The state-estimate errors with 15 pose measurements are shown in Table 3. As evident from Table 3, even nearly with the noise error for the IMU measurements, the algorithm is still able to attain very accurate estimates of the calibration parameters. Table 3 shows the accuracy result of method [16] too. By comparing the results of Table 3, the calibration parameters were more accurate in our method.Table 3The 3D errors with 15 pose measurements.In our method, a unique computation of the 24 kinematic parameters needs 8pose measurements. In method [16], it needs 4pose measurements at least. We compare two methods from 10pose measurements to 15pose measurements. The results presented in Figure 8 show that with more pose measurements, the parameter error decreases gradually.

The mean absolute estimation errors from 10pose measurements to 15pose measurements in method [16] were 4.5mm, 2.3mm, 1.41mm, 1.3mm, 0.61mm, and 0.52mm with standard deviations (SDs) of 0.4mm, 0.38mm, 0.35mm, 0.28mm, 0.09mm, and 0.09mm. Compared with method [16], the mean absolute errors of our method drop about 0.51mm, 0.32mm, 0.41mm, 0.23mm, 0.13mm, and 0.22mm. The estimation errors trend slows down after two times of the minimum number of poses measurements.Figure 8Mean absolute errors in different number of measurements.Compared with method [16], the great advantage of our method is that the system does not need to make a more motion to take the photo. After the robot executed a command, the robot would stop and the system concurrently obtained the static measurement data from the IMU.

Figure 9(a) shows the execution time of two methods with 15pose measurements. In method [16], the average time of taking a photo was 3s. In our method, the station time of robot was about 1s. The execution time of peg-into-hole is about 8s. The time of parameter identification was 0.8s. Figure 9(b) shows the comparison of execution time with different pose measurements. The time in method [16] is more than two times that in our method.Figure 9The comparison in execution time.7. ConclusionsAn IMU-based online autonomous calibration for serial robot has been proposed in this paper. In this approach, the IMU is rigidly attached to the robot tool to estimate the robot pose automatically during the working time.

An efficient approach which incorporates Factored Quaternion Algorithm (FQA), Kalman Filter (KF), and Extended Kalman Filter (EKF) to estimate the orientation of the IMU is presented in this paper. After the robot poses are estimated, the kinematics identification Dacomitinib can be carried out. Finally, the robot kinematic parameters can be corrected from the identification results in real time. The whole procedure of the robot calibration is automatic and without any manual intervention. The results of the experiments show the good accuracy, convenience, and effectiveness of the presented approach.