SHAPE MEMORY ALLOY TENDONS ACTUATED TENTACLE

ROBOTIC STRUCTURE

Models and Control

*

Nicu George Bîzdoacă,

**

Anca Petrişor

*

Faculty of Automation,Computers and Electronics, University of Craiova, Romania

*

Elvira Bîzdoacă,

*

Ilie Diaconu,

**

Sonia Degeratu

**

Faculty of Electromechanical Engineering, University of Craiova, Romania

Keywords: Robotics, Shape memory alloy applications, Serial link, Fuzzy controller.

Abstract: A tentacle manipulator is a manipulator with a great flexibility, with a distributed mass and torque that can

take any arbitrary shape. Technologically, such systems can be obtained by using a cellular structure for

each element of the arm. Shape memory alloy actuation offers an interesting solution, using the shape

transformation of the wire/structure in the moment of applying a thermal type transformation able to offer

the martensitic temperature. In order to assure an efficient control of SMA actuator applied to inverted

pendulum, a mathematical model and numerical simulation of the resulting model is required. Due a

particular possibility SMA actuator connection, a modified dynamics for wire or tendon actuation is

presented. For an efficient study a Simulink block set is developed (block for user configurable shape

memory alloy material, configurable block for dynamics of single link robotic structure, block for user

configurable wire/tendon actuation). As conventional control possibilities were explored, the fuzzy control

structure applied in this paper, offer an improved response. A more compact SMA actuation is proposed and

experimented. The results are commented.

1 INTRODUCTION

Shape Memory Alloy (SMA) are materials that,

once mechanically deformed at given temperature,

are able to recover the deformation through an

appropriate thermal cycle (Funakubo, 1987).

Between the alloys that show this property,

attention has been focused on Nickel – Titanium

alloy: it show properties which are suitable for the

applications in robotics, general propose actuator

and medicine (Faravelli and Marioni, 1996). The

nickel titanium alloys, generally refereed to as

Nitinol are four times the cost of Cu-Zn-Al alloys,

but it possesses several advantages as greater

ductility, more recoverable motion, excellent

corrosion resistance, stable transformation

temperatures, high biocompatibility and the ability

to be electrically heated for shape recovery. Other

important proprieties of the Nitinol, superelasticity

(or pseudoelasticity) refers to the ability of NiTi to

return to its original shape upon unloading after a

substantial deformation.

This is based on stress-induced martensite

formation. The application of an outer stress causes

martensite to form at temperatures higher than M

s

.

Figure 1: Martensitic and Austentic transformations.

The macroscopic deformation is accommodated

by the formation of martensite. When the stress is

released, the martensite transforms back into

austenite and the specimen returns back to its

original shape. Superelastic NiTi can be strained

several times more than ordinary metal alloys

77

George Bîzdoac

ˇ

a N., Petri¸sor A., Bîzdoac

ˇ

a E., Diaconu I. and Degeratu S. (2008).

SHAPE MEMORY ALLOY TENDONS ACTUATED TENTACLE ROBOTIC STRUCTURE - Models and Control.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - RA, pages 77-80

DOI: 10.5220/0001490800770080

Copyright

c

SciTePress

without being plastically deformed, which reflects

its rubber-like behavior. It is, however, only

observed over a specific temperature area. The

highest temperature at which martensite can no

longer stress induced is called Md. Above M

d

NiTi

alloy is deformed like ordinary materials by

slipping. Below as temperature, the material is

martensitic and does not recover. Thus,

superelasticity appears in a temperature range from

near A

f

and up to M

d

. The largest ability to recover

occurs close to A

f.

Another important feature of superelastic

materials is that their unloading curves are flat over

large strains. Thus, the force applied by a

superelastic device is determined by the temperature,

not by the strain as in conventional Hookian

materials. The basic rule for electrical actuation is

that the temperature of complete transformation to

martensite M

f

, of the actuator, must be well above

the maximum ambient temperature expected.

2 DYNAMICS OF TWO-LINK

TENDON-DRIVEN ROBOTIC

STRUCTURE

There are many methods for generating the dynamic

equations of mechanical system. All methods

generate equivalent sets of equations, but different

forms of the equations may be better suited for

computation different forms of the equations may be

better suited for computation or analysis..

Using the kinetic energy and Lagrange methods

results:

()

111

cc ss

22 22221

222

1

11

2

cs0

221

22

⎡⎤⎡ ⎤

α+β δ+ β − β θ − β θ +θ

⎡⎤

⎢⎥⎢ ⎥

θ

+•

⎢⎥

⎢⎥⎢ ⎥

θ

⎢⎥

⎢⎥⎢ ⎥

⎣⎦

δ+ β δ β θ

⎢⎥⎢ ⎥

⎣⎦⎣ ⎦

&&&

&&

&&

&

⎥

⎦

⎤

⎢

⎣

⎡

⎥

⎦

⎤

⎢

⎣

⎡

=•

2

1

2

1

τ

τ

θ

θ

&

&

(1)

Where

(

)

(

)

(

)

mm

22 22 2 22

12

lw lw mrmlr

12

11 22 1 12

12 12

α= ++ ++ + +

(2)

mll

212

β=

(3)

(

)

m

22 2

2

lw mr

22 22

12

δ= + +

(4)

with w

1

, w

2

, l

1

, l

2

the width and respectively the

length of link 1 and link 2.

Figure 2: Two link robotic architecture.

3 SHAPE MEMORY ACTUATOR

STRUCTURE

Due the actuation architecture a simple

mathematical model can be establish. Schematically

the shape memory actuation is

Figure 3: Shape memory alloy actuation structure.

