Design of an shape memory alloy-actuated biomimetic mobile robot with the jumping gait

International Journal of Control, Automation, and Systems (2013) 11(5):991-1000 DOI 10.1007/s12555-011-0015-8

ISSN:1598-6446 eISSN:2005-4092http://www.springer.com/12555

Design of an Shape Memory Alloy-Actuated Biomimetic

Mobile Robot with the Jumping Gait

Thanhtam Ho and Sangyoon Lee*

Abstract: This paper reports the design, simulation, analysis, and experiments of mesoscale four-

legged robots that can locomote by a jumping gait using only shape memory alloy (SMA) wires as ac-

tuators. Through studies of the structure and function of leg muscle groups in vertebrates’ lower mus-

culoskeletal system, three types of muscles are selected for robot leg design, and each muscle is then

replaced by an SMA wire in the robot model. Two types of robot models are proposed and analyzed us-

ing three sets of computer simulation. It can be concluded from the simulation that the sequence of

SMA muscle activation, activation arrangement of the rear and the front legs, and the foot length are

primary factors determining the jumping performance. It is observed that when the robot has three de-

grees of freedom for each leg and a foot length of 40 mm, the maximum jumping height is approx-

imately 120% of the robot’s height and the maximum distance per jump is about 35% of its length. In

addition, two robot prototypes are presented based on the design models and experimental results. The

simulation and experimental results are found to show good agreement. The overall results show that

the proposed robot design and SMA actuation method are feasible for all SMA-driven jumping robots.

Keywords: Biomimetic robot, jumping gait, legged robot, shape memory alloy.

1. INTRODUCTION

Jumping is one type of ground locomotion employed

by several animals or insects. Compared to crawling,

sliding, or walking, jumping can be an attractive choice

in terms of travel efficiency and obstacle avoidance

ability. A frog, for example, can jump forward by 10 m

despite its body length being only of the order of a few

hundred millimeters [1]. In the field of mobile robotics

research and development, numerous studies have

attempted to exploit the jumping gait. It has typically

been found that the design of jumping robots is inspired

by the structure and function of biological creatures.

Some examples are the multi-DOF (degree of freedom)

jumping robot [2], the Mowgli robot [3], and the rabbit

robot [4]. More recent jumping robots include the

miniature jumping robot [5] and the one-legged robot

with two DOFs [6].

When considering the design of jumping robot, the

actuator should be one of the primary factors determin-

ing the jumping height and distance. Considering that the

jumping motion requires an extremely large force for a

short time period, a pneumatic actuator can be consider-

ed as a suitable candidate. A pneumatic actuator has a

larger power-to-weight ratio than an electromagnetic

motor [7]. In addition, it can produce a linear motion.

However its main drawbacks are the weight and size due

to the air supply source. As a result, jumping robots that

employ a pneumatic actuator are relatively large and

heavy [3,8].

An electromagnetic motor is a popular choice for

robots in many applications [9,10]. Owing to the fact a

variety of motors are available, using motors for a

jumping robot may reduce the size and complexity of the

robot system. It has been noted that motors can be used

in both large and miniature jumping robots [4,5].

However, the output torque of an electromagnetic motor

is small though the motor speed is high. Hence, a

gearbox is usually required, and this again leads to an

increase in the weight and complexity of the system.

Recently smart materials such as piezoelectric

materials or shape memory alloys (SMA) have been

utilized to realize the bounding or crawling locomotion

of small legged robots [11,12]. In particular SMA has

attracted the authors’ interest from the viewpoint of use

in jumping robot actuators because it affords a very

favorable power-to-weight ratio [7]. For example, a 100

mm MMF (metal muscle fiber) 150 wire with 11.2 mg

weight can contract by 4.5 mm while carrying a load of

0.9 kg. In other words, an SMA wire can carry a load

that is about 80000 times heavier than its weight.

Another advantageous characteristic of an SMA wire is

its deformation behavior. The contraction and extension

of the SMA wire in the longitudinal direction is similar

© ICROS, KIEE and Springer 2013

__________

Manuscript received January 13, 2011; revised July 6, 2012and December 21, 2012; accepted February 20, 2013. Recom-mended by Editorial Board member Sukho Park under the direc-tion of Editor Hyouk Ryeol Choi. This work was supported by National Research Foundation ofKorea Grant funded by the Korean Government (2009-0077778)and also by Leading Foreign Research Institute Recruitment Pro-gram through the National Research Foundation of Korea (NRF)funded by the Ministry of Education, Science and Technology(MEST) (2011-00260). Thanhtam Ho and Sangyoon Lee are with Department of Me-chanical Design and Production Engineering, Konkuk University,Gwangjin-gu, Seoul 143-701, Korea (e-mails: [email protected], [email protected]).

