 Open Access
 Authors : M.V. K. N. S. Gayathri, P. Devendra, K. V. Ramesh
 Paper ID : IJERTCONV8IS16009
 Volume & Issue : NCSMSD – 2020 (Volume 8 – Issue 16)
 Published (First Online): 18102020
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Adaptive Sliding Mode Control of PUMA 560 Robotic ARM
M.V. K. N. S. Gayathri1,#, P. Devendra2,*, K. V. Ramesp
1Department of ECE, AU College of Engineering for Women, Visakhaptnam530017, India.
2Department of EEE, GVP College of Engineering for Women, Visakhapatnam530048, India.
3Department of Chemical Engineering, Andhra University, Visakhaptnam530003, India.
Abstract Adaptive sliding mode control has been successfully applied to the PUMA robotic arm. Nowadays robots are integral part many industrial applications. Hence control of these plays crucial role. PUMA robots are well known and in this present work, adaptive sliding mode control is used to control the position. The efficacy of the presented controller has been validated using MATLAB simulations.
Keywords PUMA robot adaptive sliding mode control.

INTRODUCTION
Programmable Universal Machine for Assembly (PUMA) was well known for its robotics. The PUMAs were the most popular robots of last decades of twentieth century. The design of such robots was classified into three categories viz.,
200 series, 500 series and 700 series. The 200 series
cables where in one cable supplies power to the servo motors and brakes and the second one exercises feedback positioning for each joint of the assembly.

MODELING OF PUMA ROBOTIC ARM
The general for of 6DOF (Degrees of freedom) configuration equation is only utilized in the present work to make into a 3 DOF robot. Here, the lass three joints were kept blocked i.e., the initial states of these joints were assigned zero, however the robot will be moving. This leads to formation of equations for the kinematics of 3DOF robot which permit us to define a new DH coordinate system that can be implemented. Here a homogenous transformation matrix
comprises of smaller units of desktop size. The 500 series
relating the
3rd
coordinate frame to the first coordinate
were designed to reach a height of 2 meters and were the most popular ones. The last one among these categories is 700 series which were developed for carrying out works such as paint, welding, assembly line etc. One common thing for all these categories is that the design contains two parts: (i) the mechanical arm and (ii) the control system. These two parts are generally interconnected by two multiconductor
frame is developed. However, the 3DOF PUMA will have the same kinematics of its 6DOF convenient with q4 , q5 and q6 set to zero. The following set of equations is considered (1). The robotic arm is shown in Fig.1.
For the configuration space equation of the robot
A(q).q B(q).qq C(q).q 2 g(q)
We set q4 q5 q6 0 , this yields
q q 1 …q 2 …q 3 …0…0…0 ,
T
qq q1q2 …q1q3 …0…0…0…q2 q3
…0…0…0…0…0…0…0…0…0T ,
1
1
2
2
3
3
q 2 q 2 …q 2 …q 2 …0…0…0T ,
112
112
1
1
2
2
113
113
1
1
3
3
123
123
2
2
3
3
223
223
2
2
3
3
412
412
1
1
2
2
413
413
1
1
3
3
B(q).qq b .q q b .q q b
.q q …b
.q q …0…b
.q q b
.q q …0…0T and
12
12

c

c
1
1
2
2
21
21
23
23
C(q).q 2 c
.q2 13
.q3
2 …c
.q 2 c
.q3
2 …c
.q 2 c
.q2
2 …0…c
.q 2 c
.q2
2 …0T
1
1
1
1
31
31
32
32
51
51
52
52
The angular acceleration is found as to be
q A1 (q). B(q).qq C(q).q 2 g(q)

c

c
2
2
2
2
Now let I B(q).qq C(q).q 2 g(q) q A1 (q).I
1
1
23
23
2
2
I1 1
b112
.q1q2
b113
.q1q3
b123
.q2
q3
c12
.q2 13
.q3
I 2 2
b
223
.q2
q3
c21
.q 2 c
.q3
2 g
I 3 3 c31 .q c .q g
2 2
1
1
32
32
3
3
2
I 4 4 b412.q1q2 b413.q1q3
I 5 5 c51 .q c .q g
2 2
1
1
52
52
5
5
2
I 6 6
These equations tell us that in order to ensure that q 4 , q 5 and q 6 keep their zero values, it is better to set
I4 I5 I6 0 ; so by holding the control torques of the last three joints as
4 b412.q1q2 b413.q1q3
5 c51 .q c .q g and 0 , the last three joints are blocked at their initial states.
2 2
1
1
52
52
5
5
2 6
Fig.1. Robotic Arm

