Journal of Robotics

Volume 2015 (2015), Article ID 471478, 9 pages

http://dx.doi.org/10.1155/2015/471478

## Dynamic Model Identification for 6-DOF Industrial Robots

^{1}College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, No. 29, Yudao Street, Nanjing 210016, China^{2}College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, No. 29, Yudao Street, Nanjing 210016, China

Received 25 August 2015; Accepted 12 October 2015

Academic Editor: Keigo Watanabe

Copyright © 2015 Li Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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 6-degree-of-freedom (DOF) ER-16 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.

#### 1. Introduction

In recent years, industrial robots have been greatly used as orienting devices in industry, especially in the shipbuilding, automotive, and aerospace manufacturing industries [1, 2]. Advanced control techniques for robots have become more and more affordable thanks to increasing power of computing resources and their dramatic cost reduction. However, the dynamical model of robot contains uncertainties in some parameters and many control methods are sensitive to their values especially in high speed operations. Hence, dynamical parameters identification approach has importance for developing model based controllers.

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 [3]. The parameter identification has attracted considerable attention from numerous researchers. Atkeson et al. [4] proposed the least square method to realize the estimation of dynamical parameters. Grotjahn et al. [5] used the two-step approach to perform the identification of robot dynamics. Gautier and Poignet [6] obtained a dynamical model of SCARA robot from experimental data with weighted least squares method. Behzad et al. [7] applied fractional subspace method to identify a robot model in simulation field. Recently, some intelligence computation algorithms have been reported as a useful tool in robot model identification. A traditional genetic algorithm (GA) was proposed to identify the autonomous underwater robot in [8]. Liu et al. [9] introduced the improved genetic algorithm to obtain the space robot model. However, while dealing with complex and large-scale parameters identification problems, the GA algorithm would be stuck on local optimum.

Artificial bee colony algorithm (ABC) was first proposed by Karaboga in 2005 [10] and successfully applied to parameters identification of aerial robot [11]. The ABC algorithm has been proved to possess a better performance in function optimization problems, compared with differential evolution algorithm (DE), particle swarm optimization algorithm (PSO), and GA algorithm [12]. As we know, usual optimization algorithms conduct only one search operation in one iteration, but ABC algorithm can conduct both local search and global search in each iteration, and as a result the probability of finding the optimal parameters is significantly increased, which efficiently avoids local optimum to a large extent. In this paper, the ABC algorithm was introduced to conquer the parameters identification problem of the industrial robots. The identification experiment was implemented on 6-DOF ER-16 robot manipulator.

The outline of this paper is organized as follows. Firstly, the linear robot dynamical model is given in Section 2. Then, Section 3 presents the identification process of the linear model based on the ABC algorithm, where excitation design, data collection, and signal preprocess are described. Later on, the experimental platform, identified results, and model validation are presented in Section 4. Finally the main conclusions are given in Section 5.

#### 2. Dynamic Modeling

Since the -DOF industrial robot is represented by a kinematic chain of rigid bodies, the exhaustive description for its motion can be found in [13]. The dynamic model of industrial robot is derived by the Newton-Euler or Lagrangian method:where is the -vector of actuator torques as well as the joint positions , velocities , and accelerations . is the inertia matrix, denotes the -vector including Coriolis and centrifugal forces, and is the -vector of gravity.

According to the modified Newton-Euler parameters [14] or the barycentric parameters [15], (1) can be rewritten as a linear form:where denotes the observation or identification matrix, which depends only on the motion data. is the barycentric parameter vector. This property considerably simplifies the parameters identification.

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 (2). The inertias of actuator rotors are generally provided by producers, and corresponding torques should be compensated for the dynamic equations. In fact, joint friction is a complex nonlinear model, especially during motion reversal. In order to simplify the model, the friction model consisting of only Coulomb and viscous friction [16] is given bywhere is the friction torques and , , respectively, mean the Coulomb and viscous friction parameters.

The integrated dynamic model of robots can be written aswhere is actuator torques including and . is the observation matrix, and is -vector of unknown dynamic parameters. In addition, the dynamic parameters of link are governed by the form:where is the inertial tensor of link . Similarly, denotes the first-order mass moment and is the mass of link .

In general, the observation matrix in (4) is not a full rank; that is, not all dynamic parameters have an influence on the dynamic model. In order to obtain a set of minimum parameters, a case-by-case analysis method is adopted [17]. Consequently, the dynamic model based on the basic dynamic parameters can be rewritten aswhere is the observation matrix. is -vector of dynamic parameters, including the basic parameters and the friction parameters. denotes the number of the minimum dynamical parameters. denotes the number of the friction parameters.

#### 3. Parameters Identification Procedures

##### 3.1. Basic Principles of Identification Algorithm

In order to introduce the search mechanism of ABC algorithm, we should define three essential components: employed bees, unemployed bees, and food source [11]. And the unemployed bees are divided into following bees and scout bees. The population of the colony bees is , the number of employed bees is , and the number of unemployed bees is , which satisfies the relation . We also define as the dimension of solution vector, that is, the number of the unknown parameters. ABC algorithm treats each unknown parameter as a food source. The detailed procedure of executing the proposed algorithm is described as follows.

*Step 1. *Randomly initialize a set of possible solutions , and the particular solution can be governed bywhere denotes the dimension of the solution vector. and mean the lower and upper bounds, respectively.

*Step 2. *Apply a specific function to calculate the fitness of the solution according to the following equations and select the top best solutions as the number of the employed bees:where is the fitness function, is the objective function, is the data length, and is the vector of the actual torques data from the first three joints. Similarly, is the vector of the predicted data from the identified model. is a weight coefficient between 0 and 1.

*Step 3. *Each employed bee searches new solution in the neighborhood of the current position vector in the iteration as follows:where , , both and are randomly generated, and is a random parameter in the range from −1 to 1. Next, we apply the greedy selection equation (11) to choose the better solution between and into the next generation:

*Step 4. *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

*Step 5. *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.

*Step 6. *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:

*Step 7. *Output the best solution parameters achieved at the present time, and go back to Step 3 until termination criterion is met.

The detailed procedure of ABC algorithm for parameters identification can be also depicted in Figure 1.