* Corresponding author.

Thanhtam Ho and Sangyoon Lee

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to the behavior of biological muscles. As a result,

through the proper design of a jumping mechanism, we

can expect jumping motion comparable to that of

vertebrates. However a jumping robot actuated by SMA

alone is quite rare. In order to incorporate SMA actuators

in the design of a jumping robot, in this study, we

propose a biomimetic design that is inspired by the

structure and function of vertebrates’ musculoskeletal

system. The use of SMA for jumping robots is expected

to reduce the weight and complexity of the robot while

still maintaining the functions of muscles during jumping.

The remainder of this paper presents the design,

simulation, analysis, and experimental tests of our small

biomimetic jumping robots.

2. DESIGN OF THE JUMPING ROBOT

The robot design is focused on the design of a small

mechanical mechanism that can jump up and forward

repeatedly. Typical constraints such as size and weight

affect the design. The most significant constraint to our

design should be the SMA actuator. Exploiting the cha-

racteristics of SMA is a critical challenge, and we pro-

pose a design that is inspired by the structure and func-

tion of muscles in the lower limbs of vertebrates.

2.1. Design of robot leg

The leg is the primary part for the jumping motion.

Jumping creatures are found to employ either direct or

indirect mechanism for leg structures. The direct me-

chanism is found in humans and vertebrate legs. In this

mechanism, the muscle directly generates the jumping

motion, and therefore, strong and fast activation of the

muscle is required while the relaxation time is not critical.

SMA materials satisfy this requirement. The indirect

jumping mechanism, on the other hand, can realize

jumping by using an energy storage device such as a

spring. The actuator in this mechanism transfers its ener-

gy to the storage device and the jumping is generated

using the stored energy. In the indirect jumping mechan-

ism, one can observe that jumping occurs during the re-

laxation phase of the muscle, and therefore, the actuator

must quickly return to the initial form. Studies of jump-

ing creatures show that the indirect jumping mechanism

found in insects such as froghoppers and fleas can pro-

duce a higher and farther jump relative to the body

length [15]. However, the direct jumping mechanism

employed by kangaroos and rabbits affords more advan-

tages for continuous jumping and landing stability. The

robot leg design proposed in this study is inspired by the

leg structure of the direct jumping mechanism, particu-

larly the human leg.

Studies of the musculoskeletal system of humans show

that the entire movement of lower limbs is realized by

nine muscle groups and tendons combined with the ske-

leton system [16-19]. Fig. 1(a) shows the musculoskelet-

al system of a human leg. The human leg can be divided

into four segments: trunk, thigh, shank, and foot. We

assume that any motion in the coronal plane can be neg-

lected in the analysis of jumping. The joints that are at-

tached at the hip, the knee, and the ankle are considered

as revolute ones.

According to the effects of the muscle on the joints,

the nine muscle groups in the lower limbs can be classi-

fied into two types. The first type is called the monoarti-

cular muscle; such muscles act on only one joint. The

iliopsoas (ILI), gluteus maximus (GMAX), vastus group

(VAS), biceps femoris (BF), tibialis anterior (TA), and

soleus (SOL) belong to this type. The second type is

called the biarticular muscle; such muscles act on two

joints of the leg. The rectus femoris (RF), hamstrings

(HAMS), and gastrocnemius (GAS) belong to this type.

Although it is extremely difficult to completely under-

stand the functions of each muscle in the jumping motion,

studies of the muscles involved in human jumping sug-

gest that both monoarticular and biarticular muscles con-

tribute to generate the power required to lift off the body

in the jumping motion. By using experimental data such

as the ground reaction force, cinematographic data, and

electromyography (EMG) data, the functions of each mus-

cle involved in vertical jumping can be clarified [20-24].

It has been reported that three monoarticular muscles,

(a) Musculoskeletal system of human leg.

(b) Simplified robot leg design: only three muscles

(GMAX, RF, and GAS) out of the nine muscles are

selected.

