Modeling, Control, and Simulation of a SCARA PRR-Type Robot Manipulator

Scientia Iranica B (2020) 27(1), 330{340

Sharif University of Technology Scientia Iranica Transactions B: Mechanical Engineering http://scientiairanica.sharif.edu

Modeling, control, and simulation of a SCARA PRR-type robot manipulator

M.E. Uk, F.B. Sajjad Ali Shah, M. Soyaslan, and O. Eldogan

Faculty of Technology, Department of Mechatronics Engineering, Sakarya University, Sakarya, Turkey.

Received 19 June 2018; received in revised form 2 September 2018; accepted 29 October 2018

KEYWORDS Abstract. In this study, a SCARA Prismatic-Revolute-Revolute-type (PRR) robot manipulator is designed and implemented. Firstly, the SCARA robot is designed in SCARA robot; accordance with the mechanical calculations. Then, forward and inverse kinematic Real-time control; equations of the robot are derived by using D-H parameters and analytical methods. The Modelling; software is developed according to the obtained Cartesian velocities from joint velocities Simulation; and joint velocities from Cartesian velocities. The trajectory planning is designed using Prismatic-Revolute- the calculated kinematic equations, and the simulation is performed in MATLAB VRML Revolute (PRR); environment. A stepping motor is used for the prismatic joint of the robot, and servo Servo motor. motors are used for revolute joints. While most of the SCARA robot studies focus on the Revolute-Revolute-Prismatic -type (RRP) servo control strategy, this work focuses on PRR-type and both stepper and servo control structures. The objects in the desired points of the workspace are picked and placed to another desired point synchronously with the simulation. Therefore, the performance of the robot is examined experimentally. © 2020 Sharif University of Technology. All rights reserved.

1. Introduction can operate without the need for large areas. For this reason, the processes such as packaging, sorting, Nowadays, the objective of production at high speeds alignment, planar welding, and assembly in the pro- with low costs and low error rates in industrial production lines are usually performed with SCARA-type duction lines has gained great importance in terms of manipulators. The rst SCARA robot was developed competitiveness. For this reason, companies often use in 1978 by Professor Hiroshi Makino at Yamanashi di erent types of robots, such as Cartesian, SCARA, University in Japan [3]. Afterwards, many types etc., in industrial applications. Cartesian systems are of SCARA robots have emerged to be used in the widely used in high-density warehouses and, generally, machine, automotive, and robot industries. have both shuttle and aisle robots that generate the In literature studies, kinematic and dynamic Cartesian structure [1,2]. SCARA (Selective Compli- modeling, simulation analysis, di erent control meth- ance Assembly Robot Arm) manipulators take up less ods, and trajectory planning have been studied both space than Cartesian systems, are easier to install, and theoretically and experimentally. Di erent decentralized and centralized (model-based) controllers have *. Corresponding author. Tel.: +90 2642956912; been tested with experimental studies of an industrial Fax: +90 2642956424 SCARA robot. E-mail addresses: [email protected] (M.E. As a result, the performance of decentralized Uk); [email protected] (F.B. Sajjad Ali Shah); [email protected] (M. Soyaslan); controllers was found to be suciently accurate for a [email protected] (O. Eldogan) large number of industrial applications [4]. Accurate results of experimental studies depend on well-made doi: 10.24200/sci.2018.51214.2065 mathematical modeling. In SCARA robots, which M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340 331 are generally used in industrial applications, it is heavy weights is a challenge. Since the base is xed very important to make both dynamic and kinematic on one point, powerful torque motors for lifting heavy calculations accurately in order to make the system loads linearly can be used easily. work properly. While Das and Dulger [5] developed a In this study, a PRR-type (Prismatic-Revolute- complete mathematical model with actuator dynamics Revolute) SCARA robot manipulator is designed. In and motion equations derived by using the Lagrangian addition, a gripper is placed on the last joint so that mechanics, Alshamasin et al. [6] investigated kinematic the objects can be picked and placed at the desired modeling and simulation of a SCARA robot by using locations. In the rst section, the usage areas of solid dynamics by means of Matlab/Simulink. Unlike SCARA robots and the studies in the literature are other studies, Urrea and Kern [7] implemented a mentioned. In Section 2, the forward kinematics of the simulation of a 5-Degree-Of-Freedom (DOF) SCARA robot is obtained by using the Denavit-Hartenberg (D- manipulator using Matlab/Simulink software. Their H) method [22]. Then, the inverse kinematic equations study has no physical application, although it bears and Jacobian matrix are obtained by using analytical similarity with the work we have done. This study methods. In Section 3, the experimental setup of enjoys some advantages over these types of works, the robot is explained. In Section 4, the control and which include only modeling and simulation. Kaleli simulation software are described. In the conclusion et al. [8] and Korayem et al. [9] designed a program section, the results and discussion are presented. for simulating and animating the robot kinematics and dynamics in LabView software. Similar to these 2. Robot kinematics works, there are various robot control, simulation, and calculation program studies in the literature [10{20]. 2.1. Forward kinematics While some of them are just based on the analysis and Robot forward kinematics deals with the relationship simulation of one type of robot arms, some give results among the positions, velocities, and accelerations of for robots in di erent types. robot joints [23]. A robot consists of links that are SCARA robots with RRP (Revolute-Revolute- attached to each other by prismatic or rotary joints. Prismatic) or PRR (Prismatic-Revolute-Revolute) Coordinate systems are placed to each joint to nd the joint con gurations are easy to provide linear move- transformation matrices that set the relation between ment in vertical directions. RRP and PRR types two neighboring joints. The transformation matrix have some advantages and disadvantages. RRP-type i1 between the two joints is shown like iT . The relation SCARA manipulators are very common in light-duty between the base frame and the tool frame is de ned by applications that require precision and speed, which is the serial joint transformation matrices. This relation dicult to achieve by human beings [21]. While the is called forward kinematics and shown in Eq. (1): prismatic joint motor is only lifting the objects in RRP type, it is lifting the whole robot structure with the 0 T = 0T 1T 2T 3T N1T: (1) objects in PRR type. Therefore, the prismatic joint N 1 2 3 4 N motor of PRR type has higher torque than that of The projected SCARA robot and the axes on RRP type. Therefore, the PRR-type SCARA robot the joints are shown in Figure 1. While d3 is the con guration is preferred in applications, where lifting length of the vertical joint, l1 and l2 are the horizontal

