## 5 Experiment and Analysis
The drilling EE mounted on six-axis force sensor 2 was drilling towards the circuit board, and the \(z\)-axis of R1 was parallel to the drill axis direction. Specifically, the drilling EE was moving while the R1 was holding steady during the procedure. The force sensor 2 was measuring the forces and torques during the drilling of the circuit board. The force sensor 1 measured the supporting forces and torques of R1 at the same time. Furthermore, the force sensors measured the force and torque until the drill penetrated the circuit board. In addition, the forces and torques were measured before and after the compensation during the experiment. The errors of positions and orientations caused by the deformation before and after the compensation resulted in different performances of forces and torques applied to the circuit board and drilling EE, respectively. When the drilling EE pressed the surface of the circuit board, the absolute value of force along the drill axis direction was increasing. At the same time, the absolute value of the force along the \(z\)-axis of the EE of R2 was increasing. After the drill penetrated the circuit board, the absolute value of forces was decreasing. Figure 10 shows the force and torque curves of R1 before and after the compensation. Figure 11 shows the force and torque curves of R2 before and after the compensation. Figure 9: The drop in the pose error of the EE. (**a**) Drop in the position error; (**b**) Drop in the orientation error. The red curve in Figure 10c is the force Fz along the drill axis which is the feed direction, and the absolute value of Fz is the biggest one among Fx, Py, and Fz. The Fz with the compensation is smaller than the one without the compensation, as the drill axis direction is controlled perpendicularly, and the other two forces are smaller than those without the compensation. This is because these two forces are used to cut the material and the bigger deformation would cause bigger forces and torques in their directions. Furthermore, the torques Tx, Ty, and Tz have the similar trend of changes. However, the absolute values of torques Tx, Ty, and Tz are small because the corresponding forces are small especially with the deformation compensation. Figure 11 shows that the forces and torques applied to the EE of R2 have the similar trend of changes, because there are interaction forces between the two arms during the experiment. Nevertheless, the absolute values of forces and torques shown in Figure 10 are not the same like those in Figure 11. This is mainly because the forces and torques represented in the frame of six-axis force sensor 1 are different with those in the frame of six-axis force sensor 2 and the measurement noise. However, the force Fz measured by the six-axis force sensor 1 is closed to the force Fz measured by the six-axis force sensor 2, and this is because the drill axis is near perpendicular to both z-axes of  
Figure 10: The forces and torques during the drilling operation of R1. (**a**) Fx is the force along \(x\)-axis; (**b**) Fy is the force along \(y\)-axis; (**c**) Fz is the force along \(z\)-axis; (**d**) Tx is the force around \(x\)-axis; (**e**) Py is the force around \(y\)-axis; (**f**) Fz is the force around \(z\)-axis. the two force sensors. Figure 10c shows that the maximum absolute value of force Fz is at 6.5 s due to the resistance changing after the penetration of the circuit board. Figure 11c shows that the force Fz has a similar maximum value as well. The forces and torques were controlled more precisely after the deformation compensation of the industrial robot. As shown in these figures, the proposed stiffness modeling and deformation compensation algorithm are effective and can be used for further study.