# Motion Control and External Force Estimation of a Pneumatically Driven Multi-DOF Robotic Forceps
## 5 Discussion  
The performance of the position control system demonstrated that smooth and stable motion could be realized. Furthermore, the position control resolution is 1\({}^{\circ}\) about the joint angles, which is the same level with the pneumatically driven forceps with a flexible joint [16]. This position control resolution is acceptable for a master-slave robotic-assisted system for laparoscopic surgery [20]. In  
Figure 11: Evaluating the grasping force estimation performance. (**a**) Experimental setup and (**b**) experimental result: comparison between the measured and the estimated forces. Figure 8, the chattering in the curves of the measured joint positions come from the measurement noise of the potentiometers, and it can be reduced by using the encoders as the position sensor. Regarding the performance of external force estimation, the maximum errors between the estimated and measured forces in all directions were less than 20% of the maximum output forces. The level of force estimation accuracy is same with that of a motor actuated forceps using strain gauges located at the shaft to calculate the force [12], and the pneumatically driven forceps with a flexible joint [16]. The maximum error in the force estimation appeared when the measured forces were near the peak, as shown in Figures 9-11. These estimation errors are mainly caused by the modeling uncertainties of the forceps joint dynamics. In particular, static frictions of the forceps mechanism and elongation of the driving wires can be critical factors to deteriorate the performance of the force estimation. Additionally, Figures 10 and 11 show that characteristic estimation errors appeared when the measured forces were 0 N. At this moment, the forceps joints moved freely and did not interact with the jig, and the joint moving directions were changed to the opposite side. The reason of the estimation errors was the dynamic modeling uncertainties of the forceps; the coulomb friction term (shown in Equation (4)) was slightly overestimated. According to the experimental results, the minimum detectable forces considering the estimation errors (i.e., the practical sensitivity of force estimation) are less than 0.5 N for translational forces regarding the joints \(q_{1}\) and \(q_{2}\), and about 0.2 N for grasping forces regarding the joint \(q_{3}\). Although it is difficult to completely cancel these estimation errors, the accuracy of external force estimation achieved in this work will be helpful to enhance the safety in particular surgical operations such as cutting, suturing, ligation, organ traction and exclusion. Moreover, the maximum translational force of this forceps covers the required force magnitude for the suturing operation in laparoscopic surgery, which is 1-2 N [21]. Regarding the grasping force, the maximum grasping force of this device is five times larger than the forceps introduced in [16], additional experiment with the real organs is necessary to justify whether this magnitude of grasping force is sufficient. The air in the pneumatic cylinders is compressible, and the route of tubes may bring delay between the controller commands and the device motion. A previous study of our group have testified that the delay is about 6 ms [22], which is negligibly small compared to the human hand operation in the master-slave system. Regarding the influence from the change in temperature and humidity, first, we used the differential pressure rather than the absolute pressure between the two sides of the piston to control the output forces of the cylinders. Hence, the change of temperature will not affect the controllability. Second, the result of an in-vivo experiment using another pneumatically driven forceps proposed by our group demonstrated that the intra-abdominal environments did not affect the position control performance, and the body fluids did not exert any adverse effects in force handling [23]. This paper focused on estimating the external force applied on the tip joints that execute most of the motions in the operation.