Fig. 1. Musculoskeletal system of human leg and out

robot leg design.

Design of an Shape Memory Alloy-Actuated Biomimetic Mobile Robot with the Jumping Gait

993

VAS, GMAX, and SOL work as the major energy gene-

rators for the jumping action [20,22]. The energy gener-

ated by these monoarticular muscles is applied directly to

the joint to which the muscles are attached. There is an

excess of energy over the amount that is needed at the

hip and the knee for jumping. This excess energy turns

out to be quite useful for generating the lift-off motion.

The biarticular muscles play an important role in the lift-

off motion. The RF muscle transfers the excess energy

from the hip to the knee while the GAS does the same

work from the knee to the ankle. Therefore, the biarticu-

lar muscles are considered as energy transporters during

jumping. For example, the energy transferred from the

knee to the ankle is estimated more than one-fourth of

the total energy needed by the ankle during lift-off.

Hence the biarticular muscles can reduce the size and

weight of the lower muscle groups. The lower segments

of leg can be accelerated more easily as a result. This

satisfies the requirements of jumping [20,25].

The contributions of each muscle type to the jumping

motion are now clear, and therefore, a proper design and

implementation based on these studies are expected to

significantly improve the performance of the jumping

mechanism. However, completely mimicking the struc-

ture of the lower limb musculoskeletal system should be

extreme difficult and complicated. Therefore, some de-

gree of modification and simplification is needed. Our

design aims to simplify the biological structure while

retaining the functions of both muscle types to the great-

est extent possible. We propose a simplified leg model

where the same number of segments as in the real leg is

maintained but the number of muscles is reduced to only

three: GMAX, RF, and GAS. Each muscle is replaced by

an SMA wire in the development of a robot model in the

computer simulation. Fig. 1(b) shows the design concept

of the robot leg.

The GMAX muscle is an important energy producer at

the hip. The energy generated by GMAX is used by the

thigh and the trunk, and it is transferred to the knee.

Therefore GMAX is retained in the model of the robot

leg. The robot leg model also includes two biarticular

muscles, RF and GAS. These muscles can contract and

stretch to produce a moment at the knee and the ankle,

respectively. Hence, these muscles are used for two pur-

poses. First, they function as energy transporters between

the joints. Second, they function as energy generators at

the knee and the ankle by replacing the monoarticular

muscles VAS and SOL (see Fig. 1(a)). Since the number

of muscles in the robot leg model is much smaller than

that in a natural human leg, three passive springs are

added with the SMA wires at each joint to form the flex-

or – extensor pairs (see Fig. 1(b)). During the contraction

of the SMA wires, the springs are extended. Springs with

low stiffness are preferred, and therefore, the spring

force is negligible compared to the actuation force of the

SMA wire. When SMA wires are not activated, the

spring force is the most important factor that helps the

SMA wire return to its initial length faster. In other

words, the springs help the robot leg recover the initial

configuration faster.

2.2. Design of the jumping mechanism

Although the robot leg design is proposed, there still

remain critical issues in the design of the jumping me-

chanism: choosing the number of legs and arranging the

legs. When jumping is used as a ground locomotion gait,

stable landing is one of the most significant problems.

Compared to other gaits, the jumping gait has a much

longer flying phase. Moreover, the robot is almost un-

controllable during the flying phase. As a result, the

landing can often become unstable. One of the simplest

methods to increase the stability of the robot during land-

ing is increasing the number of legs [26]. We can also

obtain a helpful hint from nature, namely, that successful

jumping vertebrates such as frogs and rabbits use four

legs for jumping. Therefore, we decided to design a four-

legged mechanism for the jumping robot.

In response to the second design issue of the arrange-

ment of legs, we propose two types of models, as shown

in Fig. 2(a) and (b). In model A, shown in Fig. 2(a), the

rear leg is not identical to the front one. The rear leg pos-

sesses three DOFs while the front one does two. The

three DOFs on the rear leg correspond to the hip, knee,

and ankle, each of which is controlled by an SMA wire.

In the front leg, the foot is neglected for simplification,

and the lower part is approximated to be a flat plate. This

design is based on the fact that skilled jumping verte-

brates, such as a rabbit, have a very small front foot

compared to the rear one. Due to this simplification, the

entire robot is driven by ten DOFs. Model B, shown in

Fig. 2(b), is a modified version of model A in which the

front leg is identical to the rear one. Both legs possess

three DOFs, and therefore, 12 SMA wires are required.

