Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot

Journal of Bionic Engineering 6 (2009) 29–36

Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot Thanhtam Ho, Sangyoon Lee Department of Mechanical Design and Production Engineering, Konkuk University, Seoul 143-701, Korea

Abstract This paper presents the development of a mesoscale self-contained quadruped mobile robot that employs two pieces of piezocomposite actuators for the bounding locomotion. The design of the robot leg is inspired by legged insects and animals, and the biomimetic concept is implemented in the robot in a simplified form, such that each leg of the robot has only one degree of freedom. The lack of degree of freedom is compensated by a slope of the robot frame relative to the horizontal plane. For the implementation of the self-contained mobile robot, a small power supply circuit is designed and installed on the robot. Experimental results show that the robot can locomote at about 50 mm·s–1•with • the circuit on board, which can be considered as a significant step toward the goal of building an autonomous legged robot actuated by piezoelectric actuators. Keywords: piezoelectric actuator, quadruped robot, bounding locomotion, self-contained legged robot Copyright © 2009, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(08)60099-2

1 Introduction Recently the structure and function of biological systems have often inspired mobile robot researchers not only in the design of structural mechanism but also in the control architecture[1–3]. Though the concepts are quite attractive, the direct application of biological locomotion methods to robots is extremely difficult. Therefore, some extent of simplification in the design, for example, reducing the number of legs or degrees of freedom (DOF) should be taken into consideration. In addition to biomimetic concepts, new ideas of actuators have also been sought in the robotics community recently[4–7]. Instead of hydraulic, pneumatic or electromagnetic motors, smaller and lighter actuators are desired to reduce the size and complexity of mobile robots. An attractive way can be replacing conventional actuators by so-called artificial muscles. One of the smart materials that are considered to be suitable for mobile robot applications is the piezoelectric material. Goldfarb[4] and his colleagues developed a quadruped robot that is actuated by piezoelectrical actuators. The robot has the capability of self-powered operation, but lacks biomimetic design ideas. A crawling robot Corresponding author: Sangyoon Lee E-mail: [email protected]

developed by Sahai et al.[5] is another example of legged robots that are actuated by piezoelectric actuators. Their self-contained hexapod has a very small size with 35 mm length and a light weight of 3 g. Though it was designed to move in the alternating tripod gait, it was not verified by experiments. Yumaryanto et al.[6] reported three kinds of mesoscale, piezoelectrically actuated legged robots that run as fast as 173 mm·sí1. In spite of a bio-inspired mechanism design, the robots do not have the ability of locomotion in a self-contained form due to the weakness in the mechanism. It can be found from the robot examples above that the use of piezoelectric actuators can make a significant contribution to the reduction of the robot size and weight. However, creative ideas are required to design the mechanism of legged robots because of the low force and displacement of piezoelectric actuators. A combination of piezoelectric actuator and effective design ideas in the robot mechanism can be found in a bounding quadruped robot[7]. Experimental results show that the robot has a remarkable ability in terms of the locomotion speed (470 mm·sí1) and the payload (100 g). However it is not close to an autonomous mobile robot because it requires an external power source.

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Fig. 1 Three working phases of LIPCA.

The objective of our work in this paper is to develop a mesoscale, four-legged robot that is actuated by a sort of artificial muscle, Lightweight Piezoceramic Composite curved Actuator (LIPCA). LIPCA is made of a piezoelectric ceramic layer and other layers of glass/epoxy and carbon epoxy[8]. It can have the maximum displacement of 1.5 mm at the resonant frequency as shown in Fig. 1. The quadruped robot is designed to locomote by using two pieces of LIPCA without relying on any other conventional actuators. In addition, a small and light weight power supply and control circuit is developed that is fit for the robots. The experiments with the self-contained prototype show a clear feasibility toward an LIPCA-actuated autonomous legged robot.

consumption and total mass can be reduced. Fig. 3a illustrates the displacement transfer mechanism in the design. In Fig. 3, each robot leg includes two line segments denoted by BC and CD and the segments meet at C perpendicularly. The legs are attached to the robot frame at point K and can rotate around one vertical axis there. The crank rotates around a revolution joint at point I in the plane which is perpendicular to the line BC of the leg. When LIPCA moves vertically at point A, the crank rotates and generates a movement at point B. This movement is transferred to the leg, as a result. The end point D on the leg moves in the horizontal plane. Hence,

2 Materials and methods 2.1 Design of the robot Usually each leg of mobile robots has one to four DOFs and each DOF can be realized by one actuator. In general, the maneuverability of legged robots is proportional to the number of DOFs of robot leg. For a legged robot to show complex and agile maneuver, three or four DOFs may be necessary for each leg, which entails several actuators per leg, a large amount of energy consumption, and a higher complexity of control. As shown in Fig. 2, a couple of leg configurations can be found from biological creatures. Compared with the legs of mammals, insect legs generate a less thrust force, and so the power of actuators should be used more effectively. The design of robot leg in this work is inspired by insect legs, but implemented in a simplified way. That is, each leg has a hip joint only, which helps us simplify the robot mechanism significantly. Fig. 3 shows the design concept of the robot leg. In the design of the quadruped robot, one LIPCA piece actuates two legs in which the motion of LIPCA is transferred to the leg by means of a crank. Therefore, only two pieces of LIPCA are required to actuate four legs of the robot such that the energy

(a) Typical insect leg (modified from Ref. [9])

(b) Mammal leg (modified from Ref. [10])

Fig. 2 Insect and mammal legs.

