## 5 Experiments and Results  
To perform the calibration process, the experimental study was performed on a six DOF robot manipulator (Y5100) carrying a heavy load. An API laser tracker (measurement accuracy of 0.01 mm/m, repeatability of \(\pm\)0.006 mm/m) and an accompanying laser, reflector attached to the end-effector of the robot were used for collecting the data. Figure 4 presents the experimental calibration setup. Figure 4: Experimental setup. Figure 3: Flowchart of the proposed method. The proposed approach (GA-RBF-TCM) was examined on the YS100 robot in comparison with the kinematic calibration method (KM) and SKCM [19] in the experimental study. The pool of robot configuration data contained 70 robotic configurations (\(\Omega=70\)). These measurement settings were uniformly distributed around the accessible workspace. Due to barriers such as walls and neighboring manipulators in the workplace where the robot was positioned, the accessible workspace where the data measurements were taken was a sub-workspace of the full workspace in practice. Figure 5 shows the process of searching for 20 optimal poses by examining the genetic algorithm. In the next step, the set of 20 optimal poses (set \(Q_{OCal}\)) was used in the experimental calibration in contrast to other methods. The remaining 50 poses (\(Q_{Oval}\)) were used in the validation process. The initial values of the GA were population size \(\big{(}n_{Pop}=35\big{)}\), a crossover percentage equal to 85%, 35% mutation, and a mutation rate equal to 0.1. After 100 interactions, the observability index of the best set was \(O=0.0182\). To confirm that the value of O was maximized, 1000 sets of robot configurations were randomly selected from the pool of robot configuration data. Figure 6 presents the result of the 1000 related values of the observability index related to the random set. The maximum value of these observability indexes was 0.01613. The mean value was 0.01357. From the results of the selection process, the GA method showed its ability to determine the optimal poses with a maximum observability index value. Figure 5: The process of searching for 20 optimal poses. Figure 6: Result of the observability index related to 1000 random sets. To confirm the ability of the proposed method for choosing optimal poses, an optimal set, \(Q_{OCal}\), was used to calibrate the YS100 robot using the method in [35]. The remaining 50 poses (\(Q_{OVal}\)) were used in the validation process. In addition, a set of random poses, \(Q_{randCal}\), including 20 poses from \(\Omega\), was taken to calibrate the robot using the kinematic calibration method (KM) and SKCM [19]. The non-selected 50 pose \(Q_{randVal}\) was used to verify the calibration process. This random process was repeated 100 times. For each of the 100 random processes, the mean of the positional errors of the KM and SKCM methods was compared with the mean and maximum positional errors of the proposed method, both in the calibration and validation process. Figure 7 shows the comparisons of the three methods in the calibration process. The mean of the positional error of the end-effector using the proposed method was 0.1603 mm. The maximum of the positional error of the end-effector was 0.3996 mm and the standard deviation of the positional error of the end-effector was 0.1011 mm. These results showed the effectiveness of the proposed method. It was easy to see from Figure 7 that the proposed technique outperformed the KM and SKCM methods. Using a 100 random set \(Q_{randCal}\) for the calibration, the KM had the highest of the mean of errors at 0.68 mm; the lowest of the mean of errors was 0.32 mm and the average was about 0.5 mm. The SKCM had the highest of mean of errors at 0.54 mm; the lowest of the mean of errors was 0.24 mm and the average was about 0.41 mm. From these results, it was clear that the proposed method had a better effectiveness in contrast to the KM and SKCM methods. The results were confirmed again in the validation process.