(a) Model A: 3 DOFs for each rear leg and 2 DOFs for

each front leg.

(b) Model B: 3 DOFs for both the rear and the front leg.

Fig. 2. Two models of four-legged jumping robot.


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Table 1. Main characteristics of MMF150 SMA wires.

Diameter

(mm)

Contraction

ratio (%)

Operation

voltage

(V/m)

Tensile

strength

(kgf)

Weight

(mg/m)

0.15 4.5 20.7 1.8 112

The SMA wire used in the models is the two-way

MMF150 (Metal Muscle Fiber) SMA (NT Research Inc.)

made of titanium and nickel. When MMF SMA is heated

to 70°C, it starts to contract. When it is cooled, it relaxes

and expands to its normal length. Although the principle

of operation of MMF SMA is based on the applied heat

energy, one can operate the SMA by applying electric

energy as well. This makes MMF SMA easy to control in

many engineering applications. Some essential characte-

ristics of MMF150 SMA wires are summarized in Table 1.

For installing SMA wires in the robot, we propose two

different methods: serial connection for model A and

parallel connection for model B. In the case of MMF150

SMA, the contraction ratio is 4.5%, but the absolute con-

traction length of SMA is small. To overcome this prob-

lem, one can increase the length of SMA wires, which is

applied to model A. A part named SMA holder is in-

stalled for augmenting the contraction amount of SMA

wires. The SMA holder consists of several small,

lightweight pulleys arranged at two terminals, and there-

fore, the SMA wire can be wound around the pulleys.

Therefore, the length of the SMA wire can be increased

significantly (see Fig. 2(a)). This connection method is

called SMA serial connection.

In the parallel connection method for robot model B,

first, the connection point of SMA is moved closer to the

center of each joint. By doing so, the rotation angle is

increased remarkably even if the SMA contraction length

remains quite small. One can imagine the system as a

lever where the center of each joint is the fulcrum. Since

the connection point is now closer to the fulcrum, a larg-

er SMA force is required to lift the mechanism. We sug-

gest a parallel connection of multiple SMA wires to

solve this problem.

Experiments were conducted to compare the two types

of SMA connections. The length of SMA wire required

for the serial connection is 200 mm. In the case of the

parallel connection, a bundle of five 40 mm SMA wires

is used. The 100 g payload is connected to both SMA

sets. We apply a pulse signal with a peak of 24 V. As

summarized in Table 2, the serial SMA set has an ap-

proximately five times larger contraction length than the

parallel one. The parallel SMA bundle shows an advan-

tageous contraction time: it contracts 33% faster than the

serial one. However, the extension time of the serial

SMA is shorter by about 1 sec. This can be explained by

the fact that the extension of SMA is dependent on the

cooling process. For the parallel SMA bundle, the cool-

ing process occurs slowly because the SMA wires in the

bundle are tightly packed.

3. COMPUTER SIMULATION OF JUMPING

ROBOT

We conducted several computer simulation sets in

order to verify the robot design and to determine the

optimal parameters for experiments with robot proto-

types. In the first simulation set, a parametric study is

performed to find a suitable sequence of SMA muscle

activations for each robot model. The second simulation

is used to compare the performance of the two models.

The third simulation is used to determine the effect of

foot length on the jumping height and distance.

Since the four-legged jumping robot models are

symmetric about the sagittal plane and the lateral

movement can be considered negligible, the jumping

robot can be considered as a 2D model with one rear leg

and one front leg attached to the body frame. The

simulation structure is constructed in the Working Model

2D (WM2D) software and the Matlab software. The 2D

equivalent models of the robot are built in WM2D,

which has the same configuration as the design models

shown in Fig. 2. The length and height of the models are

150 and 75 mm, respectively. The total weight is 70 g

and the weight of legs is about 20 % of the total weight.

It should be noted that the weight difference between the

two models is negligibly small. The length of links for

the rear leg of both models is 30, 45, and 25 mm from

top to bottom. Model A has a front leg that is composed

of two links of 55 and 40 mm from top to bottom. In

model B, the rear and the front legs are identical.

In all simulations, the friction coefficient between the

robot foot and the floor is set at 1 to prevent slippage.

