A complete and systematic procedure for the dynamical parameters identification of industrial robot manipulator is presented. The system model of robot including joint friction model is linear with respect to the dynamical parameters. Identification experiments are carried out for a 6degreeoffreedom (DOF) ER16 robot. Relevant data is sampled while the robot is tracking optimal trajectories that excite the system. The artificial bee colony algorithm is introduced to estimate the unknown parameters. And we validate the dynamical model according to torque prediction accuracy. All the results are presented to demonstrate the efficiency of our proposed identification algorithm and the accuracy of the identified robot model.
In recent years, industrial robots have been greatly used as orienting devices in industry, especially in the shipbuilding, automotive, and aerospace manufacturing industries [
In terms of academic research, a standard robot identification procedure consists of dynamic modeling, excitation trajectory design, data collection, signal preprocess, parameter identification, and model validation [
Artificial bee colony algorithm (ABC) was first proposed by Karaboga in 2005 [
The outline of this paper is organized as follows. Firstly, the linear robot dynamical model is given in Section
Since the
According to the modified NewtonEuler parameters [
Dynamic model of robots also contains the torques caused by joint frictions and inertias of actuator rotors apart from the effects of dynamic parameters in (
The integrated dynamic model of robots can be written as
In general, the observation matrix
In order to introduce the search mechanism of ABC algorithm, we should define three essential components: employed bees, unemployed bees, and food source [
Randomly initialize a set of possible solutions
Apply a specific function to calculate the fitness of the solution
Each employed bee searches new solution in the neighborhood of the current position vector in the
Each following bee selects an employed bee to trace according to the parameter of probability value. The formula of the probability method is described as
The following bee searches in the neighborhood of the selected employed bee’s position to find new solutions. Update the current solution according to their fitness.
If the search time trial is larger than the predetermined threshold limit and the optimal value cannot be improved, then the location vector can be reinitialized randomly by scout bees according to the following equation:
Output the best solution parameters achieved at the present time, and go back to Step
The detailed procedure of ABC algorithm for parameters identification can be also depicted in Figure
Sketch of the identification algorithm.
When designing an identification experiment for the robot, it is necessary to design proper excitation trajectories to ensure the accuracy of estimation in presence of disturbances [
The noise immunity and convergence rate of an identification experiment depend directly upon the constraints of the excitation trajectories. It is important to emphasize that the configurations for which measurements are taken must correspond to a wellconditioned reduced observation matrix since the constraints represent some limits for input/output. In the literature, the constraints of the excitation trajectories can be described as
The measured torques are obtained through collecting the data of motor current, which is described as follows:
Since there are measurement noises in experiments, it is necessary to preprocess the collection data before identification. In order to remove outliers and attenuate the effect of interference signal, a fivespot triple smoothing method is adopted to smooth the raw data according to the following equations:
In addition, the velocities and accelerations of joints cannot be measured directly. However, these pieces of information are usually obtained by joint positions, and numerical differentiation for joint positions can amplify the measurement noise and decrease accuracy of the velocities and accelerations. An analytical approach is adopted to overcome the aforementioned difficulty, which was proposed in [
An experiment is conducted to test the proposed identification algorithm. The ER16, shown in Figure
DH parameters of ER16 robot.
Link 





1 

0  0 

2 

0.16  0 

3  0  0.68  0 

4 

0.13  −0.75 

5 

0  0 

6 

0  0 

ER16 6DOF robot.
The link frame of ER16 robot.
Optimized robot excitation trajectories.
3D visualization of the optimized trajectory.
Identification procedures are carried out with ABC algorithm in Matlab 2013b programming environment on an Intel Core i73770 PC running Windows 7. No commercial tools are used. According to [
Evolutionary curves of identification algorithm.
The robot dynamic model for the first joints contains 21 parameters, 15 base parameters, and 6 friction parameters. The parameters identified by our proposed algorithm are listed in Table
Identification dynamic parameters.
Parameter  Value 


50.4438 

37.7503 

16.1693 

−23.0075 

3.2047 

1.5512 

5.9390 

46.8898 

30.9319 

−0.7515 

63.2997 

−0.4069 

2.3608 

1.4471 

−0.0448 

0.1144 

11.0195 

5.3853 

10.9173 

27.3475 

2.3092 
Comparison of the measured torques and predicted torques.
Joint 1
Joint 2
Joint 3
To verify the precision of the identified model by ABC algorithm, the correlation coefficient between the measured torques
Since our aim for current stage is to investigate the validity of the model calculated by our proposed method, we focus on the validation test. Obviously, the appropriate validation test is to use the identified model in application and evaluate its success. As shown in Figure
Robot model validation trajectory.
Comparison of the measured torques and predicted torques.
Joint 1
Joint 2
Joint 3
In this paper a systematic procedure for the dynamical parameters identification of a 6DOF industrial robot has been presented. We design optimal periodic excitation trajectories to integrate the identification experiment, data collection, and signal preprocess. All the unknown parameters are well identified by ABC algorithm. When comparing the measured torques and the predicting torques, we conclude that our proposed method can accurately estimate the robot dynamical parameters. Further, a model validation has been carried out to verify the validity of the identified model. The results of this paper are useful for researchers and manufactures of industrial robots.
The optimal trajectory parameters for the fiveterm Fourier series are listed as follows:
After many trials, the probable suboptimal or optimal search scope of the unknown parameters is listed in Table
Search scope of dynamical parameters.
Parameter  Scope 











































The authors declare that there is no conflict of interests regarding the publication of this paper
This work was partially supported by the National Natural Sciences Foundation of China (51375230) and the project of Science and Technology Support Plan of Jiangsu Province (BE20130031, BE20130102).