# Using Full Pose Measurement for Serial Robot Calibration
## 9 Discussion
Outcome of such strategy is displayed in Figure 5a,b: note blue line for positional errors \(\overline{v}\) and red line for angular error \(\overline{\rho}\) indicating a use of different registrations in Method 2. Another advantage of using \(\mathbf{\Omega}_{2}\) to transform the TCP orientations rather than \(\mathbf{\Omega}_{1}\) is that there is a much smaller dispersion of orientation errors \(\overline{\rho}\) for different noise realizations. The error bars in Figure 5b are much smaller for Method 2 (which leverages \(\mathbf{\Omega}_{2}\)) than for Method 1. This implies that orientations from the world coordinate system can be fed into an inverse kinematic solver more consistently and accurately. It may appear counter intuitive that mean position errors \(\overline{v}(\sigma_{p})\) and mean orientation errors \(\overline{\rho}(\sigma_{a})\) calculated for the same m-th pair of noise strengths \(\big{(}\sigma_{p},\sigma_{a}\big{)}_{m}\) but different GT values of DH parameters are almost the same, as Figure 3 shows. However, it should not be a surprise since we used NLS optimizer with exact error function. Scale of deviation from the default DH parameters may become an issue when the calibration is performed using approximated, linearlized errors and the Jacobian is calculated at the default DH values. Results of robot calibration obtained with Method 3 clearly reveal the consequences of scaling problem when simultaneous minimization of both position and orientation errors in one optimization is attempted, as demonstrated in Figure 6. While the mean orientation errors \(\overline{\rho}\) are almost equal for two selected values of \(w\), the corresponding position errors \(\overline{v}\) differ substantially. This method, similarly as Method 2, uses 6D data and, therefore, two registration procedures are available. In Method 3, similarly to Method 2, smaller position errors are obtained when Registration 1 is applied to the position data and smaller orientations errors are observed when Registration 2 is applied to the orientation data, as results in Figure 4 clearly indicate. Even as both Method 2 and 3 share a possibility of using different registrations for position and rotation components of a full pose, a direct comparison between the two methods clearly points to Method 2 as a better procedure, as demonstrated by the results shown in Figure 5c,d. Thus, a use of Method 3 is discouraged. The calibration strategy outlined in this paper was tested on a kinematic model of a serial open chain robot with revolute joints only. A question can be asked if the strategy can be applied to a more complex kinematic model when a serial chain has both revolute and prismatic joints. Acquisition of full 6D poses enables calculation of two registrations defined in (19): one of them minimizes a position error and the other minimizes an orientation error. Therefore, as long as full 6D poses are acquired, the outlined calibration strategy could in principle be used for robots with a mixture of revolute and prismatic joints. However, a presence of prismatic joints complicates the error function \(Err_{pos}\) in (10) by increasing a number of search variables and it requires further study to verify whether the strategy is beneficial also for robots with revolute and prismatic joints. The simulation results presented in this paper raise an important, practical question about the characteristics of 6D pose measuring sensors which are used for robot calibration. Commercially available sensors allow quick acquisition of many repeated measurements, which enables the noise in recorded data to be substantially reduced by calculating mean poses. The mean position error of robot end-effector \(\overline{v}\) calculated by Method 2 is increasing with sensor position noise \(\sigma_{p}\), as Figure 5a shows.