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Figure 1. Structure of LIPCA.

A Cockroach-Inspired Hexapod Robot Actuated by LIPCA

Abdul A. Yumaryanto Dept. of Advanced Technology Fusion

Konkuk University Seoul, South Korea azis@konkuk.ac.kr

Jaebum Ana, Sangyoon Leeb

School of Mechanical and Aerospace Engineering Konkuk University Seoul, South Korea

apojec@konkuk.ac.kr, bslee@konkuk.ac.kr

Abstract—In this paper we present the design and prototype of a six-legged walking robot which uses Lightweight Piezoceramic Composite curved Actuator (LIPCA) as its actuator. LIPCA consists of multiple layers of glass/epoxy and carbon/epoxy that encapsulate a unimorph piezoelectric ceramic actuator. It uses lightweight fiber-reinforced plastic layers, and it is a lighter structure and generates a higher force and a larger displacement than other conventional piezo-composite type actuators. Like most six-legged walking insects including cockroaches, our robot uses the alternating tripod gait where the front and rear legs on the same side move together with the middle leg on the other side for its locomotion. Two LIPCA strips in different phases are used for actuating each tripod so that only one tripod may touch the ground. All the experiments with the prototype show that LIPCA can be used as an alternative actuator for small and light mobile robots.

Keywords—biomimetic robot, hexapod, piezoelectric actuator, walking robot

I. INTRODUCTION Piezoelectric materials are smart in a sense that they can

sense changes in the environment and make a response by changing their material properties, geometry, mechanical, or electromagnetic response. Such materials have been used in the robotics field as sensors [1] and actuators [2-4].

Recent developments of piezoelectric devices are unimorph-type actuators, in which a piezoelectric ceramic material is bonded to a thin metal sheet. The secondary material in such devices amplifies the axial displacement of the actuator by constricting the lateral motion. Examples of such types can be THUNDER and RAINBOW [5].

A piezo-composite actuator named LIPCA (Lightweight Piezoceramic Composite curved Actuator) was developed for the first time at Konkuk University in 2001. LIPCA consists of multiple layers of glass/epoxy and carbon/epoxy that encapsulate a unimorph piezoceramic actuator. The primary feature of LIPCA is the replacement of the heavy metal layers in THUNDER by lightweight fiber-reinforced plastic layers. Experimental results show that LIPCA can produce 60% larger displacement and is 40% lighter than THUNDER [6]. Among several versions of LIPCA, the latest version named LIPCA C2 is used in our work. The structure of LIPCA-C2 is shown in Fig. 1.

LIPCA device can be manufactured without adhesive layers since the epoxy resin plays a role of bonding material. A glass/epoxy fabric prepreg is placed as the bottom layer on a flat base plate and a PZT-5A ceramic wafer (0.25 mm thickness) with electrode surfaces and silver-pasted copper strip wires are placed on the glass/epoxy prepreg. A carbon/epoxy unidirectional prepreg and glass/epoxy fabric prepreg are stacked over the ceramic wafer in accordance with the lay-up design. The stacked layers are vacuum bagged and cured at an elevated temperature (177 ◦C) following an autoclave bagging process.

Promising features of LIPCA as an actuator are as follows: the lightweight (5g at 100 mm × 24 mm size) compared with electromagnetic motors or pneumatic actuators; the fast time response compared with SMA (shape memory alloy) or IPMC (Ionic Polymer-Metal Composite) actuators; and the high displacement compared with other piezoelectric actuators.

LIPCA has been applied as an actuator in various fields such as for flapping wings [7] and active vibration control [8]. This paper presents another application of LIPCA in robotics field and introduces a novel alternative actuator for a mobile robot. We use it for actuating a mesoscale (about 13 cm long), six-legged walking robot. Compared to a conventional-scale robot, a mesoscale robot has a limited design space. Therefore it needs a simple design approach and a lighter and smaller actuator like LIPCA than electromagnetic motors or pneumatic actuators.

Figure 2. Design of the robot: Both LIPCA strips are placed in the middle of the body. Slot consraints are connected to the body frame by revolute joints.

II. DESIGN AND PROTOTYPE OF THE ROBOT

A. Cockroach-inspired Design The walking mechanism of our robot is inspired by an agile

six-legged insect, cockroach. We analyzed the walking kinematics of cockroaches using a German cockroach (Blattala Germanica) and an experimental apparatus composed of a high-speed camera, a computer, and a homemade walking track.