The control logic is implemented in Matlab. WM2D and

Matlab are linked by the dynamics data exchange (DDE)

protocol. Fig. 3 shows the software structure of the

computer simulation. SMA wires in the design model are

represented by the rope elements in the simulation model

in WM2D. Based on the experimental results in Table 2,

the contraction of the SMA wires is approximated to a

reduced first-order polynomial or a line. The slope of the

Table 2. Experimental results for two types of SMA

wire connections.

Contraction

length

(mm)

Time for

contraction

(ms)

Time for

relaxation

(ms)

Serial SMA set 9 150 2500

Parallel SMA set 2.5 100 3500

Fig. 3. Simulation method of the four-legged jumping

robot: the robot model is constructed in Working

Model 2D (WM2D) and the control logic is

implemented in Matlab, and the two are linked

by the dynamics data exchange (DDE) protocol.


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line corresponds to the contraction speed of the wire. The

experiment results of the serial SMA set are applied to

simulation model A, whereas those of the parallel SMA

set are applied to simulation model B.

The first simulation aims to find an optimal activation

sequence of SMA wires for jumping, because the

coordination of muscle activations is expected to have a

significant effect on the jumping motion. We first

obtained basic principles from studies on human jumping

and tried to find an optimal sequence. Although it is

impossible to completely determine the activation

patterns of muscles involved in jumping, we can find

common results from studies of the motion sequence of

body segments for jumping [21-23,27]. Bobbert et al.’s

early study of human vertical jumping shows that a jump

starts with the movement of the trunk part about 330 ms

before the body is completely lifted off the ground. Then,

the motions of the thigh and shank are respectively

initialized 270 ms and 220 ms before lift-off. The foot is

found to change its rotation angle at about the same time

as the trunk. However, a significant change in the foot

joint angle starts just 150 ms before the lift-off moment

[20].

Although the motion sequence of body segments in

jumping is not directly related to the coordination of

muscle activation, it provides a clue about understanding

how to activate the muscles in a sequence to obtain the

desired jumping performance. To determine a suitable

sequence of muscle activation, we executed a parametric

study where the parameter is the sequence of activating

the SMA wires. The SMA wires are numbered from top

to bottom and from left to right. The parametric study for

a suitable sequence of muscle activation is based on

previous studies [21-23,27]. The motion sequence of leg

segments is clear: thigh, shank, and foot. However,

developing a proper sequence of the timing and number

of SMA contractions is critical.

Since SMA1 corresponding to GMAX is directly

connected to the thigh, it is reasonable to first activate

the wire to rotate the hip joint and then initiate the

motion of the body and thigh. However, a sudden

rotation of the thigh in the clockwise direction affects the

foot: the foot slips backward on the ground. This effect

can be eliminated by activating SMA2. Since SMA2

corresponding to RF is connected to the shank, its

contraction makes the shank rotate around the knee joint

in the counterclockwise direction. This rotation causes

the foot to move forward, which counteracts the

backward movement produced by the rotation of the

thigh. This suggests that SMA1 and SMA2 should be

activated at the same time. After SMA1 and SMA2 are

activated, the robot body starts to move upward and

forward while the position of the foot is kept unchanged.

When the robot acquires a sufficient amount of

acceleration, SMA3 corresponding to GAS is activated

to start the contraction. Since the foot is connected to

SMA3, the strong and fast contraction of SMA3 causes

the foot to rotate fast in the clockwise direction and lift

off the ground for jumping while SMA1 and SMA2 are

still active.

Table 3. Activation sequence of the SMA wires for

model A.

SMA1 SMA2 SMA3 SMA4 SMA5

Time (ms) -150 -150 -100 -130 -80

Speed (mm/s) 20 20 70 20 90

Table 4. Activation sequence of the SMA wires for

model B.

SMA1 SMA2 SMA3 SMA4 SMA5

Time (ms) -150 -150 -100 -130 -130

Speed (mm/s) 20 20 70 20 20

As a result of numerous trials based on the above

principles, we propose a sequence of SMA activation for

models A and B, as shown in Tables 3 and 4, respec-

tively. This sequence not only agrees with the rotation

pattern of segments but also produces the highest and

farthest jumping. The time shown in the table indicates

the moment at which the SMA wire is activated. The

stating time, 0 ms, is the moment when both toes lift off

the ground. The speed shown in the table indicates the

contraction speed of SMA wire. It should be noted that

SMA1 and SMA2 are activated 50 ms before SMA3, but

the contraction speed of the former SMA wires is much

slower than that of the latter. This guarantees that the

motion of the foot segment starts after that of the others,

and the speed of the foot segment increases quickly

immediately before the lift-off of the rear toe.

