SMA CONTROL FOR BIO-MIMETIC FISH LOCOMOTION

Claudio Rossi, Antonio Barrientos

Robotics and Cybernetics Research Group, Universidad Polit

ecnica de Madrid, Madrid, Spain

William Coral Cuellar

Dep. G

enie

Electrique et Sist

emes de Commande, Universit

e de Technologie de Belfort-Montb

eliard, Belfort, France

Keywords:

Shape memory alloys, Biologically-inspired robots, Smart actuators control, Underwater robotics.

Abstract:

In this paper, we describe our current work on bio-inspired locomotion systems using smart materials. The

aim of this work is to investigate alternative actuation mechanisms based on smart materials, exploring the

possibility of building motor-less and gear-less robots. A swimming underwater robot is being developed

whose movements are generated using such materials, concretely Shape Memory Alloys. This paper focuses

on the actuators control in order to obtain a a sufﬁciently fast and accurate positioning.

1 INTRODUCTION

Robotics actuator technology is basically domi-

nated by two kind of actuators: electric mo-

tors/servomotors and pneumatic/hydraulic actuators.

In mobile robotics, the former is mostly used, with

exceptions being e.g. large legged robots. The (ro-

tatory) motion of the motors is then transmitted to

the effectors through gearboxes, belts and other me-

chanical devices in the case that linear actuation is

needed. Although applied with success in uncount-

able robotic devices, such systems can be complex,

heavy and bulky

. In underwater robots, propellers

are most used for locomotion an maneuvering. Pro-

pellers however may have problems of cavitation,

noise, efﬁciency, can get tangled with vegetation and

other objects and can be dangerous for sea life.

Underwater creatures are capable of high per-

formance movements in water. Thus, underwater

robot design based on the mechanism of ﬁsh loco-

motion appears to be a promising approach. Over

the past few years, researches have been develop-

ing underwater robots based on underwater creatures

swimming mechanism (Hu, 2006), (Anderson and

Chhabra, 2002), (Morgansen et al., 2007). Yet, most

Robotuna, a robot ﬁsh developed at MIT in 1994, had

2,843 parts controlled by six motors (font: MIT News,

http://web.mit.edu/newsofﬁce/2009/robo-ﬁsh-0824.html)

of them still rely on servomotor technology and a

structure made of a discrete number of elements. One

of the most advanced ﬁshe-like robot is the MIT ﬁsh

(Valdivia y Alvarado and Youcef-Toumi, 2006). This

ﬁsh has a continuous soft body. A single motor gen-

erates a wave that is propagated backwards in order to

generate propulsion.

In the last years, actuation technology in active

or ”smart” materials has opened new horizons as far

as simplicity, weight and dimensions. New materials

such as piezo-electric ﬁber composite, electro-active

polymers and shape memory alloys (SMA) are being

investigated as a promising alternative to standard ser-

vomotor technology. The potential gain in weight and

dimension would allow building lighter and smaller

robots, and even devising soft-bodied robots (Cowan

and Walker, 2008).

In order to reproduce the undulatory body mo-

tion of ﬁshes, smart materials appear to be extremely

suited. In fact, over the last years, there has been an

increasing activity in this ﬁeld. Research in the ﬁeld

of smart materials for underwater locomotion is fo-

cused into mechatronics design and actuators control.

As far as mechatronic design, much work is devoted

to building hydrofoils using, e.g. piezo-electric ﬁber

composite (Ming et al., 2009), embedding SMA wires

into an elastic material such as silicone (Wang et al.,

2008) or using SMAs as linear actuators (Rediniotis

et al., 2002). An important challenge is the control

147

Rossi C., Barrientos A. and Coral Cuellar W. (2010).

SMA CONTROL FOR BIO-MIMETIC FISH LOCOMOTION.

In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics, pages 147-152

 SciTePress

of such materials. In the case of SMAs, excellent re-

sults have been achieved by (Teh, 2008) and (Meier

et al., 2009). In this paper, we present our work on

a swimming robot, focussing on the control of the

SMA-based actuation system.

2 MECHATRONICS DESIGN

Fishes can swim bending their body in such a way

to produce a backward-propagating propulsive wave.

Such bending comes in different ways. Anguilliform

swimmers show a snake-like motion: their body can

be divided into numerous segments from head to tail

and can reproduce at least one complete wavelength

along the body. Conversely, subcarangifor, carangi-

form and thunniform swimmers only bends the sec-

ond half of the body (roughly) and the number of seg-

ments is reduced to one or two.

For our model, we have chosen to imitate the sub-

carangiform swimming style because of the reduced

number of segments w.r.t. anguilliform ﬁshes, which

simpliﬁes the study and the implementation, while

having enough degrees of freedom that allow complex

motion patterns to be reproduced. Our ﬁsh model can

also bend the front part of its body, which makes a

total of three bendable segments (cf. Figure 1).

The ﬁsh is formed by a continuous structure made

of polycarbonate 1 mm thick, which represents the

ﬁsh backbone and spines. This material has been cho-

sen for its temperature resistance, impact resistance

and ﬂexibility. Additional supporting structure made

of PVC is employed to support the silicon-based skin

of the robot. The overall length of the ﬁsh is 30 cm

(not including the caudal ﬁn). Along the backbone,

six SMA actuators are used to bend the body. Their

length is 1/3 body length (i.e. 8.5cm, not counting

the caudal ﬁn and the head) and are positioned in

pairs, in such a way to produce an antagonistic move-

ment. Thanks to this arrangement, the body segments

can bend up to ≈ 30 degrees. The diameter size of

the wires has been chosen as a trade-off between cur-

rent consumption, pull force and contraction time. We

have adopted a SMA with a diameter size of 150µm

that has a pull force of 230 grams, a consumption of

250 mA at room temperature, and a nominal contrac-

tion time of 1 second. Such contraction time allows

an undulation frequency that is enough for producing

motion in water.

