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Delta Robot Control Using Single Neuron PID Algorithms Based on Recurrent Fuzzy Neural Network Identifiers

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Delta Robot Control Using Single Neuron PID Algorithms Based on Recurrent Fuzzy Neural Network Identifiers International Journal of Mechanical Engineering and Robotics Research Vol. 9, No. 10, October 2020 Delta Robot Control Using Single Neuron PID Algorithms Based on Recurrent Fuzzy Neural Network Identifiers Le Minh Thanh1, Luong Hoai Thuong1, Phan Thanh Loc2, Chi-Ngon Nguyen2 1 Vinh Long University of Technical Education, Vietnam 2 Can Tho University, Vietnam Email: [email protected], [email protected], [email protected], [email protected] Abstract—Parallel robot control is a topic that many implemented. For example, a robot proposed by Stewart researchers are still developing. This paper presents an with two platforms ensures fixed stability in a stationary application of single neuron PID controllers based on facility [3]. In 1985, a delta robot was developed and recurrent fuzzy neural network identifiers, to control the built in the Ecole Polytechnique Federale de Lausanne trajectory tracking for a 3-DOF Delta robot. Each robot (EPFL) called delta robots focused on industrial work [4]. arm needs a controller and an identifier. The proposed controller is the PID organized as a linear neuron, that the Based on this robot, the new architecture is implemented neuron’s weights corresponding to Kp, Kd and Ki of the according to the necessary characteristics in industry and PID can be updated online during control process. That school. For example, it is a robot with high accuracy but training algorithm needs an information on the object's slow motion is widely used in 3D printers [5]. In the sensitivity, called Jacobian information. The proposed industrial sector the need to optimize production has been identifier is a recurrent fuzzy neural network using to a major challenge for robotics companies since the 1980. estimate the Jacobian information for updating the weights Delta robots have been successfully researched and of the PID neuron. Simulation results on MATLAB/ manufactured in many countries. However, the high cost Simulink show that the response of the proposed algorithm and operational control of delta robots has always been an is better than using traditional PID controllers, with the setting time is about 0.3 ± 0.1 (s) and the steady-state error interesting topic for many innovative studies. is eliminated. So that, the neural networks and fuzzy logic are applied for improving adaptive PID controllers for Delta Index Terms—delta robot, single neural PID, recurrent robot [6]. A non-parametric identifier of each robot arm fuzzy neural network, trajectory tracking using recurrent fuzzy neural network is built and trained online during control to estimate the object's sensitivity to Symbol Unit Meaning the input signal, also known as Jacobian information. 1,, 2 3 Degrees Angle of the upper leg of robot Based on the Jacobian information, a single-neuron- R mm upper disc radius adaptive PID controller will be updated online with three R mm lower disc radius connected weighs respectively three parameters Kp, Ki L1 mm upper arm length and Kd of the controller. Thus, with this principle, the L2 mm lower arm length PID controller will be automatically adapted due to the variation of the robot that classical control solutions can Abbreviation not achieve. DOF Degrees of freedom In the process of making efforts for manufacturing PID Proportional Integral Derivative delta robots to meet the industrial needs, this paper aims DC Direct current to control and conduct analysis, comparison, and RFNN Recurrent fuzzy neural network evaluation of different algorithms. The comparison and evaluation of efficiencies between traditional PID I. INTRODUCTION controllers and fuzzy-neural based PID controllers are implemented and tested in MATLAB/Simulink which the With flexible mechanisms, advantages of speed and absolute error values are used to evaluate the force, and precision delta robots have become popular performances of the closed loop system. and widely used in industry [1]. The complex structure of this robot makes them an interesting in research focus. II. DELTA ROBOT