Adaptive Sliding Mode Control of PUMA 560 Robotic ARM

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, Visakhaptnam-530017, India.

2Department of EEE, GVP College of Engineering for Women, Visakhapatnam-530048, India.

3Department of Chemical Engineering, Andhra University, Visakhaptnam-530003, 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.

1. 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.

2. MODELING OF PUMA ROBOTIC ARM

The general for of 6-DOF (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 3-DOF robot which permit us to define a new D-H 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 multi-conductor

frame is developed. However, the 3-DOF PUMA will have the same kinematics of its 6-DOF 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

1. 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.

2. 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

3. 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

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