# Risk Management for the Reliability of Robotic Assisted Treatment of Non-resectable Liver Tumors
## 4 Discussion
Each actuator changes only one coordinate in the Cartesian space; therefore, the error in this case will be mainly due to the quality of the mechanical design of the gantry subsystem. An example of this error propagation is illustrated in Figure 13a, where a 0.7 mm error is assumed (due to high-resolution motors and 2\({}^{\circ}\) maximum backlash due to the gearheads) for the actuators of the gantry mechanism. These errors are, however, minimized by using the linear guides in the robotic system design (which are well calibrated). The results are different when the errors of the spherical mechanism are considered. Assuming a maximum \(\pm\)2\({}^{\circ}\) (angular degrees) error as the actuator backlash (which is appropriated for gearheads nowadays--see, for example, gearheads from Maxon Motors [18]) the associated error (using belts and pulleys for the motion of the carriage on thecircular guides, which inherently have no backlash) is approximately 0.34 mm (due to a radius of the rails of 200 mm). This, in turn, will translate to an angular error at the center of the sphere of about 0.076\({}^{\circ}\) (which, by using the similar triangle rule, may double at a 200 mm insertion depth). Figure 13 shows this error distribution at two insertion depths (100 mm and 200 mm), showing the accuracy of the HeRo parallel robotic system (e.g., at 200 mm depth, the error is less than 1 mm). An interesting solution for needle insertion was presented in [19], where the authors used US images to determine the target volume for the needle tip directly from the graphical user interface which, in turn, served as input for the robotic system actuators. This strategy is also being considered for the further development of the HeRo robotic system, specifically for the needle insertion, since it may be valuable for the accuracy of the procedure. Consequently, the needle insertion should be automated, as opposed to other medical robotic systems where the insertion of the needle is manual (see, for example, the 7-DOF robotic system found in [20]). Moreover, the authors intend to use robust control solutions (e.g., B&R automation [21]) to ensure high reliability, even though it has been proven in the past that cheaper controlling solutions may also be used (see, for example, the medical robot proposed in [22] which is controlled by a PI controller). It is also important to note that the HeRo is designed to use commercially available medical tools (such as needles and the I-US probe), which were also common in [23]. This approach (in contrast to implementing medical tools directly in the robotic system) has the advantage of reduced development cost and increased modularity (since the robotic system may be designed to work with multiple variants of the medical tools). Figure 12: Error dispersion depending on the targeted depth for the needle target point for different insertion depths: (**a**) 50 mm depth; (**b**) 200 mm depth. Figure 13: Estimated error distributions for the needle tip using the HeRo robotic system: (**a**) linear error; (**b**) angular error at 50 mm insertion depth; (**c**) angular error at 200 mm depth.