Complexity

Volume 2018, Article ID 4258676, 11 pages

https://doi.org/10.1155/2018/4258676

## Hybrid Optimal Kinematic Parameter Identification for an Industrial Robot Based on BPNN-PSO

^{1}Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming, China^{2}School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China

Correspondence should be addressed to Hongjun San; moc.361@nujhnas

Received 25 March 2018; Accepted 16 May 2018; Published 8 July 2018

Academic Editor: Wenbo Wang

Copyright © 2018 Guanbin Gao 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 novel hybrid algorithm that employs BP neural network (BPNN) and particle swarm optimization (PSO) algorithm is proposed for the kinematic parameter identification of industrial robots with an enhanced convergence response. The error model of the industrial robot is established based on a modified Denavit-Hartenberg method and Jacobian matrix. Then, the kinematic parameter identification of the industrial robot is transformed to a nonlinear optimization in which the unknown kinematic parameters are taken as optimal variables. A hybrid algorithm based on a BPNN and the PSO is applied to search for the optimal variables which are used to compensate for the error of the kinematic parameters and improve the positioning accuracy of the industrial robot. Simulations and experiments based on a realistic industrial robot are all provided to validate the efficacy of the proposed hybrid identification algorithm. The results show that the proposed parameter-identification method based on the BPNN and PSO has fewer iterations and faster convergence speed than the standard PSO algorithm.

#### 1. Introduction

The nominal parameters of industrial robots for the mechanical design are usually not accurate due to manufacturing and assembly errors, limited precision of components, flexible deformation of linkages and joints and so on, which will lead to the decrease of the positional accuracy of industrial robots in practical applications. Kinematic calibration is an effective way to improve the accuracy of industrial robots, and parameter identification is a key step of calibration [1]. Hence, many research works have been focusing on this area. Parameter identifications are usually realized through minimizing the residuals of the end-effectors’ poses of industrial robots. It is a nonlinear or standard linear least-squares optimization process. As a commonly used algorithm, the least-squares method [2, 3] does not need to consider any prior information of the system, but its low computationality and the noise sensitivity limit its application [4, 5]. The extended Kalman filter [6, 7] is a useful method for dealing with nonlinear problems, which is possible to realize the state estimation under some mild conditions on the measuring error. However, the actual distribution of the positioning errors is not taken into account in the above work, resulting in a situation where the state estimate is not accurate enough and the filter is divergent. The Levenberg–Marquardt algorithm [8, 9] is used to solve nonlinear least-squares problems; however, it generally can only find the local minimum, which is not necessarily for the global minimum. Daney et al. [10] proposed an algorithm based on a constrained optimization method to select a set of measurement configurations in the calibration of robots. Jiang et al. [1] proposed a hybrid kinematic calibration method based on the extended Kalman filter and particle filter algorithm that can significantly improve the positioning accuracy of the robot. Xiong et al. [11] presented a systematic and practical calibration method based on the global product-of-exponential formula considering some practical constraints for an industrial robot to improve its absolute accuracy, in which all the kinematic parameters are identified via the linear least-squared iteration.

In recent years, many intelligent bionic algorithms have been used in parameter identification. Gong et al. [12] proposed a new hybrid optimization algorithm based on the bee swarm particle swarm optimization algorithm to obtain the optimum structural parameters of a manipulator. Fan et al. [13] conducted the parameter identification of a parallel mechanism based on genetic algorithm. Wang et al. [14] proposed a universal index and an improved PSO algorithm for optimal pose selection. Shi et al. [15] proposed a quantum particle swarm optimization (QPSO) algorithm based on the path-planning method, so that the base position and the end position can simultaneously reach the desired state. Fang and Dang [16] proposed a method based on the QPSO algorithm, which is suitable for the kinematic calibration of both serial and parallel robots.

As an evolutionary algorithm, PSO starts from a random solution and searches the optimal solution through iteration. However, it needs much iteration in dealing with parameter identification of industrial robots since there are more than 20 dimensions in the optimization model. BPNN can improve the convergence ability of PSO [17, 18]. Inspired by this fact, this paper proposes a kinematic parameter-identification method based on BPNN-PSO, which can greatly improve the convergence speed of the PSO algorithm. To maintain the positioning accuracy and repeatability, industrial robots are required to be calibrated regularly, especially after collisions and overload operations. Thus, the proposed method can improve the efficiency of identification greatly in the follow-up calibration of industrial robots.

This paper is organized as follows. Section 2 presents the kinematic modelling of the industrial robots with MDH model. In Section 3, the kinematic identification of the structural parameter is formulated as a nonlinear optimization problem. Simulations and experiments are conducted to verify the identification model and search for the optimal settings of PSO and BPNN in Section 4 and Section 5, respectively. Section 6 provides the conclusion.

#### 2. Kinematic Modeling of the Industrial Robot

ER20-C10 is a kind of universal industrial robot, which is a six-degree-of-freedom (6-DOF) joint-type industrial robot, as shown Figure 1. According to the D-H modified method [19], the coordinate systems for each joint of the robot are built, as shown in Figure 2. There are a base coordinate system and six joint coordinate systems in the coordinate systems, where F6 is the end-flange coordinate system. A laser tracker shown in Figure 1 will be used to acquire the end position data of the robot in experimental verification, which is a portable, highly accurate coordinate measuring system with an ADM (absolute distance measurement) accuracy of ±10 *μ*m. An active target (AT) is installed at the end of the robot as the end effector, which can assure that the tracker will not lose the laser in the process of measurement. In addition, the tool coordinate system and the world coordinate system must also be considered. is set at the measurement coordinate system of the laser tracker. is set at the center of the active target (AT) mounted on the flange, and its direction is the same as the end-flange coordinate system F6.