ADAPTIVE SLIDING MODE CONTROL
The following nonlinear system with uncertainties is considered.
dx = f(x) + g(x) u (1)
dt
Here u and x are control input and state vector respectively
The dynamics of the sliding variable s(x,t) are given in equation (2)
u = K(t)sign(s(x, t)) (3)
The adaptive law is provided as equation (4)
K = K (s(x, t) (4)
Here K > 0 and K > 0 and sliding mode is established in a finite time.

SIMULATION RESULTS
The results obtained by running the above program using MATLAB and the results are shown presented in Figs.2 to 4. One can observe from Fig.2 that the target position was reached by the robot arm after 2 seconds. However, with respect to other two arms as illustrated by Figs. 3 and 4 the arm reached the target position instantaneously indicating that the present model work well for PUMA robot with 3 DOF. Further one can notice that the three arm positions were very well in reaching the target in a short while. This means that the said model can be implemented successfully for many robotic applications.
Fig.2 Theta_1 of robotic arm
s = s x + s
(2)
x t
Let us demonstrate a new adaptive sliding mode controller u(s, t) with the same features as classical SMC such as robustness and nite time convergence. The sliding variable dynamics in equation (2) is controlled by equation (3)
Fig.3 Theta_2 of robotic arm
Fig.4. Theta_3 of robotic arm

CONCLUSION
In order to control the PUMA robotic arm, in the present investigation an adaptive sliding mode control has been successfully implemented. The efficacy of the presented controller has been validated using MATLAB simulations. The results showed that the performance of controller is superior for the robotic arm control.
REFERENCES

B. Armstrong, O. Khatib, J. Burdick , The Explicit Dynamic Model and Inertial Parameters of the PUMA 560 Arm , Stanford University, Artificial Intelligence Laboratory, IEEE 1986.

A.R. Merheb, Nonlinear Control Algorithms applied to 3 DOF PUMA Robot, METU 2008

A. Razzak (2020). Nonlinear Control of 3 DOF PUMA Robot (https://www.mathworks.com/matlabcentral/fileechange/22077
nonlinearcontrolof3dofpumarobot), MATLAB Central File Exchange. Retrieved July 4, 2020.

P. Farzin et al. "PUMA560 robot manipulator position computed torque control methods using Matlab/Simulink and their integration into graduate nonlinear control and Matlab courses." Int. J. Robotics Automation 3.3 (2012): 167191.

P. Farzin,et al. "PUMA560 robot manipulator position sliding mode control methods using MATLAB/SIMULINK and their integration into graduate/undergraduate nonlinear control, robotics and MATLAB courses." Int. J. Robotics Automation 3.3 (2012): 106150.

W.E. Dixon, et al. "A simulinkbased robotic toolkit for simulation and control of the puma 560 robot manipulator." Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No. 01CH37180). Vol. 4. IEEE, 2001.

V.M. Becerra, et al. "Hardware retrofit and computed torque control of a Puma 560 Robot updating an industrial manipulator." IEEE Control Systems Magazine 24.5 (2004): 7882.

J.J. Luo, G.Q. Hu, (2005). Study on the simulation of robot motion based on Matlab. JournalXiamen Univ. Natural Sci., 44(5), 640.

M.W. Spong, S. Hutchinson, M. Vidyasagar. Robot modeling and control. 2006.

M.W. Spong, M. Vidyasagar. Robot dynamics and control. John Wiley & Sons, 2008.