Control and Development of a 3D Printed SCARA

robot as an Underactuated System

Yeong Chin Koo, ∗ Muhammad Muammar Sapian Sauri,Teck Seng Kong, Kok Hang Poh, Ahmad Saiful Azhar,

Muhammad Nasiruddin Mahyuddin ∗∗

∗ School of Electrical and Electronic Engineering, Universiti Sains Malaysia,Pulau Pinang, Malaysia. e-mail: kooyeongchin@yahoo.com)

∗∗ School of Electrical and Electronic Engineering, Universiti Sains Malaysia,Pulau Pinang, Malaysia. e-mail:nasiruddin@usm.my )

Abstract: Selective compliance assembly robot arm (SCARA)is a particular kind of industrial robotwhich is widely adopted in industrial environments and also widely used by researchers as a benchmark toevaluate controllers. The SCARA robot in this project is 3D printed and it is underactuated, i.e. there is only1 actuator driving a two-degrees of freedom 2 planar robot arm mechanism. Non-collocated linearisationis discussed and control technique to address the underactuation condition is further elucidated in thepursuit to design a suitable controller. PD controller and PD controller with robustification signal aresimulated on an underactuated 2 DOF planar robot arm model. The relationships of these degree offreedom with the orientation of end effector were determined through kinematic analysis by applyingDenavit-Hartenberg convention. The effects of torques on the motion of underactuated SCARA robotwere determined through dynamic analysis. Most of the mechanical structure of the prototype wasfabricated by using 3D printer. Hardware construction to simulate the effects of possible faulty 2nd jointangle of SCARA robot arm is also discussed for future work on control scheme evaluation on a genericunderactuated system.

1. INTRODUCTION

Selective compliance assembly robot arm (SCARA)is a particu-lar kind of industrial robot which is widely adopted in industrialenvironments. In wafer handling industry, for example, the pre-cision and motion smoothness requirements of wafer handlersare demanding for stricter margin (He et al., 2019). Waferhandling SCARA robot can transfer and align wafers duringdifferent working procedures. SCARA is also widely used byresearchers as a benchmark to evaluate controllers (Visioli andLegnani, 2002). The work in (Chi et al., 2018) uses 2 degrees-of-freedom (DOF) SCARA robot to evaluate a hybrid trackingcontroller. The third axis, devoted to the vertical motion of theend-effector, is dynamically decoupled from the others, so that,in general,only the first two links are considered (i.e., the robotis assumed to be planar).

In the harsh demanding environment where the SCARA robot iscommissioned to operate over long hours, a down-time sessionto inspect the faults in the actuator is often discouraged. Thiswould incur cost to the production line as eventually it willlead to lost in revenues and valuable resources (Atmojo et al.,2018). Besides, to gain better customer profits in the industryof electronic manufacturing, minimizing the downtime is anessential requirement (Takiguchi et al., 2019). To create a fail-and-safe system, i.e. if one of the actuator of the SCARA isfaulty, can the remaining actuator be able to compensate for themissing actuation? This would subject the two-link planar robotarm to be under-actuated in some sense.

An underactuated system is a system where its input variablesis less than the number of independent variables that define thesystem configuration (Moreno-Valenzuela and Aguilar-Avelar,

2018; Spong, 1994). Thus, the design of control system foran underactuated system is more complicated as some of thesystem’s configuration variables cannot be controlled directly.Underactuated systems can be found in many fields suchas robotics, flexible systems, mobile system, and locomotivesystems (Moreno-Valenzuela and Aguilar-Avelar, 2018). It iswell known in the field of underactuated robots (UAR) thatUARs possess second-order nonholonomic constraints (Orioloand Nakamura, 1991; Mareczek et al., 1999). Available controlalgorithms for UAR are based on strong inertial couplingbetween links (Spong, 1994), employing brake assumption (Araiand Tachi, 1991). Therefore, this paper is to discuss the controlof an underactuated system of 2 DOF SCARA robot.

