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1 INTRODUCTION

Parallel robots were developed as superstructure

machines with motors included in the basic structure

to drive the attached arms. The advantage of this

design is that it reduces the weight in the arms and

therefore provides very high acceleration and speed.

On the other hand, they have a low load capacity. A

simplified drawing of a parallel (delta) robot is shown

in Figure 1.

Figure 1. Three-axis parallel delta-type robot [2]

Parallel Robot Controlled by PLC and its Digital Twin

R. Michalík, J. Hrbček & A. Janota

University of Žilina, Žilina, Slovakia

ABSTRACT: Modern ways of device development use the concept of a digital twin. A digital twin is an accurate

digital copy of something that exists or is planned to be realized in the physical world. The digital twin is not

only a virtual model of the physical system, but also a dynamic data and status information carrier obtained

through a series of IoT-connected sensors that collect data from the physical world and send it to machines. The

digital twin provides an overview of what is happening to the device in real time. This is very important in

industry as this information is helpful to reduce maintenance issues and ensure production performance. This

work focuses on the design and creation of a cybernetic physical system and its digital twin, based on CAD

system modeling in conjunction with simulation and programming tools connected to real and simulated

control systems. This process accelerates the development of the application implementation with the

possibility to create a PLC control program and tune the system already in the design phase. Thus, the physical

realization can be done in parallel with the programming and creation of the HMI interface. Modular

programming will further accelerate software development [1]. The created system and its digital twin serve as

a unified teaching tool without the need for real devices to be used by many students and users. This approach

allows testing of program algorithms without the risk of damaging physical devices and is also suitable for

distance learning.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 15

Number 4

December 2021

DOI: 10.12716/1001.15.04.19

868

Pierrot et al. [3] provide an efficient description of

the Delta kinematic structure and describe

implementation focused on high speed control of a

parallel robot. Mathematical models of delta robots

developed with different methods and considering

various views are available in a number of

publications, e.g. in [4] there are simulations used first

to obtain the inverse solution and spline curves and

spline function, followed by obtaining the direct

solution; in [5, 6] dynamics modelling and verification

of a new structure of spatial parallel manipulators are

presented; Liu et al. [7] obtain the forward kinematic

solution by geometric method and analyze the

workspace of the Delta robot. A special attention is

paid to control of parallel delta robots: Aguilar-

Mejia et al. [8] use an adaptive neural network

controller to solve the problem of tracking trajectories;

Rachedi [9] attempts to incorporate the nonlinear

inverse dynamic model of the system in the H∞

control scheme; Bengoa et al. [10] present a new

model based control approach, the stable Extended

CTC (Computed Torque Control); Stapornchaisit et al.

[11] discuss bilateral control in delta robot by using

Jacobian matrix.

Delta robots can be implemented with linear or

rotary actuators. Linear actuators can be hydraulic

pistons or electric linear motors, which are similar in

principle to standard electric motors, except that the

stator is elongated. More commonly used linear

actuators are mechanical actuators that use standard

electric motors that include a transmission part that

converts rotary motion into translational motion. This

is, for example, a connection between a helix and a nut

that is fixed so that it does not rotate with the helix,

which moves in a corresponding direction along the

helix depending on the direction of rotation. The

group of delta robots with rotary drives makes up the

vast majority of industrial robots. Stepper motors or

servo motors are used as rotary drives, which makes it

possible to determine the exact position of the rotation

angle of a particular axis.

A digital twin can be used to speed up design and

creation. A digital twin is an exact digital copy of

something that exists or is planned to be built in the

physical world. By creating a digital twin, we can

improve processes, increase efficiency, and discover

any problems that may arise. We can then apply these

adjustments and improvements to the existing system

with a much lower risk and higher return on

investment.

2 PROBLEM DEFINITION

The goal of the work is the design and realization of a

parallel robot based on a simulation model, the so-

called digital copy (digital twin). By using a digital

copy, the commissioning time of the system shall be

reduced. This solution procedure is intended to create

a methodology for optimizing the development of

applications for industry. Based on the investigation

of the application possibilities, a list of tasks for

application determination is created. The control PLC,

in addition to controlling the parallel robot, will form

a network node to which embedded devices can be

connected. Currently, there is a trend in the field of

industrial buses to unify these standards and thus

eliminate their mutual incompatibility.

3 CREATING A MODEL AND A DIGITAL TWIN

OF THE ROBOT

Design and creation of cyber-physical systems and

their digital copies, based on CAD system modeling

with tools in conjunction with simulation and

programming tools, connectable with real control

systems and simulated (PLC sim), accelerate the

development of application implementation and

increase efficiency, with the possibility of creating a

control program for PLC and system tuning already in

the design phase, which achieves a more economically

advantageous and overall more economical solution.

