# Using Full Pose Measurement for Serial Robot Calibration
## 8 Results
Figure 4: Comparison of two registration procedures for robot calibrated with Method 3 and data generated using large deviations from the default DH parameters: (**a**) dependence of the mean positional error \(\overline{\eta}\) of robot end-effector on positional noise \(\sigma_{p}\) in sensor 6D data; (**b**) dependence of the mean orientation error \(\overline{\rho}\) of robot end-effector on angular noise \(\sigma_{a}\) in sensor 6D data. Figure 3: Comparison of two registration procedures for robot calibrated with Method 2 and data generated using: (**a**,**b**)—small deviations from the default DH parameters \((\Delta\mathbf{\alpha}_{1},\Delta\mathbf{r}_{1},\Delta\mathbf{d}_{1})\); (**c**,**d**)—large deviations \((\Delta\mathbf{\alpha}_{2},\Delta\mathbf{r}_{2},\Delta\mathbf{d}_{2})\). Dependence of the mean positional error \(\overline{\eta}\) of robot end-effector on positional noise \(\sigma_{p}\) in sensor 6D data in (**a**,**d**); dependence of the mean orientation error \(\overline{\rho}\) of robot end-effector on angular noise \(\sigma_{a}\) in sensor 6D data in (**b**,**d**). Figure 5 shows the outcomes of three calibration procedures: Method 1 based on 3D sensor data, and Method 2 and 3 based on 6D sensor data (in Figure 5b,d noise \(\sigma=\sigma_{p}\) in mm for Method 1 and \(\sigma=\sigma_{a}\) in degrees for Method 2 and 3). Two different registration procedures are applied to the same data as in the previous section. Figure 6: Comparison of robot calibrations using two different scaling factors \(w\) in error function \(Err_{full}\) in Method 3: (**a**) dependence of the mean positional error \(\overline{v}\) of robot end-effector on positional noise \(\sigma_{p}\) in sensor 6D data—Registration 1 was used; (**b**) dependence of the mean orientation error \(\overline{p}\) of robot end-effector on angular noise \(\sigma_{a}\) in sensor 6D data—Registration 2 was used. Data generated using large deviations from the default DH parameters. procedures were used in robot calibration with Method 2 and 3: for positional error \(\overline{v}\), Registration 1 was used (blue line in Figure 5a,c, the same as in Figure 3c for Method 2 and the blue line with triangle markers in Figure 5c, the same as blue line in Figure 4a for Method 3). For angular error \(\overline{\rho}\), Registration 2 was used (red line in Figure 5b,d, the same as in Figure 3d for Method 2 and the red line with triangle markers in Figure 5d, the same as red line in Figure 4b). Error bars \(\delta v_{m}\) in Figure 5a,c and \(\delta\rho_{m}\) in Figure 5b,d are the corresponding standard deviations calculated in (25) from \(N_{rep}\) repeated simulations of noisy sensor data. On each subplot, the two graphs are slightly shifted horizontally for a visualisation effect. Robot GT parameters used in simulation of 6D data were obtained by modifying the default DH parameters with large deviations \((\Delta\mathbf{\kappa}_{2},\Delta\mathbf{r}_{2},\Delta\mathbf{d}_{2})\) shown in Table 2. Similar results for \(\overline{v}\) and \(\overline{\rho}\) were obtained when small deviations \((\Delta\mathbf{\kappa}_{1},\Delta\mathbf{r}_{1},\Delta\mathbf{d}_{1})\) were used in simulations. Figure 6 shows outcome of robot calibration for Method 3 with two different values of the scaling factor \(w\) in \(Err_{full}\) in (18). Results for Method 3 presented in Figures 4 and 5c,d were obtained for \(w=1\). For each of the selected cases where the minimization of the error function was repeated from 300 different starting points, all initial DH parameters led to the same solution. Fitted DH parameters depended on noise strengths, choice of error function and GT values of DH parameters.