# Investigation on the Tip Positioning Accuracy of Cable-Driven Serpentine Manipulators
## 1 Introduction  
Cable-driven serpentine manipulators (CDSMs) use cables to drive joints' motion to produce the bending and stretching motions. CDSMs have many advantages: They can actively adapt to the changes of the external environment because of the hyper-redundant degree of freedom (DOF); they have high maintainability because of using a reconfigurable module; they can access places that are untouchable to humans; for example, their entire structure can be sealed so that they can operate in harsh environments [1; 2; 3]. However, CDSMs also have their own shortcomings: They are more difficult to control due to the hyper-redundant; cables as driving devices reduce their stiffness; their accuracy is relatively lower than the rigid joint-link manipulators. CDSMs are different from traditional manipulators. The traditional serial manipulator puts the driving device at the motion joint. However, the driving device of the CDSM is installed on the base, which reduces the mass and inertia of manipulator. Consequently, the CDSM can improve the responsiveness and load capacity of manipulator. The CDSM has the advantages on variable configuration, higher load-bearing ratio, and larger task space. However, due to the flexibility of the cable, especially when the manipulator is too long, the tip positioning accuracy of the manipulator's end will be affected severely. At present, research on CDSMs has mainly focused on mechanism design, kinematic modeling, dynamic modeling, control system, and trajectory planning [4; 5; 6]. [PERSON] et al. [7] described the current status of serpentine robot design and path planning underway in their research group and pointed towards future directions of research. [PERSON] et al. [8] presented a method to simplify the motion planningprocess and demonstrated the effectiveness of the presented method by simulations and experiments on a 25 DOFs cable-driven snake robot prototype. [PERSON] et al. [9] presented the modeling and control of a planar snake robot composed of modular, single DOF bending units, and optimized key control and design parameters to produce curvature profiles that maximize the robot's forward speed. [PERSON] et al. [10] studied the mapping relationship among the driven space, joint space, and task space of a cable-driven continuum robot and analyzed the decoupling algorithm based on piecewise constant curvature assumption. [PERSON] et al. analyze the workspace of cable-driven continuum robots [11], and proposed a comprehensive static model for cable-driven continuum robots [12]. [PERSON] et al. [13] studied a novel dynamic modeling methodology that captures curvature variations along a segment using a finite set of kinematic variables and this dynamic model is implemented using the principle of virtual power for a continuum robot. [PERSON] et al. [14] designed and built a wire-driven serpentine robot arm which is made of a number of rigid nodes connected by two sets of wires. [PERSON] et al. [15] proposed a real-time position compensation control method based on flexible cable deformation. [PERSON] et al. [16] studied a cable-driven parallel robot for 3D printing to obtain a larger workspace rather than traditional 3D printing devices. [PERSON] et al. [17] conceptualized and designed a waist rehabilitation robot driven by cables and pneumatic artificial muscles (PAMs). [PERSON] et al. [18] proposed using cable angle position sensors in addition to cable length measurements in order to improve the accuracy of a cable-driven parallel mechanism (CDPM). [PERSON] et al. [19] studied the sliding mode control of the cable-driven redundancy parallel robot with six degrees of freedom based on the cable-length sensor feedback. [PERSON] et al. [20] developed a calibration method for a particular parallel cable-driven robot using a camera for 3D pose sensing. [PERSON] et al. [21] introduced a pose-sensing system for soft robot arms integrating a set of macrobend stretch sensors. [PERSON] et al.