The use of digital twin technology improves

software sustainability and rapid software

development. The created digital twin will serve as a

teaching tool for programming without the need for a

real device.

The digital twin of the delta robot is implemented

in SceneViewer 4.1. It is a free downloadable software

from B&R. The principle of our project solution is

shown in Figure 2. In order to create a fully functional

digital copy of this workstation, it was necessary to

modify the 3D model that was created. The

modification of the model consisted of its division

into four independent parts and the creation of a

movable connection using joints (Revolve joints). The

connection to the control system is realized by

transferring variables using OPC UA via Ethernet TCP

/ IP network connection.

Figure 2. The principle of our solution using a digital twin

4 CONSTRUCTION OF A REAL DEVICE

The hardware realization of the delta robot is based

on a simple structure with three stepper motors

80MPD1.300S014-01 (Figure 4 on the left side) in the

base part driving the connected arms. The basic

construction is made of 30 mm aluminum profiles.

The main part - the base for the effector - is fixed with

arms connected to the motors. The motors are

attached to the aluminum profiles using brackets

(Figure 4 on the right side), which we designed in the

Fusion 360 program and cut out with a laser from iron

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plate. The complete structure of our delta robot is

shown in Figure 5. The Delta robot is controlled by a

PLC (type PPC3100) to which a Raspberry PI 4

MODEL B with a Raspberry V2 image recognition

camera is connected (Figure 3).

Figure 3. Hardware configuration in the Automation Studio

Figure 4. Left: Stepper motor 80MPD1.300S014-01 [12],

right: console model designed in Fusion 360

Fig

ure 5. Our constructed delta robot

5 COMMUNICATION INTERFACE

REQUIREMENT

An important requirement is the use of a

deterministic, reliable and fast communication bus.

Ethernet POWERLINK (EPL) is an open real-time

Ethernet protocol that uses the CANopen object

dictionary concept and its communication

mechanisms to provide features such as

interoperability, flexibility and configurability. Our

solution therefore uses an industrial EPL network to

connect I/O system with inverters for stepper motors,

as well as conection to an embedded system

(Raspberry Pi 4, which processes the image) to a PLC.

This open network protocol has been implemented in

an embedded system. The communication cycle time

is 2000 µs. Image processing is done by Raspberry Pi

using operating system Raspbian Jessie kernel 5.10

with implemented RT -PREEMPT. RT -PREEMPT is a

patch for the Linux kernel that turns Linux into a real-

time operating system. The cyclic test program

provides a simple way to evaluate the maximum

latency of the system. The cyclic test measures how

long it takes to respond to an interrupt generated by

the CPU timer. The measured maximum latencies

dropped from 960 µs to 71 µs. The PLC programming

is done via the Ethernet TCP / IP protocol.

6 PROGRAM CREATION FOR RASPBERRY PI

Image processing is a method that performs certain

operations to obtain an enhanced image or to obtain

useful information from an image. We use an 8MP

v2.1 camera to capture images. It is also possible to

use another external USB camera. The OpenCV library

has more than 2,500 optimized algorithms that

include a comprehensive set of computer vision and

machine learning algorithms. These algorithms can be

used to detect and recognize faces, identify objects,

track moving objects, extract 3D models of objects,

and so on. In our application, we use an algorithm to

detect shapes: square, rectangle / trapezoid, triangle,

and circle. After evaluating the shape, information

about the type of shape and its coordinates is sent to

the PLC (Figure 6 and Figure 7).

Figure 6. Programs for deterministic communication and

image processing

Figure 7. A view on a robot effector

7 CREATING A CONTROL PROGRAM FOR PLC

We have created a hardware configuration according

to Figure 3. By adding an XDD file (XML device

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description) from the source code for

openPOWERLINK to the Automation Studio

programming tool, we have an embedded system

available. Communication parameters and I / O

variables were set in the Automation Studio. The

programming language for PLC programming is

structured text (ST - higher programming language

according to the IEC 61131 standard). The ACP10_MC

and TRF_DATA13 libraries, which are part of the

Automation Studio [2] and [13], were used to control

the delta robot. The implementation of motor control

algorithms uses the "PLCopen motion control"

standard, which defines the basic function blocks that

can be used repeatedly for several hardware platforms

[14]. This reduces development, diagnostics and

maintenance costs. We have implemented our own

forward and inverse kinematics; the forward

kinematics is described in chapter 8. A visualization is

also created for the control program, which allows the

user to select several modes of operation: manual

motor control, learning mode - training of movement

from sensed positions and movement based on the

recognized shape.