In this paper, control of an underactuated system of 2 DOFSCARA robot is studied and analysed. A fully functionalprototype of SCARA robot is also designed and developed. Thesecond actuator can be ‘deliberately’ severed so as to create themalfunction condition thereby creating the underactuated condi-tion. Collocated and non-collocated linearisation are discussedin the pursuit to design a suitable controller for an underactuatedSCARA robot arm. The outline of the paper is as follow. Thenext section presents the design of the SCARA robot from theaspects of kinematic modelling, dynamic analysis and controldesign using the non-collocated linearisation. After that, themechatronics system design and hardware system integrationare also presented.

2. SYSTEM DEFINITION OF THE SCARA ROBOT

In this section, the design of the SCARA robot is presented.The designed SCARA robot has 3 Degree of Freedom (DOF),contributed by 2 revolute joints and 1 lead screw joint. Through

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Fig. 1. SCARA ROBOT

Table 1. D-H Parameters

Joints, i θi (rad) di (m) αi (rad) ai (m)

1 θi d1 0 l12 θ2 d2 0 l2

kinematic analysis, the relationships between the DOF and theorientation of end effector were determined. Then, dynamicanalysis is carried out to determine the effects of torques on themotion of SCARA robot.

2.1 Kinematic Analysis based on the Denavit-Hartenberg

The kinematic analysis of the robot is developed based onthe Denavit-Hartenberg (D-H) Convention presented in (Niku,2001). The D-H Convention involves three elements: schematicdiagram, D-H parameters, and transformation matrix. Theschematic diagram of the robot is illustrated in Figure 1.From the schematic diagram, the D-H parameters are obtainedand tabulated in Table 1. With the D-H parameters, thetransformation matrix (Equation 1) can be constructed.

0T1 =!""#

1 0 0 00 1 0 00 0 1 d1

0 0 0 1

$%%&

1T2 =!""#

Cθ1 −Sθ1 0 ℓ1Cθ1Sθ1 Cθ1 0 ℓ1Sθ10 0 1 d2

0 0 0 1

$%%&

2TE =

!""#

Cθ2 Sθ2 0 ℓ2Cθ2Sθ2 −Cθ2 0 ℓ2Sθ20 0 −1 00 0 0 1

$%%&

0TE =0 T1

1T22TE

=

!""#

Cθ12 Sθ12 0 ℓ2Cθ12 + ℓ1Cθ1Sθ12 −Cθ12 0 ℓ2Sθ12 + ℓ1Sθ1

0 0 −1 d1 + d2

0 0 0 1

$%%&

(1)

where C = cos, S = sin, θ12 = θ1 + θ2

2.2 Dynamic Analysis of the SCARA Robot

For a fully actuated system, many control techniques wereintroduced in the literature for the design of optimal, robust,adaptive, and learning controllers (Spong et al., 1992). All thecontrol techniques are possible because fully actuated systems

have a few of strong properties that assist the control design,such as feedback linearizability, passivity, matching conditions,and linear parameterizability. However, one or more of theabove-mentioned properties are normally lost for underactuatedsystem. Therefore, control design for underactuated system ismore complicated and difficult with lesser results available inthe literature.

Consider the Lagrangian formulation of the dynamics of ann-degree-of-freedom system (Spong, 1998):

D(q) #q + C(q, $q) $q + g(q) = B(q)τ (2)

where q ∈ Rn is the vector of generalized coordinates, τ ∈ Rm

is the input generalized force (m < n), and B(q) ∈ Rn×m has fullrank for all q.

For a suitable partition of the vector q of generalized coordinatesas qT = (qT1 ,q

T2 ), where q1 ∈ Rn−m and q2 ∈ Rm, the system 2

can be written as

d11 #q1 + d12 #q2 + h1(q1, $q1,q2, $q2) + φ1(q1,q2) = 0 (3)

d12 #q1 + d22 #q2 + h2(q1, $q1,q2, $q2) + φ2(q1,q2) = b(q1,q2)τ (4)

where h1 include Coriolis and centrifugal terms, and φ1 containsthe terms derived from the potential energy, such as gravitationaland elastic generalized force. The m × m matrix b(q1,q2) isassumed to be invertible.