In Figure 3 l

v

is the variable length of shape

memory alloy wire, the l is the robotic link length

between the articulation point and the shape memory

alloy wire connection, r is the distance between the

second end of the SMA wire (which is a fixed point)

and the articulation point of the link (fixed point

too).

Using simple mathematical computation the

mathematical dependence can be established

(

)

222

v

1

lrl

arccos

2lr

⎛⎞

−+

⎜⎟

θ=

⎜⎟

⎜⎟

⎝⎠

()

2

1v

fl⇔θ =

(5)

The graphic of θ

1

as function of lv (considering

the real domain variation for

[

]

1

0,θ∈ π

) is linear,

that the liniarisation in modeling can be done

successfully.

The explanations concern the structural variation

of SMA actuator, which are limited superior by l

v

and inferior by 0.5 l

v

. The mathematical model

including the SMA actuation can be developed in

two ways: First is possible to consider for position

control, ONLY the length variation of the SMA

actuator. This approach is a correct one, the

ICINCO 2008 - International Conference on Informatics in Control, Automation and Robotics

78

additional torque, provided by the particular

proprieties of SMA, enforces the actuation. The

situation corresponds to tendon actuation or wire

actuation. Using the substitution:

v

1v

2

22 2

v

2l

l

llr

lr 4

lr

−

θ=

⎛⎞

−−

−

⎜⎟

⎜⎟

⎝⎠

&

&

(6)

2

v

1vv

22

22 2 22 2

vv

2l

2

ll

llr llr

lr 4 lr 4

lr lr

−

θ= − −

⎛⎞ ⎛⎞

−− −−

−−

⎜⎟ ⎜⎟

⎜⎟ ⎜⎟

⎝⎠ ⎝⎠

&& &

&&

(

)

22 2 2

vv

2

v

2

2

22 2

33

v

3

4l l l r

l

llr

lr 4

lr

−−

−

⎛⎞

⎛⎞

−−

⎜⎟

−

⎜⎟

⎜⎟

⎜⎟

⎝⎠

⎝⎠

&

(7)

Analyzing the equilibrium conditions, results

that

()

111

bτ= θ and

222

v

lrl=+, state which

correspond to real case.

Second way makes a simplifying assumption:

because the SMA connection with single link

structure can be choose near to the articulation point,

we can assume that the entire SMA torque is directly

used for movement. Then the mathematical model

can be expressed as

()

()

2

11 1

11

SMA 1 1 1

gm w cos

mw

b

32

⎛⎞

θ

τ= θ+ +θ

⎜⎟

⎜⎟

⎝⎠

&&

(8)

4 CONTROL OF SHAPE

MEMORY ALLOY TENTACLE

ROBOTIC STRUCTURE

In order to investigate the SMA robotic structure

comportment a Quanser modified platform was used

for experiments. The basic control structure uses a

configurable PID controller and a Quanser Power

Module Unit for energizing the SMA actuators.

In order to investigate the SMA robotic structure

comportment a Quanser modified platform was used

for experiments. The basic control structure uses a

configurable PID controller and a Quanser Power

Module Unit for energizing the SMA actuators.

PID controller was changed, in order to adapt to

the particularities of the SMA actuator. A negative

command for SMA actuator corresponds to a

cooling source. The actual structure use for cooling

only the ambient temperature.

The best results arise when a PI controller is

used. The PI experimented controller parameters are:

the proportional parameter K

R

=10 and the

integration parameter is K

I

=0, 05.

Figure 4: Quanser modified platform.

The input step is equivalently with 30

0

angle

base variation and the evolution of this reference is

represented with the response of real system in

Figure 5. The control signal variation is presented in

Figure 6.

Figure 5: System response,

for step input.

Figure 6: PI controller

response, for step input.

For negative step, the evolution of the system

and the control variable evolution are presented in

Figure 7 and Figure 8.

Figure 7: System response,

negative step input.

Figure 8: PI controller

response, negative step

input.

Using PID, PD controller the experiments

conduct to less convenient results from the point of

view of time response or controller dynamics.

SHAPE MEMORY ALLOY TENDONS ACTUATED TENTACLE ROBOTIC STRUCTURE - Models and Control

79

Using heat in order to activate SMA wire, a

human operator will increase or decrease the amount

of heat in order to assure a desired position to

robotic link. Because of medium temperature

influence, can not be establish, apriori, a clear

control law, available for all the points of the robotic

structure workspace. A simple and efficent control

structure can be implemented.

Figure 9: Fuzzy control structure.

For an efficient control it is proposed the

following definition for input and output members:

- input 1 is the first derivate of pozition error, with 3

fuzzy member: Negative, Zero, Pozitive

- input 2 is pozition error with 3 fuzzy member:

Negative, Zero and Pozitive

- output is temperature heating with 3 fuzzy

member: Temperature Negative (temperature under

austenitic start transformation), Temperature Zero

(temperatures between start and final austenitic

transformation), Temperature Positive (temperature

above temperature of final austenitic

transformation).

Table 1: Fuzzy rules for the proposed controller.

e

&

e

P Z N

P TP TP TP

Z TZ TZ TZ

N TN TN TN

The result of the numerical simulation are

promising, related to the simplicity of the control

structure, for the case of the sinusoidal reference

with frecvency of 5 rad/sec.

Figure 10: Fuzzy robotic structure output evolution.

5 CONCLUSIONS

The simulations, the mathematical model and the

initial experiments developed in the article offer a

background in studying the serial link robotic

control possibilities. The results respect the real

evolution of the structure. In the future, the authors

will explore improvement of the control

performnces and the extension of the experiments to

n link robotic structure.

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