2.1 Shape Memory Alloys

SMAs are materials capable of changing their crys-

tallographic structure (from austensite and marteniste

Figure 1: Lateral and upper view of the deformable struc-

ture. Note the location of the SMA wires along the body.

Figure 2: Principle of the bendable structure. The SMA

wire is parallel to the spine segment. As it contracts, it

causes the polycarbonate strip to bend.

phases), due to changes in temperature. When an

SMA wire is subjected to an electrical current, Joule

resistive heating causes the SMA actuator to contract.

SMAs have the advantage that they work at low cur-

rents and voltages, are extremely cheap and are easily

available commercially. Nitinol, one of the most com-

mercially available SMAs, is an alloy of nickel and

titanium (NiTi). It is characterized by a high recovery

stress (> 500MPa), low operational voltage (4 −5 V ),

a reasonable operational strain (≈ 4%) and a long life

(up to 10

cycles).

The behavior of SMAs is more complex than

many common materials: the stress-strain relation-

ship is non-linear, hysteretic, exhibits large reversible

strains, and it is temperature dependent. For this rea-

son, a low-level control electronics has to be designed

in order to have a position control close-loop precise

enough for the application at hand. An important

characteristics of SMAs is that they can also be used

as sensors. In fact, once heated applying a given cur-

rent, one can measure their resistance and calculate

the actual percentage of shrinking. This measurement

can be used as feedback for achieving precise position

control.

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148

3 SMA CONTROL

The control accuracy of smart actuators such as SMAs

is limited due to their inherent hysteresis nonlineari-

ties (see Figure 3) with a local memory. The exis-

tence of minor loops in the major loop because of a

local memory also makes the mathematical model-

ing and design of a controller difﬁcult for SMA ac-

tuators. Therefore, to enhance the controllability of

a smart actuator, the Preisach hysteresis model (Vis-

intin, 1995) has emerged as an appropriate behavioral

model. Nevertheless, the modeling is difﬁcult and the

model equation remains complex. So even though

this model is commonly used (Choi et al., 2004), the

use of a heat transfer model and sensor hardware has

also been proposed.

As pointed out earlier, SMAs provide the possibil-

ity to develop controller systems without sensor hard-

ware. The detection of inner electrical resistance al-

lows to regulate the actuator movement (Ikuta et al.,

1988). The method consists in measuring the elec-

trical resistance of an SMA element (Teh, 2008) as

a form of temperature measurement. An advantage

of this method is that the hysteresis on the resistance

curve is smaller than the hysteresis on the temperature

curve, which makes the linear approximation more

accurate.

The maximum contraction of the wire can be mea-

sured as

∆L

SMA

M f

− R

SMA

A f

, (1)

where R

SMA

M f

(Ω) is the SMA resistance in marten-

site ﬁnish temperature (relaxed SMA), L

(Ω/m) is

the linear resistance and R

SMA

A f

(Ω) is the resistance

at austenite ﬁnish temperature (i.e. at maximum con-

traction).

Figure 5 shows the performance of a mock-up for

a current of 350mA. The angle shown in the ﬁgure is

in good accordance with the theoretical value of 28

◦

(cf. Figure 2). Note that the wires’ speed and strain

contraction depends on how fast and by how much the

wire temperature is increased. In our tests, we have

veriﬁed that SMAs wires can be fed with a current

of up to 500mA without compromising their behavior,

achieving faster response and higher percentages of

contraction.

3.1 Controller Tuning

In order to tune the control system, we set up a mock-

up of a segment of the ﬁsh’s backbone, corresponding

to a 10 ×2cm stripe of 1mm thick polycarbonate, with

a 174mm long SMA wire in a V-shaped conﬁguration,

in order to double the pull force (see Figure 4).

Figure 3: Histeresis of the SMA. (A

, the austenite start

temperature; A

, the austenite ﬁnish temperature; M

, the

martensite start temperature; and M

, the martensite ﬁnish

temperature).

Figure 4: The test mock-up.

For the control, we used a PID (proportional-

integral-derivative) controller, which responds to the

equation

u(t) = K

e(t) + K

e(t)dt +K

de(t)

, (2)

where e(t) is the signal error and u(t) is the con-

trol input of the process. K

are the propor-

tional, integrative and derivative gains. Then by pos-

ing K

= K

, where T

is the integral time

constant and T

is the derivative time constant, the

PID controller can be written in the s domain as

U(s) = K



1 +

+ T



E(s). (3)

Following Ziegler-Nichols, we have tuned the val-

ues to the three parameters (K

) of the PID con-

troller based on the analysis of the open and close

loop of the system to be controlled. The dynamics

behavior of the system is deﬁned using the following

ﬁrst-order linear transfer function:

G(s) =

−sτ

1 − sγ

, (4)

where the coefﬁcients K

,τ

and γ

are obtained from

the response of the open loop system to a step in-

put. Starting from the stabilized system at y(t) = y

to u(t) = u

, a step input is applied from u

to u

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149