Figure 1. Joint axes and implemented SCARA robot. 332 M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340

2 3 2 3 Table 1. D H parameters. c1l1 + c12l2 P1 6 7 6 7 a b c d s1l1 + s12l2 P2 i i1 ai1 i di O = P = 6 7 = 6 7 : (4) 4 d3 5 4P35 1 0 0 0 d3 1 1 2 0 0 1 0 Eqs. (5){(7) can be easily understood from Eq. (4): 3 0 l1 2 0 4 0 l 0 0 2 P1 = c1l1 + c12l2; (5) a i1: Angle between zi1 and zi around xi1; b ai1 : Distance between axes zi1 and zi throughout xi1; P2 = s1l1 + s12l2; (6) c i : Angle between xi1 and xi around zi; d di : Distance between axes xi1 and xi throughout zi. P3 = d3: (7)

2.2.1. Calculation of 1 angle lengths of the other two joints. The length of d3 is Eqs. (5) and (6) are rearranged as follows: calculated considering the height of the gripper. The 2 2 transformation matrices are obtained as in Eq. (2) by (c12l2) = (P1 c1l1) ; (8) the D-H method: 2 2 (s12l2) = (P2 s1l1) : (9) 2 3 2 3 1 0 0 0 c1 s1 0 l1 Eqs. (8) and (9) are summed up together as follows: 6 7 6 7 0 60 1 0 0 7 1 6s1 c1 0 07 1T =4 5 ; 2T =4 5 ; 2 2 2 2 0 0 1 d3 0 0 1 0 l2 = P1 P2 + l1 2l1(P1c1 + P2s1): (10) 0 0 0 1 0 0 0 1 Eq. (11) is obtained when b1 is used instead of (P1c1 + 2 3 P2s1): c2 s2 0 l2 6s c 0 07 2 2 2 2 2T = 6 2 2 7 : (2) l2 = P1 P2 + l1 2l1b1: (11) 3 4 0 0 1 05 0 0 0 1 Figure 2 shows the 1 derivation illustration. Due to the existence of b1, v1 also can be derived by analytical The abbreviations c and s represent the terms \cosine" methods as in Eq. (13). The variables in Figure 2 are and \sine". The DH parameters are given in Table 1. calculated as follows: b = (P c + P s ); (12) The forward kinematic matrix is obtained through 1 1 1 2 1 Eq. (3) by the product of the transformation matrices. v1 = (P1s1 + P2c1); (13) 2 3 2 2 2 c12 s12 0 c1l1 + c12l2 r = v1 + b1; (14) 6 7 0 6s12 c12 0 s1l1 + s12l27 3T = 4 5 : (3) 2 2 2 0 0 1 d3 r = P1 + P2 ; (15) 0 0 0 1 q v = P 2 + P 2 b2; (16) 2.2. Inverse kinematics 1 1 2 1 Inverse kinematics is the process of nding the values of joint variables according to the given position and orientation data of the end e ector. In other words, for the movement of the end e ector to the desired position, we need to nd the rotation and linear motion values of joints by means of inverse kinematics. Any found mathematical expression may not be a physical solution. There may also be more than one solution for the end e ector to go to the desired position. In other words, the robot manipulator can reach the desired positions with di erent solutions. In this study, the inverse kinematics solution is obtained by the analytical method. The third column of the forward kinematic matrix is shown in Eq. (4), and it gives the x, y, and z position coordinates of the robot. Figure 2. Derivation illustration of 1. M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340 333

