A new method for recognizing geometric parameters of industrial robots

The geometric parameters of the robot were identified by using the proposed improved PSO algorithm in comparison with the basic PSO algorithm, linearly decreasing weights-based PSO (WPSO) algorithm, and hybridization-based PSO (BPSO) algorithm in MATLAB R2016b.
The population for the proposed PSO method was set to 200, the learning factors were c1 = c2 = 1.49, the inertial weights were wmax= 0.8 and wmin= 0.4, the coefficient of variation in the population during the iterative process of the algorithm was pm = 0.2, and the coefficient of the iterative process of the globally optimal solution was P = i, where i is the number of iterations of the particle swarm at the given time. The direction T was set to 200, and signified the total number of iterations of the swarm. The step size was set to two, the maximum number of iterations was set to 200, and we used the average of six iterations and the average fitness value of each algorithm, as shown in Table 3.
Table 3 shows that the classical PSO algorithm had an average fitness value of 5.39 over six iterations, and delivered the worst performance. The average fitness values of the BPSO and WPSO algorithms were 4.58 and 4.02, respectively, while the proposed BWPSO-RP algorithm yielded the best average fitness value of 3.12. Its average adaptive accuracy was higher than those of the PSO, WPSO, and BPSO by 42.1%, 22.4%, and 31.9%, respectively.
The curve of optimal iterations of the proposed method in Fig. 4.

iterative curve of algorithm.
The trend of iterations of the improved PSO algorithm is shown in Fig. 4. Combined with the information listed in Table 3, it is evident that it had a higher accuracy of convergence than the ordinary PSO algorithm when updating the speed and positional information of the swarm because its particles had been optimized during the iterative process.
Figure 5 shows the absolute positional errors of the robot along the x-, y-, and z-axes before and after its optimization by the proposed method.

Error in x, y, and z axes before and after robot calibration.
It is evident from Fig. 5 that before error compensation, the absolute positional errors of the industrial robot on the x-, y-, and z-axes oscillated in the interval [− 40, 40] mm, with a maximum error of 40 mm. After error compensation, these errors decreased, and oscillated in the interval [− 0.25, 0.25] mm with a maximum error of 0.25 mm.

Absolute position error before and after robot calibration.
Figure 6 shows that the absolute positional error of the robot oscillated in the interval [5,40] mm before error compensation, with a maximum value close to 40 mm and a minimum close to 5 mm. After error compensation, its absolute positional error decreased to oscillate in the interval [0.0.2] mm, with minimum and maximum errors of 0 mm and 0.2 mm, respectively. Therefore, the improved PSO algorithm improved the accuracy of positioning of the industrial robot. This, along with Table 3, shows that the proposed method also had the optimal stability.
To further validate the effectiveness of the proposed algorithm, we randomly generated 15 points in the space of movement of the industrial robot. The errors in the absolute position of the robot along the x-, y-, and z-axes on the validation set before and after its calibration are shown in Fig. 7.

Error in X, Y, and Z axes before and after robot calibration (validation set).
Figure 7 shows that error in the position of the robot on the x-, y-, and z-axes oscillated in the interval [− 30,30] mm before calibration. The error incurred in the calculation of individual points was close to 50 mm. After calibration based on the proposed BWPSO-RP, however, these errors decreased to oscillate in the interval [− 0.2,0.2] mm. The error at certain points was close to 0 mm. This further verifies the effectiveness of the BWPSO-RP algorithm.
Figure 8 shows errors in the absolute position of the robot on the validation set before and after its calibration.

Absolute position error before and after robot calibration (validation set).
From Fig. 8, it can be seen that the absolute position error of the validation set before calibration is in the interval of [-10,50] mm, and the absolute position error of most points is near 25 mm, and the absolute position error of the validation set falls back to [0.1,0.4] mm after calibration with the BWPSO-RP algorithm, and the absolute position error of most of the points is in the interval of [0.1,0.2] mm, and from the validation results of the validation set It can be seen that the BWPSO-RP algorithm can effectively improve the absolute localization accuracy of industrial robots.
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