One important result found from the first simulation

set is that if the front and rear legs are activated

simultaneously, the robot should be able to perform a

vertical jump but not a forward jump. A forward jump

cam be performed only when the rear leg muscles are

stimulated before the front ones. Tables 3 and 4 show

that each SMA in the front leg is activated 20 ms after

the corresponding one in the rear leg. As a result, while

the rear leg SMA wires are activated, the front ones are

not activated yet. When only the rear legs are extended,

the motion of the robot body can be modeled as a

rotation around the temporary center at the end of the

front leg (see Fig. 4). The center of mass of the robot is

accelerated to move forward and upward. This motion

continues until the motion of the front leg starts. As the

motion of the front leg is added to the existing motion,

Fig. 4. Rotation of the robot body around the instantan-

eous center of rotation when the rear leg SMA

wires are activated and the front ones are not

activated yet.


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the robot can move forward. The simulation results

shown in Fig. 5 indicate that model A can achieve a

maximum height of 45 mm (60% of the robot’s height)

and a distance of 35 mm (25% of its length) in each jump.

Both the height and the distance were measured 400 ms

from the moment at which the first SMA wire was

activated.

In addition to the jumping height and distance, the

rotation angle of each segment of the rear leg is

measured, as shown in Fig. 6. In the figure, it should be

noted that the time origin is set at the moment when the

robot starts the flying phase. Since the rear toe lifts off

the ground about 30 ms before the front one, the data

after the lift-off moment of the rear toe is not considered

(shadow area). The change in the thigh angle α, shank

angle β, and foot angle γ are represented by the thin solid

line, dashed line, and thick solid line, respectively. Fig. 4

shows the angles α, β, and γ. The activation sequence and

time of each angle in the simulation are found to match

Bobbert’s data [20]. The rotations of the thigh and shank

start first. In the case of the foot angle, a significant

change is found at -90 ms, which is around half of the

time period from the first motion of the leg part to the

lift-off moment of the rear toe.

The second set of simulations was performed to

compare the performance of models A and B. In this

simulation, the activation sequence shown in Tables 3

and 4 are applied to models A and B, respectively.

Compared to the first simulation set, the major change is

in the front leg structure and the SMA wire connection

method. It is observed from this simulation that the

jumping distance can be improved by about 10% in

model B, which is shown in Fig. 7. However, the

improvement in the jumping height is negligibly small.

Considering the fact that model B entails the cost of a

more complicated structure, more difficulty in the

control, and larger power consumption, the two models

can be considered comparable.

The third set of simulation was performed to

investigate the effect of the foot length on the jumping

performance. It is inspired from studies that the shape

and length of the foot is another important factor that

affects the jumping distance and height [21-23,27]. It can

be observed from creatures such as frogs, kangaroos, and

rabbits that as the foot length increases, the animal can

jump farther. A longer foot increases the impact force

between the foot and the ground during jumping. As a

result more power can be generated for jumping [28].

We used model B for this simulation, where the foot

length ranged from 25 to 40 mm. Except for the foot

length, the other parts of model B remained unchanged.

The simulation results in Fig. 8 show that the increase

in foot length has a positive effect on the overall jumping

performance. Both the jumping distance and the jumping

height can be improved significantly with an increase in

the foot length, as shown in Fig. 8. Compared to the

results in the second simulation where the foot length is

25 mm, the jumping distance is 1.5 times larger and the

jumping height is two times higher when the foot is 40

mm long. This simulation result supports studies of the

relationship between the foot length and the jumping

performance. It also suggests a simple way to improve

the jumping performance when developing jumping

robots. However, there is a limit to the increase in the

foot length. As the foot becomes longer, the torque at the

ankle needs to be larger and the muscle power must be

sufficiently stronger to guarantee a jumping motion.

Distance (mm)

Time (ms)

Fig. 5. Jumping height (dashed line) and distance (solid

line) curve of robot model A.

Rotation angles (deg)

Time (ms)

Fig. 6. Rotation angles of the rear leg segments before

lift-off: thigh angle α (thin solid line), shank

angle β (dashed line), and foot angle γ (thick

solid line).