1 = '1 '2; (17)

'1 = A tan 2(v1; b1); (18)

'2 = A tan 2(P2;P1): (19)

The inverse kinematics of the rst rotational joint is obtained through Eq. (20) when Eqs. (18) and (19) are substituted into Eq. (17). Because of two di erent values of v1 from Eq. (16), there are also two di erent values of 1. This shows that there are two solutions.

1 = A tan 2(v1; b1) A tan 2(P2;P1): (20)

2.2.2. Calculation of angle 2 Figure 3. Derivation illustration of (1 + 2). Method 1: When Eqs. (5) and (6) are multiplied by P2 and P1, respectively, Eqs. (21) and (22) are obtained as follows: The nal form of Eq. (28) is as follows: l1b2 P [c l = P c l ]; (21) c12P1 + s12P2 = : (30) 1 12 2 1 1 1 l2 When Eqs. (24) and (30) are solved mathematically P [s l = P s l ]: (22) 2 12 2 2 1 1 together on the same graph, Figure 3 is obtained. Eq. (23) is obtained after subtracting Eq. (22) from Figure (3) can be solved as follows: Eq. (21) and, accordingly, some arrangements are 1 + 2 = A tan 2(v1; b2) A tan 2(P2;P1): (31) made. When 1 value from Eq. (20) is placed in Eq. (31), Eq. (32) is obtained. l2[c12P2 s12P1] = l1[P2c1 P1s1]: (23) 2 = A tan 2(v1; b2) A tan 2(v1; b1): (32) When v is written instead of P c P s , we get: 1 2 1 1 1 2.3. Multiple solution

l1v1 Two di erent values of v1 observed in Eq. (16) show c12P2 s12P1 = : (24) two-solution ways. These solution ways are discussed l2 in this section. Figure 4 shows the two solutions of Method 2: object orientation. Eqs. (21) and (22) are summed up together as follows: - Left side solution: (1) l2[c12P2 + s12P1] = P1P2 l1[P2c1 + P1s1]: (25) 2 = 2A tan 2(v1; b1); (33) 1 Eq. (26) is obtained when b2 is used instead of (c12P2 + (1) (1) 1 = A tan 2(P2;P1) 2 : (34) s12P1). 2

b2 = c12P2 + s12P1: (26) b1 is rearranged as follows:

2 2 2 2 P1 + P2 + l1 l2 b1 = (P1c1 + P2s1) = : (27) 2l1

After placing b1 value in Eq. (25), we get:

P 2 + P 2 l2 + l2 c P + s P = 1 2 1 2 : (28) 12 1 12 2 2 Eq. (29) is obtained with some arrangements in Eq. (28).

2 2 2 2 P1 + P2 l1 + l2 b2 = : (29) 2l1 Figure 4. Two solutions of object orientation. 334 M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340

