## 1 Introduction  
As robotics technology advances, there are more and more efforts to create and control continuum robots that excel in kinematic redundancy. These robots are agile and flexible because of their backbone-less structure, which the biological world has inspired [1, 2]. Such robots are called elephant's trunk or snake-arm robots. This study focuses on three inextensible segments of trunk-type robot's position and orientation control. Most trunk-type robots are currently used for robotically assisted surgery [3, 4], specifically in minimally invasive surgery [5, 6]. In the mentioned surgery area, trunk-type robot pose control is crucial, while the continuum robot has to move along a narrow path. This paper presents a control method for trunk-type robots that are more dedicated to tasks requiring robot end-effector spatial control while holding the end-effector position as close as possible to the target. For instance, the authors state that such a concept has the potential to apply continuum robots that are used in urban search and rescue tasks [7], bomb disposal [8], and inspection and repair of aero-engines [9, 10]. Continuum robot flexibility and mobility features encourage scientists to look for new kinds of robot-type structure designs and control to adapt robots to other applications. A continuum robot consists of flexible segments, which, in principle, have a bending motion [1, 2]. This bending motion gives two degrees of freedom (DOF) for one section [11]. However, depending on the robot segment type, some segments can also have a linear motion, adding one more DOF. According to this continuum, the robot segment can either have two or three DOF, depending on its type [11, 12]. Adding more degrees of freedom to the robot requires additional sections stacked on top of each other. The soft and continuous backbone structure is the main reason why such a multisegment robot is called the continuum. Additionally, continuum robot DOF perfectly describes robot flexibility. For example, it shows that three-segment continuum robots can have between six and nine DOF, which is more than enough for various tasks. Continuum robots, according to their structure, are divided into three main groups: concentric tube continuum robots [13], pneumatically or hydraulically actuated continuum robots [14], and tendon-driven continuum robots [15]. The concentric tube continuum robot consists of elastic tubes with different diameters. According to their diameter, each elastic tube shows into the other (starting from the minor tube diameter to the most prominent tube diameter). Pulling these tubes' ends controls the motion of such a robot. Concentric tube continuum robots primarily operate in surgery because of their small-diameter segments. Pneumatically or hydraulically actuated continuum robots are made of plastic pipes, which usually resemble corrugated pipes in terms of their shape. Compressed air--pneumatic energy, rather than compressed fluid--is the source for these robot types. Pneumatically or hydraulically actuated continuum robots are often used in urban search and rescue tasks. Tendon-driven continuum robot segments consist of spacer disks laid out on the segment elastic backbone (elastic tube). \"Tendons\" are made of metallic wires and control segments. Tendon-driven continuum robots are utilized primarily in surgery because of the beneficial features of wire usage. However, this specific structure can be adapted not only for the maintenance and repair of aero-engines but also to aid people living with disabilities in completing daily living activities, like an assistive robot [16]. The tendon continuum robot group differs from other continuum robot groups. Its more robust and rigid segment construction gives the continuum robot other technical opportunities to execute particular tasks, such as painting [17]. There are two main segment design variants for the tendon-driven continuum robot: extensible [18; 19] and inextensible [20; 21]. This study presents the latter.