It is observed that when a cockroach walks, it uses the alternating tripod gait where the front and rear legs on one side and the middle leg on the opposite side move concurrently. In addition, the front, middle, and rear legs do different functions while walking. The rear leg is used to thrust or accelerate the body while the front leg is used to decelerate the body. The middle leg has two functions: one is to decelerate and the other is to accelerate the body while stabilizing the body in the lateral direction. This result agrees with the experimental results in [9]. The tripod gait and the functions of each leg of cockroaches are reflected in the design of our robot.

B. Placement of the LIPCA Actuator Our six-legged robot is actuated by two LIPCA strips that

move in different phases as an actuator. Each LIPCA is used to move one set of legs for the alternating tripod gait where one

set of legs stroke on the ground while the other set swings above the ground.

Each LIPCA strip is placed in the body frame using simply-supported joints (see Fig. 2). One of the edges of LIPCA is hinge-jointed on the frame and the other uses a slider joint. By the application of a high AC voltage, the LIPCA strips move up and down alternately except the edges, which are constrained to the body frame. With this configuration the maximum vertical displacement occurs in the middle part of the LIPCA.

C. Transfer Mechanism and Leg Design We constructed two kinds of transfer mechanisms to

convert a LIPCA displacement into a stroke in order to realize a walking mechanism. The first mechanism is for connecting the middle part of LIPCA to the hip part of the leg and the second one is for joining the hip part and the foot. On the rear legs, the displacement of LIPCA is transferred using a slider-crank mechanism, which amplifies the displacement. The front and middle legs are directly connected without any amplification because they do not make a significant effect on the velocity. Theoretically the hip displacement of the front leg is equal to that of the middle one, while the hip displacement of the rear leg is larger than the displacement of LIPCA.

Figure 3. Slider-crank mechanism of the leg: This figure shows the amplification of the displacement from LIPCA ( 'pp − ) to hip ( dd −' ).

Figure 4. Stroke mechanism in the rear leg: The slot rotates in the same orientation of the leg while constraining point O in the horizontal and

vertical directions.

The amount of amplification can be calculated as follows:

''

ppddAmp

−−=

(1)

where

( ) ( )( )211

2211 cossin' θθθθ ∆+−−−∆+= LsLLd (2)

( )211

2211 cossin θθ LsLLd −−−= (3)

−

=∆ −−

qp

qp 'tantan 11θ (4)

All the parameters in the right-hand side of (2), (3) and (4) are known from the geometry of the robot (see Fig. 3).

To convert the vertical displacement of the hip into the horizontal and vertical displacements of the foot, a slot is installed between the hip and foot. The slot is connected to the body frame by a revolute joint. In Fig. 4, if the hip is lowered from A to A′ position, then the foot moves from B to B′. Since the slot (the point O) between the hip and the foot constraints the movement in the vertical and horizontal directions, the slot rotates in the same orientation of the leg because of the revolute joint.

The horizontal displacement (Bx – Bx′) of the foot creates a thrust for accelerating the body forward. The position of the slot has an influence to the displacement of the foot and the direction of the leg. We place the slot in various positions somewhere between hip and foot depending on the expected leg function. Because the function of the front leg is only a

stabilizer, the slot is placed slightly forward. For positioning the slot in the rear leg we used an optimization method (explained in the next subsection) in order to maximize the displacement in the horizontal direction. The orientation of the middle leg is between that of the front and that of the rear one.

D. Optimization The stroke of the rear leg mainly depends on the vertical

displacement of the slider in the slider-crank mechanism and the position of the slot. We need to optimize the position of the slot in order to obtain the maximum stroke in the horizontal direction. Here all the parameters are shown in Fig. 4 and Ax, Ay, Bx, and By are measured relative to the coordinate axis placed at the point O. The objective function to be maximized is as follows:

Figure 5. Various views of the robot with its dimension (in mm). There is asymmetry position between the middle leg in left and right side causing the robot to move imperfectly straight.

Figure 6. Prototype of the LIPCA robot. LIPCA is the largest part of the robot, thus its size influences overall dimension of the robot.

( )

( )

−

+−

−

++==−′ 11

2222yx

x

yx

xxxAA

LAArA

LAxfBB

(5)

The above function is subject to: mm20mm15 ≤≤ xA ; mm 55mm 10 ≤≤ yA , which comes from

limited design space , and mm 5 −≤−′yy BB , where

( )

( ) '

22

+++=

yx

yyArA

LrAB

,

+=

22yx

yyAA

LAB

(6)

The design variables to be calculated are Ax and Ay and the rest of the variables are known. The result of the optimization is that the slot should be placed 15 mm horizontally behind the hip (point A) and 23.3 mm vertically below the hip. This configuration will produce 8.7 mm in the backward stroke.