- Right side solution: The Jacobian matrix in robotics is used for

(2) many calculation methods such as smooth trajectory 2 = 2A tan 2(v1; b1); (35) planning and execution, singularity determination, 1 derivation of dynamic equations of motion, and torque (2) = A tan 2(P ;P ) (2): (36) calculations. The linear and angular velocities at 1 2 1 2 2 the SCARA robot can be found in terms of joint 2.3.1. Examination of the solution's existence velocities. The linear velocity can be de ned in terms v1 value from Eq. (16) can be written as follows: of the position of the end e ector. After conducting q the intermediate operations, the Jacobian matrices are 2 2 v1 = r b1; (37) obtained through Eqs. (41) and (42): p 2 3 v1 = (r b1)(r + b1): (38) l1 sin 1l2 sin(1+2) l2 sin(1+2) 0 4 5 Jv()= l1 cos 1+l2 cos(1+2) l2 cos(1+2) 0 ; To ensure solution existence, the condition of (r b1 0 0 1 (41) 0) must be provided as in Eq. (38). 2 3 Reachable maximum and minimum lengths of 0 0 0 arms are shown in Figure 5. 4 5 Jw() = 0 0 0 : (42) If the analysis is carried out according to Figure 5, 1 1 0 then:

rmax = l1 + l2; (39) 3. Experimental setup

rmin = l1 l2: (40) A rigid linear mechanism is preferred for the installa- tion of the SCARA manipulator. This linear mecha- The existence of solutions is available under the above nism allows the robot arm to move up and down. The conditions. reason why this mechanism is preferred includes the ease of control provided by the stepper motor, precise feed steps, and handling load capacity. The e ective range of motion of the mechanism on the horizontal axis is 275 mm. The accuracy is 0.05 mm by the applied quality ball screw. The horizontal movement speed in the loaded condition is 100 mm/s, and the maximum horizontal lift load is 10 kg. TB 6600 motor driver and Arduino Uno control card are used for stepper motor control, which provides linear motion. In addition, the servo motor used in the gripper is also controlled by the Arduino control card. Figure 6 shows the linear mechanism used in the system and the stepper motor control connection scheme [24] used in the horizontal axis motion. Two servo motors of Dynamixel AX12A [25] were Figure 5. Maximum and minimum points achievable by used for rotary joints of the system. With many feed the arms. back functions, these servo motors have programmable

Figure 6. Linear mechanism and stepper motor connection diagram. M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340 335

Figure 7. Open CM9.04 and 485 exp. control cards, servo motor, and pin connections.

and automatic and manual control operations are performed via this interface. The trajectory planning is the planning of the movement of the robot according to the desired trajectory, velocity, acceleration, and time from the present position to the desired position of the end e ector. It is desired for the robot to be able to move smoothly and vibrationless without exceeding the limits of the actuator and without crashing any object in the workspace. In the linear trajectory method, even if all robot joints with n degrees of freedom follow a linear trajectory, the end e ector does not pass linearly between the two points. By adding parabolic parts to the beginning Figure 8. Experimental setup. and end of the trajectory, the continuity of position and velocity is ensured. In addition, a smooth velocity integrated infrastructure, a ready-made network con- by using a constant acceleration motion at a parabolic nection system, reducers, ready-made joints, and easy trajectory is also ensured. The linear trajectory plans mounting inserts. Motors have a constant torque added with parabolic parts for the rotary and linear rate of 1.5 Nm and a speed rate of 59 rpm. The joints of the robot are shown in Figure 11. The graphs gripping of the motor is accomplished with a small show the displacement, speed, and acceleration values servo motor and the gripper mechanism. The control of each joint based on time. of Dynamixel servo motors in revolute joints is done The robot is automatically simulated in the MAT- with an OpenCM9.04-C control card with an ARM LAB VRML [26] environment while simultaneously Cortex-M3 32-bit processor and OpenCM485 EXP reaching the desired point through the automatic expansion module. Figure 7 shows the control card, control panel. Thus, experimental studies can be servo motor, and pin connections, and Figure 8 shows monitored through the computer software interface. the experimental setup. Figure 12 shows the automatic control panel and 3D simulation screen. 4. Control and simulation

Due to the di erent types of motors used in the 5. Conclusion SCARA system, the control was done with Arduino and OpenCM9.04 control cards. All kinematic and An academic study was carried out with an imple- other calculations used in robot motion were performed mented experimental setup of the Prismatic-Revolute- with the MATLAB program. The control cards are Revolute-type (PRR) SCARA manipulator. A robot communicated through MATLAB software and, ac- arm was produced that picked the product from any cording to the values entered in the simulation screen, coordinate on the workspace and placed it to the the robot moves at desired speeds. The objects in desired coordinate. Numerous pages of codes were the working space were taken from their places and written in the MATLAB environment to perform the moved to the desired coordinates. Figure 9 shows the required calculations and control operations of the ow chart of the process until the SCARA manipulator system. Forward and inverse kinematic calculations at the home position picks the object from a certain were solved. In addition, the results of the robot's coordinate and places it to the desired coordinate. trajectory plans were obtained for all joints. The Figure 10 shows the robot's main control panel and MATLAB program communicated with the control kinematic calculation interface. Kinematic calculations cards OpenCM9.04 and Arduino, and the robot was 336 M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340

