# On the Control and Validation of the PARA-SILSROB Surgical Parallel Robot
## 4 Discussion  
This paper presents the control architecture and preliminary validation results performed under laboratory conditions. A master-slave architecture was implemented, where the master console consists of two commercially available devices (3D Space Mouse, version Space Mouse Pro, developed by 3 DConnexion, Munich, Germany, 2001), with each offering six-DOF. This setup is well-suited for the six-DOF parallel robot that controls the laparoscope and positions the robotic modules responsible for manipulating the laparoscopic instruments. The master console generates linear and angular velocity vectors, which are further used to control the mobile platform. The developed GUI incorporates controls that facilitate switching seamless transitions between the parallel robot control and the manipulation modules for the surgical instruments attached to the mobile platform. Notably, the same master console is also used to manipulate the tips of the surgical instruments. Based on the results presented in Figure 22, namely, the comparative time history diagram of the velocity vectors for both the input (generated by the master console) and output (resulting from the actuators' displacements), it can be concluded that the output closely tracked the input signal. It is important to note that there was a significant difference in the sampling time of the recordings (input vs. output signals), namely, -0.01891s (with a standard deviation of 0.0065) vs. 0.005 s, respectively, which is why the output signal had approximately eight times more values than the input one (23,822 vs. 2747). To compute the root-mean-square error between the two signals, the input signal, which had fewer values, was interpolated using the \"spline\" method in matrix laboratory (MATLAB). The spline method has provided good results (52) for 1D vectors compared with linear or even polynomial interpolation. Even if it can be a source of errors when comparing the input-output signals, the accuracy of the spline interpolation is expected to be good because of the large number of points. The normalized results are presented in Table 2.  
Figure 22: The time history diagram showing input velocity vectors (translations and rotations along and around the OX, OY, and OZ axes) using the 3D Space Mouse devices (the dashed blue lines) and the Mobile Platform (MP) velocities (the magenta lines). The RMSE values obtained for the PARA-SILSROB were very good, which was anticipated. These values validated the efficiency of the implemented control system, thus demonstrating its strong response to arbitrary input signals and the spline interpolation as well. Furthermore, they also validated the reliability of the robotic system itself. The potential sources of error outlined in Table 2 can be affected by factors such as system calibration, the sensors used during the calibration process, latency in the command and control system, vastly different sampling time between the input signal (the 3D Space Mouse), the output signal, the interpolation method, and the error of the Newton-Raphson numerical method used to compute the forward kinematic solution (where a fixed and relatively small number of iterations was used to decrease the computation time). To mitigate some of these errors, improvements were made to the control logic, the mechanical structure was recalibrated, and a threshold was implemented in the control logic to account for disturbances caused by erroneous readings from the two 3D Space Mouse devices. Compared with the results presented in [53; 54; 55], the errors obtained during the testing phase of the PARA-SILSROB robot (Table 2) validated both the functionality of the mechanical structure and the robustness of the command-and-control system. The accurate positioning and orientation of the laparoscopic camera and instruments depend heavily on the mechanical architecture, including the gears, transmissions, and various machined parts of the robot. Each of these components were meticulously selected and crafted to ensure optimal performance.