The SCARA system in ( 2) can also be written as:

d11 #q1 + d12 #q2 + h1 + φ1 = τ1 (5)

d12 #q1 + d22 #q2 + h2 + φ2 = τ2 (6)

where

d11 = m1ℓ2c1 + m2(ℓ

21 + ℓ

2c2 + 2ℓ1ℓc2 cos(q2)) + I1 + I2

d22 = m2ℓ2c2 + I2

d12 = m2(ℓ2c2 + ℓ1ℓc2 cos(q2)) + I2

h1 = −m2ℓ1ℓc2 sin(q2) $q2

2 − 2m2ℓ1ℓc2 sin(q2) $q2 $q1

h2 = m2ℓ1ℓc2 sin(q2) $q21

φ1 = (m1ℓc1 + m2ℓ1)g cos(q1) + m2ℓc2g cos(q1 + q2)

φ2 = m2ℓc2g cos(q1 + q2)

Remark: In this work, the actuator for the second link is assumedto be malfunctioned or faulty. Therefore, the control input forthe second actuator τ2 = 0 creating an under-actuated system.In addition, since the SCARA robot developed is a planar robotarm, gravitational force does not have any effect on the dynamicsystem (g = 0), thus φ1 = φ2 = 0.

3. POSITION CONTROL OF UNACTUATED JOINT

Collocated partial feedback linearisation property is an in-teresting property holds for the entire class of underactuatedmechanical system (Spong, 1998). This is a virtue as a result ofpositive definiteness of the inertia matrix. The non-collocatedpartial feedback linearisation, in the other hand, is a propertyfor a restricted class of underactuated system.

Non-collocated linearisation is used to overcome the nonlinear-ities in the dynamics of the 2nd joint. Investigation carried outin this paper assumes no perturbation. Solving the 2nd row of(5) for #q1 and substituting the result into the first row yields,

d∗12 #q2 + h∗1 = τ1 (7)

d12 #q1 + d22 #q2 + h2 = 0 (8)

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0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4q2

0 20 40 60 80 100 120 140 160 180 200-1

0

1

2

310-3

Fig. 2. 2nd joint angle output (rad) of an underactuated (or mal-functioned actuator) SCARA robot with its correspondingcontrol effort. The set point is 0.3 rad with kp = 0.02 andkd = 0.072 without perturbation.

where

d∗12 := d12 −

d11

d12d22 (9)

h∗1 := h1 −d11

d12h2 (10)

Applying the computed torque technique for the 1st joint, themotor torque results as

τ1 = ν2d̄∗12 + h̄∗1 (11)

with ν2 denoting the new control input and d∗12 and h∗1 are

estimated terms. Inserting (11) in (7) and inserting the secondrow of (11) yields,

#q1 = −1

d12

'(ν2d∗

12 + ∆)d22

d∗12

+ h2

((12)

#q2 =1

d∗12

)ν2d∗

12 + ∆*

(13)

where ∆ denote estimation error. The idealised completelydecoupled and linearised system can be represented as,

#q1 = −d22

d12ν2 −

h2

d12

#q2 = ν2

which is a double integrator system with 1st joint dynamics asa non-holonomic constraint. This can be stabilized by a PD-controller,

ν2 = kpe2 + kd $e2 (14)

with e = [e2 $e2] ∈ R2 with e2 defined as qd

2− q2 and $e2 = − $q2

where qd is the constant desired angle. One can obtain the non-perturbed homogeneous error differential equation,

#e2 + kd $e2 + kpe2 = 0 (15)

with control parameters kp > 0, kd > 0. The controller in (14)can be enhanced by a robustification signal of the followingform,

ν2 = kpe2 + kd $e2 + ηsign(r) (16)

where r = e2+ ρ $e2. In this study, η is set to be 0.067 throughoutcases.

Figure 2 shows the 2nd joint angle output of an underactuatedSCARA robot with its corresponding control effort. The setpointwas set to 0.3 radian. There is an apparent overshoot at 30 secand eventually settles within 70 sec. Figure 3 shows the 1st jointangle output (rad) (actuated). Figure 4 shows the 2nd joint angleoutput of an underactuated (or malfunctioned actuator) SCARArobot with added robustification signal of various parametersetting. ρis the tuning knob to adjust the level of robustification.If this is adjusted too strong, then, there will be singularity issueto be resolved. The performance comparison between the PDcontroller with robustification signal with the PD controller onlywas demonstrated in the presence of bounded noise as in Figure5.