8 CONTROL SYSTEM

The forward kinematics determine the position and

orientation of the tool center point given the values

for the actuated joint angles of the robot. Drawing of

the delta robot spheres is shown in Figure 8.

Figure 8. Drawing of the delta robot spheres

To find the coordinates (x, y, z), we need to solve

set of three equations of spheres which can be created

with radius re. From the equation for a sphere:

( ) ( ) ( )

2 2 2

i i i e

x x y y z z r− + − + − =

(1)

here are equations of three spheres:

( ) ( )

11e

x y y z z r+ − + − =

(2)

( ) ( ) ( )

2 2 2

2 2 2 e

x x y y z z r− + − + − =

(3)

( ) ( ) ( )

2 2 2

3 3 3 e

x x y y z z r− + − + − =

(4)

modified as:

2 2 2 2 2 2

1 1 1 1

x y z y y z z r y z+ + − − = − −

(5)

2 2 2 2 2 2 2

2 2 2 2 2 2

2 2 2

x y z x x y y z z r x y z+ + − − − = − − −

(6)

2 2 2 2 2 2 2

3 3 3 3 3 3

2 2 2

x y z x x y y z z r x y z+ + − − − = − − −

(7)

When:

2 2 2

i i i i

w x y z= + +

(8)

then:

( ) ( )

( )

2 1 2 1 2

x x y y y z z z

−

+ − + − =

(9)

( ) ( )

( )

3 1 3 1 3

x x y y y z z z

−

+ − + − =

(10)

( ) ( ) ( )

( )

2 3 2 3 2 3

x x x y y y z z z

−

− + − + − =

(11)

When we subtract (4)-(5):

x a z b=+

(12)

y a z b=+

(13)

then:

( )( ) ( )( )

1 2 1 3 1 3 1 2 1

a z z y y z z y y



= − − − − −



(14)

( ) ( )

2 2 1 3 3 1 2

a z z x z z x



= − − − −



(15)

( )( ) ( )( )

1 2 1 3 1 3 1 2 1

b w w y y w w y y



= − − − − − −



(16)

( ) ( )

2 2 1 3 3 1 2

b w w x w w x



= − − −



(17)

( ) ( )

2 1 3 3 1 2

d y y x y y x= − − −

(18)

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Now we can substitute (12) and (13) in (5):

( )

2 2 2

1 2 1 2 2 1 1

2 2 2

1 2 1 1

a a z a a b y z z

b b y z r

+ + + + − − +

+ + − + − =

(19)

Finally, we need to solve this quadratic equation

and find z, and then calculate x and y from (12) and

(13).

To meet the requirement of safe process control,

the system would need to be analyzed to implement

safety functions with a PLC. The articles [15], [16] and

[17] address this issue.

9 CONCLUSION

We have successfully designed a delta robot model,

which we used in SceneViewer to create a digital twin

that is connected to a PLC control system

programmed in Automation Studio. The variables are

transmitted using OPC UA. A digital twin of the robot

helped us to facilitate and optimize the construction

of a real delta robot. We constructed the delta robot

from aluminum parts and plastic parts printed on a

3D printer. The robot controller allows you to control

it manually in three axes, learn endpoint positions,

and run a shape recognition subroutine using the

openCV library and render them to the robot

endpoint. The result of the project is a fully functional

parallel robot that can be used in teaching and in

promotional activities. Also, a digital twin of the robot

can be used for simulation, experimentation, and

training, either with a connection to the robot or

without the need for physical hardware. Employment

of robotics in specific, high-value naval applications is

an opportunity that exists but has not been fully used

yet [18].

ACKNOWLEDGEMENTS

This work has been supported by the Educational Grant

Agency of the Slovak Republic (KEGA) Number 008ŽU-

4/2019: Modernization and expansion of educational

possibilities in the field of safe controlling of industrial

processes using the safety PLC and by Grant System of

University of Zilina No. 1/2020. Project number 7991.

REFERENCES

[1] Marr, B.: 7 Amazing Examples of Digital Twin

Technology in Practice, Last accessed 29. 06. 2021,

https://www.forbes.com/sites/bernardmarr/2019/04/23/7

-amazing-examples-of-digital-twin-technology-in-

practice/.

[2] B&R Industrie Elektronik GmbH: Control Expert,

Automation Studio B&R Help Explorer. 2021.

[3] Pierrot, F., Benoit, M., Dauchez, P. and Galmiche, J. -M.:

High speed control of a parallel robot, EEE International

Workshop on Intelligent Robots and Systems, Towards a

New Frontier of Applications, 1990, pp. 949-954, vol. 2,

doi: 10.1109/IROS.1990.262518.

