Complexity

Volume 2019, Article ID 1891365, 12 pages

https://doi.org/10.1155/2019/1891365

## Model Predictive Control of Robotic Grinding Based on Deep Belief Network

^{1}Guangzhou University, China^{2}South China University of Technology, China

Correspondence should be addressed to Shouyan Chen; nc.anis@20058298951

Received 10 November 2018; Revised 10 February 2019; Accepted 25 February 2019; Published 27 March 2019

Academic Editor: Sing Kiong Nguang

Copyright © 2019 Shouyan Chen 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

Considering the influence of rigid-flexible dynamics on robotic grinding process, a model predictive control approach based on deep belief network (DBN) is proposed to control robotic grinding deformation. The rigid-flexible coupling dynamics of robotic grinding is first established, on the basis of which a robotic grinding prediction model is constructed to predict the change of robotic grinding status and perform feed-forward control. A rolling optimization formula derived from the energy function is also established to optimize control output in real time and perform feedback control. As the accurately model parameters are hard to obtain, a deep belief network is constructed to obtain the parameters of robotic grinding predictive model. Simulation and experimental results indicate that the proposed model predictive control approach can predict abrupt change of robotic grinding status caused by deformation and perform a feed-forward and feedback based combination control, reducing control overflow and system oscillation caused by inaccurate feedback control.

#### 1. Introduction

The deformation occurs during robotic grinding process has significant impact on robotic grinding dynamic and robotic grinding performance [1, 2]. Two ways are mainly presented in current studies to solve this problem. One way is to optimize mechanical structure of robotic machining system or increase stiffness and stability of robot machining system. The other is to adjust machining trajectory by off-line planning or real-time force control according to the robot dynamic model [3].

The real-time force control approaches presented in current studies include adaptive control, fuzzy control, and control based on neural network [4]. Mendes et al. [5] proposed an adaptive fuzzy control approach, which is based on Hybrid force/motion control system, to cope with contact issues between robot and a given surface. Fu et al. [6] proposed an adaptive fuzzy force control model, which includes a speed control loop and a position control loop to control both feed rate and position of robot, to achieve stable robotic deburring control. Yen [7] proposed an adaptive control method based on recursive fuzzy wavelet neural network to optimize motion control parameters of three-axis robot in real time.

The above feedback control approaches implement only when trajectory deviations appear, which may result in overshoot, control overspill, and system oscillations. In view of this, some scholars attempt to implement model predictive control approach to achieve feed-forward compensation control [8, 9]. Many nonlinear model predictive control approaches are then proposed. Wilson [10] discussed the performances of three model predictive control approaches applied to robot system control. The three approaches are nonlinear model predictive control (nMPC) approach, PID-based nonlinear model predictive control (PID nMPC) approach, and simplified nonlinear model predictive control (SnMPC) approach. The results of discussion indicated that the performance of nonlinear model predictive control approach is susceptible to system model errors. Some scholars try to improve nonlinear model predictive control approach by using intelligent algorithms such as neural network [11–13]. Li [14] proposed a nonlinear model control method based on neural dynamic network, where the neural dynamic network is used to obtain optimal values of the formulated constrained quadratic programming (QP) problem derived from the cost function of nonlinear model predictive control model. Zeng [15] used Gaussian radial basis function (RBF) neural networks to improve the nonlinear model predictive control approach applied in the control of nonlinear multivariable systems. Dalamagkidis [16] proposed a nonlinear model predictive control approach based on recurrent neural network to achieve the predictive control of propeller self-rotation process while unmanned aerial vehicle engine is damaged.

In this paper, a model predictive control approach based on a deep belief network (DBN) is proposed to control robotic deformation and reduce rigid-flexible effect on robotic grinding dynamics. The following parts are arranged as follows: Firstly, the dynamic model of robotic grinding is established with the consideration of rigid-flexible coupling effect. Based on this, the model predictive controller of robotic grinding is designed. Since the accurate parameters of robotic grinding dynamics model and model predictive controller are hard to acquire, a deep belief network is designed to access nonlinear predictive model of robotic grinding. Simulation and experiments are finally carried out to verify performance of the proposed approach.

#### 2. Rigid-Flexible Coupling Dynamics of Grinding Robot

Traditional grinding dynamics model can be expressed as [17]where is the cutting force; is the system mass matrix; is the system damping; is the system dynamic stiffness; is the grinding tool position; and , are its first and second derivatives. Since the stiffness of CNC is large and the deformation is small, the grinding tool position is approximate to the planned position. However, the stiffness of robot is not sufficient which may lead to large deformation and large deviation between grinding position and planned position. Therefore, the relationship of the grinding position , the planned position , and the deformation can be expressed asSimilarly, the relationship of the force acts to robot end-effector , the cutting force , and the force caused by robotic grinding deformation is

##### 2.1. Robotic Grinding Deformation

Robotic grinding deformation consists of extrusion deformation and periodic deformation. The extrusion deformation is caused by relative motion between grinding tool and workpiece, while the periodic deformation is caused by relative motion between blades and workpiece. Therefore the grinding deformation can be expressed as where is the extrusion deformation; is the periodic deformation. The generation of extrusion deformation is shown in Figure 1. The grinding tool is driven toward the workpiece at a feed rate of to perform cutting. According to traditional grinding theory, there are sliding and extrusion state before the actual grinding is conducted. Based on this, an assumption is made that the deformation generated when the grinding tool cut-in workpiece is mostly derived from extrusion deformation, written as where is the dynamic stiffness matrix of robot grinding system; is the extrusion deformation at time . The value of extrusion deformation can be regarded as the accumulation of the difference between the feed rate and the removal speed from time to time , written as Similarly, the relationship between periodic deformation force and the periodic deformation can be expressed aswhere is the circular frequency of grinding tool; is the number of blades,; is the tool rotating speed; is the corresponding phase; is the corresponding maximum cutting deformation. Therefore, the actual grinding position can be obtained by (6) and(8): Substituting (9) and (1) into (3), the dynamic model of robot grinding can be expressed asFor the convenience of discussion, is named as robot grinding force in the following text.