Ho and Lee: Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot

the mechanism not only transfers motion from the actuator to the leg but also converts the motion. As a result some movements can be generated from the leg. Fig. 3b displays the relationship of the displacement of LIPCA and the displacement of robot leg: the maximum displacement of LIPCA at the resonant frequency is about 1.5 mm, which is amplified to 3 mm displacement with 5 degree rotation range by means of the transfer mechanism.

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making a pair of legs in such a way, we can reduce the number of actuators for the locomotion. The pattern in the bounding gait is also simple because only four steps are required for one locomotion period (see Fig. 4). Such a simple moving pattern can make the leg and the whole mechanism simple. The control work can also become less complicated for robots to attain this gait.

Fig. 4 Bounding gait of a Siberian (modified from Ref. [11]).

(a)

A

I

B

C

K

LIPCA displacement Crank rotation D Leg movement

(b)

Fig. 3 Transferring and amplifying mechanism (modified from Ref. [7]).

In the study of animal motions, the locomotion gait is the arrangement of the feet when animals move. Among several gaits, the bounding gait in Fig. 4 is considered to be suitable for a mesoscale robot because of the following reasons. In the bounding gait, two rear legs have the same movement and two front legs do too. By

Using one DOF per leg can lead to a simple design, but more careful consideration is necessary for driving the robot to move forward. Usually, at least two DOFs are required for each leg in order to implement both lifting and swinging. For example, one DOF can be used for swinging the leg but it cannot lift up the leg from the ground at the same time. One of the first research works in reducing the number of DOFs in each leg was presented by Buehler and his coworkers in Scout quadruped robots. In Scout I[12], each leg has only one DOF and four servos are used to realize the motion of the legs. The robot has the ability of walking, turning and climbing by using the controlled momentum transfer. In the second version, Scout II[13], a passive element spring is added to each leg for the compliance. The reliability of the system is increased by this modification. These works are good examples of one DOF leg robot system, but the control methods to achieve the motions are still complicated. The control methods can be suitable for a large system like Scout robots but are not applicable to a mesoscale robot like ours. The problem could be solved in our robots by making a difference of the lengths of front and rear legs. Fig. 5 shows how this angle can contribute effectively to the forward movement. The principle is as follows: the leg moves in a plane parallel to the robot frame (with an angle Į to the floor in Fig. 5). Hence, in Fig. 5, when the leg moves to the left, the tip of foot leaves the floor; this behavior is similar to lifting the leg up off the ground. When the leg moves to the right, the tip contacts the floor and generates a pushing force, which enables the robot to move forward.

Journal of Bionic Engineering (2009) Vol.6 No.1

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It is clear that the robot has five DOFs. When x denotes the state vector whose components are DOFs of the robot, the vector x can be written as follows:

x

>Mr , xr , yr , Mf , D @

T

.

(1)

The position coordinates of the robot body are Upward Ground noncontact

Į

p [ x, y ]T , pf Downward Ground contact Contact point

Į

Fig. 5 Robot frame angle (Į) and the tip of the leg[7].

2.2 Analysis and implementation The kinematic analysis of the bounding quadruped robot is conducted based on the following assumptions: rigid legs, frictionless joints, slipless contact between the leg and the floor. Since the robot contains two pairs of legs and each pair is driven by one LIPCA, two sides of the robot configuration are symmetric. Therefore, it is possible to consider the robot as a 2-D model with one rear leg, one front leg and a body frame. The center of gravity of robot (or center of the robot frame) has only a planar motion due to the symmetry of bounding model while the legs include one rotation. Fig. 6 shows the top and side views of the robot design, while the rotation of each leg can be observed in the top view, the side view shows the 2-D kinematics model of the robot.

[ xf , yf ]T , pr

[ xr , yr ]T .

(2)

Here p, pf and pr are position coordinates of the robot body, the front leg, and the rear leg respectively. And ijr and ijf are rotation angles of the rear and the front leg and Į is the slope angle of robot frame. The position of the robot body can be determined by the components of state vector, p

ªxº « y» ¬ ¼

ª xr º ªsin M r cos D º ª  sin D º ªcos D º « y »  lr « cos D »  r « sin M sin D »  L « sin D » ¬ ¼ ¬ ¼ ¬ r¼ ¬ ¼ r

(3) The velocity of the robot can be calculated by taking the derivatives of position vector. The velocity of the robot body is p

ª x º « y » ¬ ¼

Ex ,

(4)

where the matrix E is the Jacobian E

ª r cosM r cos D « ¬  r cos Mr sin D

1 0 0 r sin M r sin D  lr cos D  L sin D º 0 1 0 r sin Mr cosD  lr sin D  L cosD ¼»

(5) In order to verify the design ideas, a bounding prototype was fabricated using acrylic material based on the design shown in Fig. 3. In the bounding prototype, the upper LIPCA is connected to the two rear legs and form one pair, and the lower LIPCA and the front legs form the other pair. The weight of the prototype is about 50 g and the length, width, and height are 120 mm, 115 mm, 75 mm, respectively.

