## 1 Introduction
However, further validation of the catheter driver is required. Similarly, in [19], the authors integrated the master-slave components into a singular unit. The slave platform replicates an operator's action on the master handle via a linear actuator, while a clutch mechanism allows the device to reposition the master unit for continuous catheter motion. Nevertheless, single-unit systems impede remote operation, which requires a distinct master and slave unit. Furthermore, [PERSON] et al. [20] developed a master-slave robotic platform with two degrees of freedom (2-DOF) for catheter and guidewire continuous motion during RPCI. However, the system utilized a user-defined scaling factor to achieve master-slave position accuracy during procedures. Likewise, the researchers in ref. [21] evaluated the design of a 2-DOF RCS system for teleoperated catheter navigation. The tool manipulator relies on a linear drive mechanism and a slip ring framework to translate and rotate the catheter within a vascular phantom by reproducing the operator's axial and radial motion at the master unit. Nonetheless, the system required a constant scaling factor for master-slave position mapping. Motion scaling is a complementary motion control strategy used in telerobotics. However, it holds better potential in teleoperated systems with high network latency, such as the Da Vinci robot [22]. The endovascular RCS developed by [PERSON] et al. [23] endeavors to replicate the interventionalist's natural dexterity, requiring a minimal learning curve. The master unit has a quick-release mechanism with friction wheels to advance or retract the catheter or guidewire. The RCS utilized an adaptive input shaper and the proportional-integral-derivative (PID) controller for position control at the master-slave ends. Overall, these existing studies utilized motion scaling or conventional controllers to track the accuracy of master-slave positions during robot-assisted procedures. Nevertheless, tuning conventional controllers could be simplistic and imprecise resulting in a loss of performance. However, to enhance operational safety during robotic interventions, some other studies have developed different approaches, such as position control [24; 25; 26], motion scaling or compensation [20; 21; 27; 28], and force feedback [29; 30]. Nonetheless, there is limited proof of their stability and robustness for position control tasks that involve flexible endovascular tools. Furthermore, manufacturing constraints and miniature size requirements complicate the integration of force sensors at the tool's tip. The choice of the slave robot's drive mechanism and motion control strategy is an essential criterion for safe tool navigation during R-PCI. As shown in Figure 1, the conventional drive mechanisms include (1) ball screws, a belt drive, and roller screws and (2) clamping and translation mechanisms, while magnetic actuation helps to manipulate a robotic catheter's tip. For instance, gripping or ball screw actuation provides the necessary thrust for the catheter's translational motion. However, these actuation designs subject the endovascular tools and RCS to backlash and hysteresis, motion nonlinearities, and uncertain disturbances. These are due to frictions, inertial forces, or temporal interruptions when restoring the master's device to its starting position during translation operations. While backlash in endovascular tool motion has been addressed [27; 31; 32], nonlinearity in RCSs is yet to receive any attention. The latter causes control complexities, such as motion lags in slave robots during catheterization [27]. Hence, existing systems operate at lower displacement step values. Modeling the slave robot's motion dynamics to characterize uncertain disturbances, e.g., hysteresis in the under-actuated RCS, is challenging and imprecise [34]. In addition, this could be a vital underlying factor hindering robot autonomy in R-PCIs.