Mathematical Problems in Engineering

Volume 2019, Article ID 8385904, 19 pages

https://doi.org/10.1155/2019/8385904

## A Method for Obtaining Optimal Path in Angle and Avoiding Collision for Robotic Belt Grinding

Correspondence should be addressed to Tie Zhang; nc.ude.tucs@toborem

Received 4 June 2019; Revised 21 August 2019; Accepted 3 September 2019; Published 11 November 2019

Academic Editor: Francisco J. Montáns

Copyright © 2019 Tie Zhang 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

The angular variation of the joints may be large, and collision between workpieces and tools may occur in robotic grinding. Therefore, this paper proposes an optimal robotic grinding path search algorithm based on the recursive method. The algorithm is optimized by changing the position of the tool coordinate system on the belt wheel; thus, the pose of the robot during grinding is adjusted. First, the position adjustment formula of the tool coordinate system is proposed, and a coordinate plane is established to describe the grinding path of the robot based on the position adjustment formula. Second, the ordinate value of this coordinate plane is dispersed to obtain the search field of the optimal robotic grinding path search algorithm. Third, an optimal robotic grinding path search algorithm is proposed based on the recursive method and single-step search process. Finally, the algorithm is implemented on the V-REP platform. Robotic grinding paths for V-shaped workpieces and S-shaped workpieces are generated using this algorithm, and a grinding experiment is performed. The experimental results show that the robotic grinding paths generated by this algorithm can smoothly complete grinding operations and feature a smaller angular variation of the joint than other methods and no collision.

#### 1. Introduction

Currently, industrial robots are widely used for curved belt grinding. Generally, the robotic grinding path is generated by offline programming. When the generated robotic grinding path is executed to grind a curved surface, the angular variation of the joint may sometimes be large, and therefore, the robot joint angle may exceed the limit. Collision may occur in robotic grinding, such as collision between workpieces and tools and collision between robots and tools. To avoid exceeding the limiting joint angle and collision in robotic grinding, the robotic grinding path generation algorithm should be optimized to make the generated robotic curved surface grinding path feature smaller angular variation of the joint and no collision.

Many scholars have made in-depth research on the path planning of robot belts grinding. For example, Tsai et al. studied the robot path planning problem of the automatic mold polishing system and concentrated the solution into a core system to generate a trajectory that meets the requirements [1]. Basañez and Rosell have proposed a graphical task-level robot programming tool that allows users to set parameters and select polishing curves according to their need [2]. Zhao et al. proposed a robot blade grinding system controlled by a PC and a robot controller [3]. Wei Wang proposed a new algorithm based on the optimization curve interval by considering the curvature constraint of grinding the workpiece surface, integrating the precision and efficiency of the robot belt grinding [4]. Kharidege et al. proposed an automatic planning and programming system that can accommodate workpiece surfaces of different shapes [5]. Liu et al. divided the surface of complex parts into several simple surfaces when planning the path, which improved the efficiency of path planning [6]. Considering the collision problem of grinding the surface of complex parts, many scholars have studied the collision-free path planning of robots and proposed many classical algorithms, such as the C-space method [7, 8] and artificial potential field method [9–12]. Scholars such as Kuffner and Lavalle proposed the RRT algorithm, which can solve the robotic collision-free path planning issue in high-dimensional C space [13]. Scholars such as Shibata and Murakami proposed a quick robotic collision-free path planning algorithm, which can transform C space to deformed C space by using the artificial attraction potential energy method. Deformed C space does not include a restricted area, thus greatly simplifying robotic collision-free path planning in C space. This algorithm approximates restricted areas and potential energy functions to reduce calculation effort and realize quick planning [14]. Scholars such as Li et al. improved the artificial potential field method based on the regression search method. The algorithm plans a collision-free track by using the new potential field function to make the algorithm avoid local optimal solutions and unreachable areas [15].

The artificial potential field method is simple and highly efficient; thus, the approach is widely applied in the track planning of manipulators. Tsuji et al. noted that track planning based on the artificial potential field method can be divided into force control methods and motion speed control methods [16]. Ge and Cui proposed a new repulsive potential field function based on the artificial potential field and further studied the goals nonreachable with obstacles nearby (GNRON) issue associated with the artificial potential field method [17]. Masoud et al. added a component tangent to the repulsion field, which can assist robots in bypassing obstacles [18, 19]. Bosscher and Hedman combined the potential field method with machine vision and applied their repulsion speed approach to a real-time collision avoidance algorithm for robotic manipulators [20]. Bayro-Corrochano et al. transformed the potential field to the position correction of a robot to drive a 5-degree-of-freedom robot to avoid obstacles [21]. Wu et al. obtained the minimal distance between a robot and obstacles using a camera and moved the robotic manipulator to avoid obstacles by altering the driving speed [22].

In recent years, intelligent methods, such as artificial neural network algorithms, genetic algorithms, and fuzzy algorithms, have been applied in robotic collision-free path planning. Scholars such as Gómez-Bravo combined the genetic algorithm with the RRT algorithm to avoid collision in the hybrid environment of CaPaMan robots and SCARA robots [23]. Scholars such as Pires proposed a robotic collision-free avoidance method based on a multitarget genetic algorithm [24]. Lee et al. used recurrent neural network and reinforcement learning combined with V-REP simulation platform to design the shortest path planning of mobile robots considering the shortest time [25].

Research on collision-free optimization and joint angle optimization in robotic belt grinding is very limited. Therefore, this paper studies joint angle optimization and collision-free optimization methods for the development of robotic belt grinding path generation algorithms. First, the position adjustment formula of the tool coordinate system is proposed, and a coordinate plane is established to describe the robotic grinding path based on the position adjustment formula. Second, the ordinate value of this coordinate plane is discretized to obtain the search field of the optimal robotic grinding path search algorithm. Finally, the optimal robotic grinding path search algorithm is proposed based on the recursive method and single-step search process. The practicability of this algorithm is verified by simulation and grinding experiments. Meanwhile, the author’s previously published article [26] failed to consider the problem of excessive joint angle increment in the collision avoidance and planning process, which is unfavorable to robot motion control. Thus, based on the modeling method of [26], this paper improves the trajectory retrieval algorithm. Not only collision avoidance but also the total change of joint angle in the process of robot motion is considered, so that the algorithm can obtain a robot trajectory with a small total joint change in the situation of ensuring that the motion trajectory does not collide. Moreover, this paper validates this conclusion by using V-shaped parts experiments.

#### 2. Generation of Robotic Belt Grinding Path

##### 2.1. Principle of Robotic Belt Grinding Path Generation

In order to generate the robot trajectory, it is necessary to generate cutter points on the grinding surface of the workpiece and establish the coordinate system {*M*_{i}} on each cutter point. The method of generating cutter points is as follows. First, the machined surface of the workpiece is extracted and converted into NURBS surface [27]. Then, the processing path of NURBS curve format is generated by using the equal section method. Then, according to the set bow height error, the curvature estimation method is used to generate cutter points. Due to the limitation of space, this paper simply introduces the method of generating cutter points, which can be referred to the article [26] published by the author before. The cutter point coordinate system is shown in Figure 1, where {*T*} represents the inherent coordinate system of the workpiece and *i* is the sequence number of the cutter point. The direction of the *Z* axis of {*M*_{i}} is normal to the curved surface pointing to the exterior. The direction of the *X*-axis of {*M*_{i}} is the tangent of the grinding cutter path at the cutter point. The direction of the *Y*-axis of {*M*_{i}} can be determined by the right-hand rule.