Distance (mm)

Time (s)

Fig. 7. Jumping heights and distances of simulation

models A (dashed line) and B (solid line).


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Jumping height (mm)

Time (s)

Fig. 8. Jumping heights of simulation model B: dashed line, foot length of 25 mm; solid line, foot length of 40 mm.

In the third simulation, we can explain the effect of the

foot length on jumping in terms of the joint angles during the jumping motion. The joint angles at the hip, knee, and ankle are denoted by θh, θk, and θa, respectively, in Fig. 9(a). Figs. 9(b) and 9(c) show the variation of the joint angles for the front leg and the rear leg for a foot length of 25 mm. The corresponding plots for a foot length of 40 mm are displayed in Figs. 9(d) and 9(e).

(a) Joint angles at hip, knee, and ankle denoted by θh, θk,

θa, respectively.


Time (s)

(b) Front leg with a foot length of 25 mm.


Time (s)

(c) Rear leg with a foot length of 25 mm.


Time (s)

(d) Front leg with a foot length of 40 mm.


Time (s)

(e) Rear leg with a foot length of 40 mm. Fig. 9. Variation of joint angles at hip, knee, and ankle in

computer simulation. If we compare the 25 and the 40 mm long foot models,

we find that the latter shows larger variations, specifically, an increase of 85%, 27%, and 36% for θh, θk, and θa, respectively, for the front leg and an increase of 117%, 45%, and 29% for θh, θk, and θa, respectively, for the rear leg. The latter model also shows a jumping phase


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for a longer time period, with an increase of about 50%. As a result of the significant increase in the joint rotation angles and the jumping time period, the 40 mm long foot model can be used to realize longer and farther jumping.

4. PROTOTYPES AND EXPERIMENTS

Two robot prototypes were fabricated using a CNC

machine to realize the design models and to verify the simulation results. Most parts are made of acrylic. Prototype A in Fig. 10(a) has ten MMF150 SMA wires as in the case of model A. Each SMA wire is approximately 200 mm long and is wound around pulleys in the form of a serial connection. The length, width, and height of the prototype are 150, 65, and 65 mm, respectively. The weight of the legs is approximately 20 % of the total weight of 80 g. In prototype B shown in Fig. 10(b), SMA wires are connected in a parallel connection. The length and height are equal to those of the first one, but the width is 50 mm, which is smaller by 15 mm. The weight is 65 gram.

The activation sequence of SMA wires for each prototype was set according to the simulation results shown in Tables 3 and 4. In order to control the activation period and contraction speed of SMA, a combination of pulse signals and PWM signal is used.

Fig. 11 shows the control signal for SMA wires. The pulse signal in Fig. 11(b) is a rectangular signal with a peak of 24 V and a width of 100–200 ms. The pulse signal is not continuous but is divided by the PWM signal in Fig. 11(a). The width of the pulse signal decides the contraction time of the SMA wire whereas the duty time of PWM controls the contraction speed.

A set of jumping experiments was conducted on a plywood plate. The robot prototypes were controlled using an off-board circuit. For both prototypes, three trials, each of which consists of five cycles, were executed. SMA wires were actuated during a cycle according to the activation sequence in Tables 3 and 4, i.e., Table 3 for prototype A and Table 4 for prototype B. The experimental results in terms of the jumping distance and jumping height are presented in Tables 5 and 6, where each value is the average value of the three trials.

Experimental results show that the average jumping distance and height for prototype A are approximately 25 mm and 5 mm, respectively. The total time from the start of jumping to landing is approximately 3 sec, more than 90% of which is taken up by the elongation time of the SMA wire. The jumping performance of prototype A is considered quite poor compared to the simulation results owing to fabrication problems. Since SMA wires are wound in several turns, it is difficult to keep the wires stretched when a voltage is not applied. As a result, the total contraction of the wires is reduced and the rotation of leg segments also decreases. Moreover, the strength of a single SMA wire is not large enough to generate force for jumping.

The overall jumping performance of prototype B was found to be better than that of prototype A. The second robot can jump forward by about 35 mm and upward by about 10 mm. This improvement is attributed to the parallel connection of SMA wires in prototype B, where a much larger force is generated by the SMA wire bundle

(a) Prototype A based on Model A.

(b) Prototype B based on Model B.

Fig. 10. Two robot prototypes.

(a) Primary PWM signal.

(b) Pulse signal.

(c) Control signal.

Fig. 11. Control signal for SMA wires.