Figure 9. Algorithm of the control system . M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340 337

Figure 10. (a) Main control panel. (b) Kinematic calculations interface. moved synchronously by the simulation software. Step- motor powers can be increased to produce a commercial per motor in the prismatic joint and servo motors in and industrial robot arm. Such a robot like this other joints were used. Although di erent types of can be easily used in mass production lines in the motors made it dicult to control the system, very industry, where picking and placing operations are successful results were achieved. In future studies, the done. 338 M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340

Figure 11. Trajectory planning results.

Figure 12. (a) 3D simulation screen. (b) Automatic control panel. M.E. Uk et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 330{340 339

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on Cartesian robot for liquid food industry", 12th Biographies International Workshop on Research and Education in Mechatronics, Kocaeli, Turkey, pp. 283{287 (2011). Muhammed Enes Uk graduated as salutatorian in Mechatronics Engineering from Sakarya University, 17. Korayem, M.H., Maddah, S.M., Taherifar, M., et al. \Design and programming a 3D simulator and Turkey in 2017. He is currently working in GUI controlling graphical user interface of ICaSbot, a cable design and model-in-the-loop testing of vehicle air suspended robot", Scientia Iranica B, 21(3), pp. 663{ conditioning systems at Santor A.S. (Cooperation 681 (2014). of Sherpa Engineering and Figes A.S.). His research 18. Sayyaadi, H. and Eftekharian, A.A. \Modeling and interests include robotics, control, and GUI design. intelligent control of a robotic gas metal arc welding system", Scientia Iranica, 15(1), pp. 75{93 (2008). Faris Bin Sajjad Ali Shah was born in Pakistan, 1994. He received a Turkish Government Scholar- 19. Gulzar, M.M., Murtaza, A.F., Ling, Q., et al. \Kine- ship for BSc degree in Mechatronics Engineering from matic modeling and simulation of an economical scara manipulator by Pro-E and veri cation using MAT- Sakarya University, Turkey and graduated in 2017. He LAB/Simulink", IEEE International Conference on is currently a Roboticist and Automation Engineer Open Source Systems & Technologies (ICOSST), pp. in TARA Robotics Automation Company. He is an 102{107 (2015). expert on ABB Industrial Robots including Palletizing, 20. Ibrahim, B.S.K.K. and Zargoun, A.M.A. \Modelling Material Handling, and Arc Welding Applications. and control of SCARA manipulator", Procedia Com- His research interests include robotics, programming, puter Science, 42, pp. 106{113 (2014). designing, modeling, and simulation. 21. Urrea, C., Cortes, J., and Pascal, J. \Design, con- struction and control of a SCARA manipulator with 6 Mucahit Soyaslan received BSc and MSc degrees in degrees of freedom", Journal of Applied Research and Mechatronics Engineering from Kocaeli University and Technology, 14(6), pp. 396{404 (2016). Gaziosmanpasa University, Turkey in 2010 and 2012, respectively. He is currently a Research Assistant at 22. Denavit, J. and Hartenberg, R.S. \A kinematic no- tation for lower-pair mechanisms based on matrices", the Mechatronics Engineering Department of Sakarya ASME J. Appl. Mechan., 77(2), pp. 215{221 (1955). University, Turkey and is working towards PhD degree. His research interests include electrical machine design, 23. Bingul, Z. and Kucuk, S. \Ileri_ kinematik, ters robotics, and AS/RS systems. kinematik", In Robot Teknigi I, pp. 104{200, Birsen Yaynevi, Turkey (2005). Osman Eldogan received BSc, MSc, and PhD de- 24. TB6600 Stepper Motor Driver (2017). https://www. grees in Machine Engineering from Istanbul Technical dfrobot.com/product-1547.html University, Selcuk University and Marmara University, 25. Dynamixel-All in one actuator, Robotis Inc (2014). Turkey in 1984, 1988, and 1994, respectively. He is http://www. robotis.us/dynamixel/ currently a Professor and the Head of the Mechatronics 26. Virtual Reality Modeling Language (VRML) - MAT- Engineering Department of Sakarya University, Turkey. LAB & Simulink (2017). https://www.mathworks. His research interests include machine dynamics, mech- com/help/sl3d/vrml.html anism technique, and vehiazzcle technology.