0 20 40 60 80 100 120 140 160 180 200

-30

-25

-20

-15

-10

-5

0

Fig. 3. 1st joint angle output (rad) (actuated).

0 20 40 60 80 100 120 140 160 180 200

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Fig. 4. 2nd joint angle output (rad) of an underactuated(or malfunctioned actuator) SCARA robot with addedrobustification signal of various parameter setting.

0 20 40 60 80 100 120 140 160 180 2000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Under the presence of bounded noise

Fig. 5. Performance comparison between the PD controller withrobustification signal with the PD controller only in thepresence of bounded noise

4. MECHATRONIC DESIGN

The mechatronic design of the designed SCARA robot is basedon the work by Idegraaf (2016), which is illustrated in Figure 6.This design uses 1 stepper motor coupled with power screw to

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produce z-axis motion for the robot. As the power screw rotates,the entire block of robotic arm will move in z direction dependson the direction of rotation of power screw.For the end effector,the 3d-printer filament extruder in Figure 6 is replaced withrobotic gripper. That robotic gripper is a simple mechanismmade from wooden stick and actuated by a servo motor todemonstrate the motion of picking up and moving the debris.Most of the mechanic parts of the prototype are printed with3D-printer. In this study, the vertical actuation (in z directionby prismatic joint) is ignored as the focus was given on theunderactuation control technique on the planar mechanism (thefirst 2 revolute joints).

Fig. 6. SCARA Robotic Arm Design inspired by the work in( Idegraaf (2016))

Figure 7 shows the SCARA Robot built in this project. Therobot contains 2 links like conventional SCARA Robot, resultingvarious combination for translational motion in x and y-planeby providing torque to the joints.

As observable in Figure 8, the upper arm and lower arm areactuated by different stepper motor. The torque produced by thestepper motor is transmitted by using timing belt and pulley.The timing belt pulley can be removed or severed to createthe underactuated condition for further study and evaluationon various control schemes. The joints of printed arms havethreaded pattern to match the shaped of timing belt and hencethe rotational motion for the arms can be realized.

Figure 9 shows the block diagram for the mechatronics system.As observable in Figure 9, the prototype robot is controlledby using Arduino Mega 2560 and Arduino IDE software. Thesystem is powered by the 12Vdc Power Supply. The RAMPS1.4 shield is installed on the Arduino where its function is tocontrol the power distribution to stepper motors and Arduino.The DRV8825 stepper motor drivers and L298D DC motordriver are required for Arduino to control the motor speed anddirection.

Fig. 7. Assembled SCARA Robot Prototype

Fig. 8. Detailed View of the Arm. The underactuation can bedeliberately introduced by severing or removing the pulleyconnecting to the second joint.

ArduinoMega 2560

RampShield

12 V power DCsupply

End-effector servo-motor

stepper motorsdrivers

actuator 2

actuator 1

focus of interest

deliberately severed for simulatingunderactuation

Fig. 9. Block Diagram for Mechatronics System

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5. CONCLUSION AND FUTURE WORK

In this paper, a SCARA prototype is presented and discussedin terms of kinematic and dynamic analysis. Collocated andNoncollocated linearisation are presented in designing a suit-able controller for an underactuated SCARA robot arm. PDcontroller and enhanced PD controller algorithm was evaluatedon an underactuated two-link planar robot model in simulation.Mechatronic design and hardware system integration to evaluatethe controller in the future hardware implementation work werediscussed. The setup can be used to investigate further theaspect of fail-and-safe mechanism associating with the controltechnique for an underactuated system. This can be beneficial foran industrial application in which SCARA robots are intensivelyused.

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Chi, J., Yu, H., and Yu, J. (2018). Hybrid tracking controlof 2-dof scara robot via port-controlled hamiltonian andbackstepping. IEEE Access, 6, 17354–17360. doi:10.1109/ACCESS.2018.2820681.

He, Y., Mai, X., Cui, C., Gao, J., Yang, Z., Zhang, K., Chen,X., Chen, Y., and Tang, H. (2019). Dynamic modeling,simulation, and experimental verification of a wafer handlingscara robot with decoupling servo control. IEEE Access, 7,47143–47153. doi:10.1109/ACCESS.2019.2909657.

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