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compared to the SMA wire of prototype A. However, the

time period for each jumping cycle is increased to 4 sec.

This is attributable to the cooling process of SMA wires.

The parallel connection of SMA wires makes the cooling

process of SMA more difficult. From the results in Table

5, it is also observed that both the jumping distance and

the jumping height of prototype A deteriorate as the

number of cycles increases. This is because the SMA

wires are cool and fully extended in the beginning, which

can make the contraction length of wires larger and the

jumping performance better. However, such a tendency

is not found in the experimental results of prototype B

(Table 6). This indicates that the jumping performance of

prototype B depends on the SMA contraction length

much less than does that of prototype A.

Although experimental performance of the robots is

not as satisfactory as the simulation results, they support

the design ideas for improving performance of SMA-

actuated jumping robots. First, the front leg with a long

foot in prototype B can help to obtain a larger jumping

height and distance compared to prototype A. This result

is quite compatible with the simulation result. Second,

the parallel connection of SMA leads to an improvement

in jumping performance, though the cooling time may be

slightly longer. Overall, model B is considered to be a

better choice for developing all SMA-actuated jumping

robots.

5. CONCLUSION

This paper reported the design, simulation, and

analysis of two types of four-legged jumping robots that

are actuated by SMA wires only. The robot design is

inspired by the musculoskeletal system of vertebrates.

The functions of monoarticular and biarticular muscles

are studied carefully and applied in a simplified fashion.

Among nine primary muscle groups, three (GMAX, RF,

GAS) are selected in the rear leg of robot models. Robot

models A and B are identical except for the structure of

the front leg: 2 DOFs in model A and 3 DOFs in model B.

Through parametric studies using computer simulation,

a suitable sequence of SMA muscle activation is

determined. The simulation results of model A show that

the maximum jumping height is about 60% of the robot’s

height and the maximum distance per jump is about 25%

of its length. The second set of simulations shows that

robot models A and B are comparable in terms of the

jumping performance and the complexity of the structure

and control. However, a simulation with different foot

lengths shows that both the jumping distance and the

jumping height can be improved significantly with an

increase in the foot length. When the foot length is

increased from 25 to 40 mm, the jumping distance

becomes 1.5 times larger and the jumping height

becomes 2 times higher. It can be concluded from the

three sets of simulations that the muscle activation

sequence, activation arrangement of rear legs and front

legs, and foot length are primary factors to determine the

jumping performance. Among the factors, the activation

sequence is considered the most critical one.

In addition, two robot prototypes that were fabricated

based on the design models are described and experi-

mental results are discussed. These prototypes are

different not only in terms of the structure of the front

legs but also the SMA connection method. Although the

simulation and the experimental results contain some

discrepancy in terms of the jumping height and jumping

distance, the tendency of the simulation results is

confirmed by the experimental ones. The overall results

show that the proposed robot design and SMA actuation

method provide feasibility for all SMA-actuated jumping

robots.

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Table 5. Jumping distance and jumping height of proto-

type A.

Cycle

#1

Cycle

#2

Cycle

#3

Cycle

#4

Cycle

#5

Jumping

distance (mm) 28.3 25.2 24.4 24.1 23.8

Jumping

height (mm) 6.1 5.3 5.1 5.1 4.2

Table 6. Jumping distance and jumping height of proto-

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#1

Cycle

#2

Cycle

#3

Cycle

#4

Cycle

#5

Jumping

distance (mm) 35.4 35.6 36.1 34.5 34.7

Jumping

height (mm) 10.8 10.2 9.3 11.1 9.5


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Thanhtam Ho received his B.S. degree from Mechatronics Dept. at Hochiminh City University of Technology, Vietnam and his M.S. and Ph.D. degrees in Mechanical Design and Production Engineering from Konkuk University, Seoul, Korea in 2005, 2008, and 2012, respectively. His research interests consist of the humanoid robot arm,

biomimetics robots, medical robot, lateral position control for the roll-to-roll printing system and computational simulation.

Sangyoon Lee received his Ph.D. degree in Mechanical Engineering from Johns Hopkins University in 2003. Since then, he has been a professor at Konkuk Uni-versity. His research interests include robotics, control, automation, roll-to-roll printed electronics, and robotics appli-cations to bioengineering.

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Design of an shape memory alloy-actuated biomimetic mobile robot with the jumping gait