E. Prototype The main parts of the robot, except the actuator, are the

body frame, linkages, and legs. The body frame of the robot is made using balsa wood and all the linkages are made of 1.5 mm diameter carbon composite rod which has a high specific strength and stiffness. Therefore we can expect a good

performance with the application of a high frequency. The legs are made using metal rod to get a high impulse. The total weight of the robot is 35 grams and the dimension is 135 mm (length) × 55 mm (width) × 65 mm (height). The schematic view and the prototype are shown in Fig. 5 and Fig. 6, respectively.

Figure 7. Tripod gait shown in frame-by-frame stick figure of in the air: Three white triangles at the end of feet show one set of tripod actuated by the upper LIPCA and three black triangles (full line) show the other set actuated by the lower LIPCA. The pictures apparently show the leg movements which are

very small (in the order of mm) due to small displacement of the actuator. Horizontal lines are drawn as the reference line for the motion of each foot.

Figure 8. Experimental apparatus for robot walking

III. EXPERIMENTS AND RESULTS To measure the walking performance of our robot we

conducted several experiments. The experimental apparatus (Fig. 8) consists of an oscilloscope (EZ DS-1080C) and a power supply, high-voltage signal function generator (TD-2 Power Supplier, Face International Co.). Both LIPCA strips were driven with a square function of three separate voltages, with one LIPCA lagging the other by the phase of 180°. The actuator was excited by the power supplier with ±100V, ±150V, and ±200V (200, 300, and 400 V peak-to-peak respectively) at different operating frequencies (2, 10, 20, 30, and 40 Hz) for each voltage input. For each frequency we measured the speed three times and took the average value.

The robot uses the alternating tripod gait for walking (Fig. 7). Although the displacement of foot is very small (in the order of millimeter) it can produce a forward motion because of the configuration of six legs. Each tripod set of legs experiences two phases, swing phase (the state where a leg does not touch the ground) and stance phase (the state where a leg touches the ground), alternately. In locomotion on the ground, three legs push downward and act as support to ensure the other three legs move upward.

Fig. 9 shows the average speed of the LIPCA robot at several different frequencies and voltages. As the operating frequency increases, the alternating tripod gait frequency becomes larger, and thus the robot moves faster. The voltage of the power supply changes the displacement of LIPCA, and thus the rear leg stroke onto the ground becomes larger to increase the speed. At frequencies higher than 30 Hz, changing the voltage from 200 Vpp to 300 Vpp brought a larger effect on the velocity than the change from 300 Vpp to 400 Vpp. In this frequency with a high displacement (produced in 300 Vpp), the swing phase takes a longer time than the stance phase and in this condition increasing the displacement does not produce a severe change in the velocity.

IV. DISCUSSION AND CONCLUSIONS We have reported the design, prototype, and experiments of

a mesoscale, light, and agile walking robot, which is actuated by a smart material, LIPCA, and inspired by an agilely walking

insect, a cockroach. The experimental results show that LIPCA can be used as an alternative actuator for mobile robot applications.

Compared with MG3 [4] that was built at Vanderbilt University, our robot is slower at the same input frequency and voltage. However, unlike MG3 that has a frequency-based turning capability, our robot can walk straight at any frequency. This implies that our robot has a potential to increase the maximum speed with the application of a higher the frequency. In addition, the design that reflects the agile and stable walking kinematics of cockroaches is expected to produce a better performance in uneven terrains.

As a future work to improve the performance of the robot, we have several plans, some of which are already in progress. As for changing the mechanical configuration, we consider using the slider-crank mechanism for the front and rear legs and changing the supported joint of the LIPCA in the middle. The performance can also be enhanced by using a light and flexible cable and by adding more friction on the legs. The second prototype of our LIPCA-actuated robot and a light and

Figure 9. Performance of the robot for various applied voltages and frequencies

small power supply converter are under development, with the goal that the robot becomes a self-powered LIPCA-actuated robot. In the second prototype we also use two LIPCA strips as the actuator, but we place them in the middle instead of fixing them in the edges. Thus, the front and rear legs are directly connected to the edge of LIPCA without any amplification mechanism. The structure is also built stronger so that the robot can carry a power supply converter. We have completed a dynamic simulation of the second prototype, and it is expected to walk faster by 30 % than the first one in real experiments.

ACKNOWLEDGMENT The authors would like to thank Prof. Kwang Joon Yoon,

Prof. Taesam Kang, and Dr. Inpil Kang for helpful discussions. This work was supported by Korea Research Foundation Grant (Intensive Research Center Program 2004, KRF-2004-005-D00047) and the support is sincerely appreciated.

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