. Robot arms access the surgical target through multiple ports [3], but many studies have tried to reduce the number of ports. The da Vinci Si can perform single-port surgery using new curved instruments [4]. Recently, the da Vinci SP was developed specifically for single-port surgery [5]. Another type of wire-driven robot is the SPORT Surgical System (TITAN Medical, Canada) [6], which has triple-segment robot arms with a slit structure and can carry out smooth motion in a single port. Furthermore, flexible surgical robot arms that can be attached to endoscopes were developed to perform endoluminal surgery [7], and an interleaved continuum-rigid manipulator was studied to improve dexterous workspace and accurate actuation [8]. We are developing a wire-driven surgical robot for single-port surgery, as shown in Figure 1a. Two major features of this robot are a joint structure to secure stiffness and double segments to fit the working volume in a single port. Most wire-driven robots are symmetrically controlled with rotating pulleys. In such robots, all wires can be controlled independently for precise movement and other features, as shown in Figure 1b. The proximal joints and distal joints each have two degrees of freedom (DoFs), and the whole body is capable of rotational and translational motion. Consequentially, the end-effector can achieve a six-DoF motion. There are two well-known structures of a snake-like surgical robot arm: the slit structure and the joint structure [9]. The slit structure is a flexible pipe with slits in various patterns, as shown in Figure 2a. The SPORT System is a representative example. The slit structure can make a smoothly curved configuration, and the model is simplified to the curvature model. However, this structure does not have enough stiffness to perform some general surgical operations, including sutures. An articulated robot arm with a joint structure consists of orthogonally stacked joints, as shown in Figure 2b. One example is the da Vinci Si. A joint structure cannot be curved in a perfect curvature configuration, but it has stronger stiffness than a slit structure. The set of stacked joints that share the connected wires is called a segment. One segment with orthogonally stacked joints can bend with a two-DoF motion. In single-port surgery, dual robotic arms have to be able to maintain a triangular configuration like a crab's claw, and an articulated arm with multiple segments is essential to establish the working space, as shown in Figure 2c. The motion of the distal segments is affected by the motion of the proximal segments because the wires that control the distal segment pass through all stacked joints (see Figure 2c). The blue wire is  
Figure 1: Wire-driven surgical robot with joint structure: (**a**) suturing test of prototype; (**b**) conceptual diagram of working principle. Figure 2: Structure of snake-like surgical robotic arms: (**a**) single segment with slit structure; (**b**) single segment with joint structure; (**c**) double segment with joint structure. connected to the median linkage with a wire crimp terminal and controls only the proximal segment. The red wire controls the distal segment and passes through all joints. This phenomenon is called the coupling problem, which must be solved to control robot arms with multiple segments. The accuracy of the robot model heavily influences the robot's performance.