Delta robots were proposed in 1939, when Pollard built a robot to control the position of a spray gun [2]. In this A. Parallel Robot Model context, other robots with the same structure have been The model of delta robot is presented in Fig. 1 [7]-[9]. Manuscript received January 16, 2020; revised August 15, 2020. In this model, BiDi stitching is modeled into two material Corresponding author: Chi-Ngon Nguyen points located at Bi and Di. Each of them has a weight mb © 2020 Int. J. Mech. Eng. Rob. Res 1411 doi: 10.18178/ijmerr.9.10.1411-1418 International Journal of Mechanical Engineering and Robotics Research Vol. 9, No. 10, October 2020 and is connected by rigid, weightless rods. Thus, the cos sin 0Rl cos 1 1 1 1 dynamic model of this model consists of 4 solid objects, rB sin11 cos 0 0 in which the AiBi (i = 1, 2, 3) stitches move around the 1 0 0 1 l sin axes perpendicular to the OA B plane. At A with mass 11 i i i (6) m and remaining solid objects (including three points Rlcos cos cos 1 1 1 1 1 mounted at Di) with mass (mp+3mb), can be considered as Rlsin sin cos a moving table of linear motion. Three points located at 1 1 1 1 l sin Bi having mass mp, where mp is the operation mass. 11 The coordinates of vector rD1 are calculated as follows: r r u D11 P PD xP cos11 sin0 r y sin cos 00 (7) P 11 zP 0 0 1 0 xP cos1 r y sin r P 1 zP Combining equations (6) and (7) we have: cos1 R r l 1 cos 1 cos 1 xP Figure 1. Parallel robot model 3RUS [9]. rr sin R r l sin cos y (8) DBP111 1 1 1 The set of robot actuating includes: l11 sin zP q 1 2 3 xPPP y z . Substituting (8) into (1), we get the equation linked to the first pin. Similarly, with the second and third legs, we B. Establishing the Linking Equations get the link equation of the robot as follows: 2 From Fig. 1, we have the linking equation for points B1 2 f1 = l 2 - cosα 1 R-r +l 1 cosα 1 cosθ 1 -x P and D as follows: 1 2 - sinα R-r +l sinα cosθ -y - l sinθ +z2 =0 T 1 1 1 1 P 1 1 P 2 l r r r r 0 . (1) 2 2 DBDB1 1 1 1 f2 = l 2 - cosα 2 R-r +l 1 cosα 2 cosθ 2 -x P (9) 2 where r , r are the positioning vectors of points B and - sinα R-r +l sinα cosθ -y - l sinθ +z2 =0 D1 B1 1 2 1 2 2 P 1 2 P 2 D1 in the Oxyz coordinate system, calculated according to 2 f3 = l 2 - cosα 3 R-r +l 1 cosα 3 cosθ 3 -x P the vector equation: 2 2 - sinα3 R-r +l 1 sinα 3 cosθ3-y P - l 1 sinθ 3 +z P =0 r r U . (2) BAAB1 1 1 1 C. The Kinetic Energy and Potential of the Robot In which, the coordinates vector r , U in the A1 AB11 The kinetic energy of the AiBi stages is calculated as coordinate system Ox1y1z1 have the forms: 1122 T TII (10) rR [ 00] Ai B i11 y A i B i y i A1 22 (3) U AB [ l1 cos 1 0 l 1 sin 1 ] 11 The kinetic energy of mass mb is set at B1 as follow Replace (3) with (2) and get the rB1 coordinate in 11 T m v2 m l 2 2 (11) Ox1y1z1 coordinate system mbi22 b B b1 i rB1 R l1cos 1 0 l 1 sin 1 (4) The kinetic energy of a moving table and mb masses is 112 2 2 2 The cosine matrix indicates the direction of the (12) T3 mP 33 m b v P m P m b x P y P z P Ox1y1z1 coordinate system with the Oxyz coordinate 22 system as: Combining the kinetic expressions above, we get the cos11 sin 0 model kinetic expression of the robot: A sin cos 0 (5) z 1 1 1 1 T I m l 2 2 2 2 0 0 1 1yb 1 1 2 3 2 (13) 1 2 2 2 Infer the coordinates of the rB1 vector in the Oxyz mP 3 m b x P y P z P coordinate system: 2 © 2020 Int. J. Mech. Eng. Rob. Res 1412 International Journal of Mechanical Engineering and Robotics Research Vol. 9, No. 10, October 2020 The potential energy of a robot is calculated as follows: mmp3 b y p 1 21 sin 1R r l 1sin 1 cos 1 y p (22) gl1 m 1 mb sin 1 sin 2 sin 3 2 (14) 22 sin 2R r l 1sin 2 cos 2 y p g3 mb m P z P 2s3 in 3R r l 1sin 3 cos 3 y p D. Set the Differential Equation of Motion of the Delta mp3 m bz p 3 m b m p g 21 z p l 1 sin 1 Robot (23) We use the Lagrange factor to set the differential 222zpp l 1 sin 2 3 z l 1 sin 3 equation of motion of this model with helium links with the following form: 2 2 l1 cos 1 R r l 1 cos 1 cos 1 xp r 2 (24) d T T fi sin1 R r l 1 sin 1 cos 1 y p (15) Qki k 1,2, ., m 2 dt qk q ki1 q k l11 sin z p 0 where qk is the extrapolation coordinates of the robot, fi is 2 l2 cos R r l cos cos x the linking equations, Qk is the extrapolation force, i is 2 2 1 2 2 p 2 the Lagrange factor.
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