## 2 Related Work  
The trunk-type tendon robot's control differs from traditional industrial robots, like Cartesian, cylindrical, polar, and SCARA robots, and from robotic arms or parallel delta robots. The main reason trunk-type tendon control differs from traditional industrial robot control lies in the robot segment construction and motion constraints. While conventional industrial robots utilize rigid links, which move in spatial space with inextensible joints [27], the trunk-type robot does not have rigid links [1; 2] but uses a connecting disk (Figure 1). As mentioned before, a trunk-type tendon robot segment spine is usually flexible, and the connecting disk between adjacent segments neither directly causes bending the section nor is used for segment motion. Joints, in this case, serve as connecting pieces in series to get one continuum robot spine (Figure 1). The only way to control this trunk-type robot is to bend robot segments. Each of the robot segments' motion is like the arc of a circle, in which the radius is continuously changing while the section is being bent (Figure 2a,b). Knowing this and having a clear view of the robot segment structure sheds light on trunk-type robot design approaches. Some methods implement robot control by using forward kinematics solutions. One example is an operator that directly controls robot actuators via an open-loop user interface [16]. The following example is a robot actuator torque closed-loop control system [28]. Here, the idea is that a robot is used mainly for grasping the object. The robot segment bends around the object and stops when robot actuators produce the same torque as the opposing load torque. However, there are more trunk-type robot control approaches with inverse kinematics solutions. One proposal is to analyze the trunk-type robot kinematic characteristics with a computer program when the robot's trajectory end-moving platform is assigned [29]. Then, from model parameters using the spatial backbone modal method, the robot's kinematic model is established. Nevertheless, the latter method is only valid for hyper-redundant trunk-type robot control. There are also trunk-type robot control techniques where researchers delve into motion planning. One example is the motion planning method for solving the inverse kinematic problems of endoscopic operations of continuum manipulators [30]. The proposed method suggests robot control in a predefined complex environment. Another strategy has the operator control the surgical continuum robot on an arbitrary path in real time and not via a predefined path [31]. The latter paper proposes two-path generation algorithms. One of those algorithms represents an optimization  
Figure 1: Three-segment trunk-type tendon robot structure illustration. method with sequential quadratic programming. The other algorithm uses differential kinematics with a PID (Proportional Integral Derivative) control algorithm. The robot inverse kinematic model from the joint space to the wire-length space is the basis for these algorithms' operation. There is a robot inverse dynamics approach with Euler-Lagrange equations, specifically for trunk-type robots with spherical piezoelectric actuators [32]. In [32], the researchers compared the Euler-Lagrange dynamics method with the analytical potential method. The authors conclude that the latter method is more accurate and efficient than the former. One of the inverse kinematics methods implements robot control using the modified Denavit-Hartenberg procedure (modified D-H table) and Jacobian matrices using this D-H table [33]. This method relies on the idea that the trunk-type robot segment \"is bending with constant curvature\". Consequently, parameters that define each of the robot segments are an outcome of circle arc parameters (the arc length is \(L\); the curvature is \(k\)) and one angle \(\varphi\), which defines segment orientation around the \(z\)-axis (Figure 3a). To improve the D-H method, researchers propose adaptive fuzzy-based fault-tolerant control, as in [6].