[4] Zhang, J., Shi, L., Gao, R. and Lian, C.: The mathematical

model and direct kinematics solution analysis of Delta

parallel robot, 2009 2nd IEEE International Conference

on Computer Science and Information Technology, 2009,

pp. 450-454, doi: 10.1109/ICCSIT.2009.5234909.

[5] Ahangar, S., Mehrabani, M. V., Shorijeh, A. P., and

Masouleh, M. T.: Design a 3-DOF Delta Parallel Robot

by One Degree Redundancy along the Conveyor Axis, A

Novel Automation Approach, 2019 5th Conference on

Knowledge Based Engineering and Innovation (KBEI),

2019, pp. 413-418, doi: 10.1109/KBEI.2019.8734975.

[6] Ardestani, M. A. and Asgari, M.: Modeling and analysis

of a novel 3-DoF spatial parallel robot, 2012 19th

International Conference on Mechatronics and Machine

Vision in Practice (M2VIP), 2012, pp. 162-167.

[7] Liu, C., Cao, G. and Qu, Y.: Workspace Analysis of Delta

Robot Based on Forward Kinematics Solution, 2019 3rd

International Conference on Robotics and Automation

Sciences (ICRAS), 2019, pp. 1-5, doi:

10.1109/ICRAS.2019.8808987.

[8] Aguilar-Mejia, O., Escorcia-Hernandez, O., Tapia-

Olvera, O., Minor-Popocatl, H. and Valderrabano-

Gonzalez, A.: Adaptive Control of 3-DOF Delta Parallel

Robot, 2019 IEEE International Autumn Meeting on

Power, Electronics and Computing (ROPEC), 2019, pp.

1-6, doi: 10.1109/ROPEC48299.2019.9057075.

[9] Rachedi, M.: Model based control of 3 DOF parallel delta

robot using inverse dynamic model, 2017 IEEE

International Conference on Mechatronics and

Automation (ICMA), 2017, pp. 203-208, doi:

10.1109/ICMA.2017.8015814.

[10] Bengoa, P., Zubizarreta, A., Cabanes, I., Mancisidor, A.

and Portillo, E.: A stable model-based control scheme for

parallel robots using additional sensors, 2015 IEEE/RSJ

International Conference on Intelligent Robots and

Systems (IROS), 2015, pp. 3170-3175, doi:

10.1109/IROS.2015.7353816.

[11] Stapornchaisit, S., Mitsantisuk, C., Chayopitak, N. and

Koike, Y.: Bilateral control in delta robot by using

Jacobian matrix, 2015 6th International Conference of

Information and Communication Technology for

Embedded Systems (IC-ICTES), 2015, pp. 1-6, doi:

10.1109/ICTEmSys.2015.7110816.

[12] B&R Industrial Automation GmbH. Basic information:

80MPD1.300S014-01. Last accessed 29. 06. 2021,

https://www.br-automation.com/en/products/motion-

control/80mp-stepper-motors/stepper-motors-with-

incremental-encoder-ip20/80mpd1300s014-01/.

[13] Hrbček, J., Šimák, V., Hruboš, M.: Riadenie motorov

použitím systému B&R. EDIS 2017. ISBN 978-80-554-

1327-3.

[14] Olejár, M., Cviklovič, V., Brachtýr, B., Jablonický, J.:

Riadenie pohonov prostredníctvom PLC. 1. vyd. Nitra:

Slovenská poľnohospodárska univerzita. 2015. pp. 193.

ISBN 978-80-552-1409-2.

[15] Rástočný, K., Pekár, L. and Ždánsky, J.: Safety of

signalling systems – opinions and reality, Proceedings of

the 13th International Conference TST 2013, Ustroń,

Poland, Springer, ISBN 978-3-642-41646-0, pp. 155-162,

October 2013.

[16] Zhang, H., Jiang, Y., Hung, W. N. N., Yang, G., Gu, M.

and Sun, J.: New strategies for reliability analysis of

Programmable Logic Controllers. Mathematical and

Computer Modelling, vol. 55, issues 7-8, pp. 1916-1931,

2012.

[17] Rástočný, K., Ždánsky, J., Balák, J., Holečko, P.:

Diagnostics of an output interface of a safety-related

system with safety PLC, Electrical Engineering, 99(4),

pp. 1169–1178, 2017, doi: 10.1007/s00202-017-0624-1.

[18] National Research Council 1997. Technology for the

United States Navy and Marine Corps, 2000-2035:

Becoming a 21st-Century Force: Volume 2: Technology.

Washington, DC: The National Academies Press, doi:

10.17226/5863.