Fig. 6 Kinematic model of the bounding robot.

2.3 Power electronics For building a self-contained mobile robot, a small and light power supply circuit is required. In addition to meeting the dimension requirements, it must be able to produce a high output voltage and drive LIPCA with a little distortion in the output voltage. LIPCA consists of multiple layers of glass/epoxy, carbon/epoxy, and a unimorph piezoelectric ceramic

Ho and Lee: Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot

Fig. 7 LIPCA impedance.

It was verified for the operation of robots that the most suitable frequency applied to LIPCA is between 40 Hz and 50 Hz. However, the impedance of LIPCA is very small in the range while the applied voltage is still kept high (about 370 V peak-to-peak). As shown in Fig. 7, the LIPCA impedance in this frequency range is only about tenth of that at 0 Hz, as a result, the increase in current and overloading occur. Increasing internal resistance of the power supply may prevent the overload. But since the LIPCA works like a capacitor, the hysteresis in RC circuit becomes significant. The distortion appears in the output voltage signal and LIPCA may not work properly. So the primary requirements of the power supply for the LIPCA robot is not only light weight and high output voltage but also less signal distortion (small internal resistance). Several attempts have been made to solve the problem, and one of them is a hybrid converter using a boost converter with a cascaded charge pump[14], which was used for the microbot[5]. The advantages of this method are that the circuit is very light (30 mg) and is possible to provide a fairly high voltage (250 V). However, the drawbacks are that the circuit is very complicated and its power is not enough for big piezocomposite actuators such as LIPCA. Another approach is using transformer, a PICO DC-DC converter chip.

Some advantages are that we can obtain a high voltage and high power output with a light weight. Among various PICO converters, the 5AV250D converter is most suitable for our requirements. The plug-in package chip uses 5 VDC input and generates dual DC ±250 V output. It is also simple, stable, and light (4 g). Fig. 8 shows the diagram of the power supply. The circuit is separated into two sides: low voltage and high voltage. In the left side, the control work and signal generation are performed while the right side creates a high voltage and amplifies the signal to generate high voltage signal for LIPCA. In the power supply and control electronic circuit for the robot, we used six PICO chips in order to increase the power of high voltage source so as to reduce the overloading. A smaller internal resistor is set, and the distortion is decreased. The circuit incorporates an ATmega128 microcontroller chip as the Pulse Width Modulation (PWM) module and controller. We also use a high voltage operational amplifier APEX PA97 which is particularly designed for capacitive loads instead of traditional driver topologies such as H-Bridge in order to simplify and stabilize the circuit. The complete circuit is shown in Fig. 9.

Isolator

Impedance (Komh)

actuator. The piezoelectric ceramic layer of LIPCA takes the most important role, and it provides the impedance property of LIPCA. Experiments were performed to determine the impedance of LIPCA and the result is displayed in Fig. 7. Experimental results show that the impedance of LIPCA has capacitive characteristics, and it decreases fast with the increase of applied frequency.

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Fig. 8 Diagram of the power supply.

Fig. 9 Power supply for LIPCA robot.

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3 Results and discussion

Velocity (mm·sí1)

Numerous experiments were conducted on a flat plywood panel to evaluate the performance of the prototype. In the first set of experiments, an external power supply and an oscilloscope were used to supply a high voltage and measure the frequency of AC voltage. A square signal voltage was used because it could produce more power and a higher displacement of LIPCA than ramp or sine signals. LIPCA was actuated by about 370 Vpp signal with the frequency in the range of 5 Hz and 80 Hz, beyond which the prototype cannot move properly. The first set of experiments is for measuring the locomotion velocity at different frequencies. We excited the LIPCA pieces of each prototype and measured the time for the robot to move to the end on the track. By changing the frequency, we could get the velocity data of the prototypes at various frequencies. Fig. 10 shows the velocity data of the bounding prototype.

The second set of experiments was applied to the bounding prototype in order to find out how much load it can carry. After attaching an additional payload to the bounding robot, we had it run the whole track and measured the time. From these experiments, the maximum payload of the bounding prototype was found to be about 100 g. The bounding prototype has the ability to carry an additional load up to 100 g at the speed 67 mm·sí1. The last set of experiments is for testing the locomotion capability of the robot with the 75 g power circuit on board (see Fig. 11). It is found from the experiments that the bounding prototype is able to carry the power supply and move at about 50 mm·sí1. With a 300 mA Lithium-Polymer battery as the main power source, the robot can move constantly for about five minutes. Fig. 12 shows a sequence of pictures that illustrate the self-contained locomotion of the robot.

Fig. 10 Velocity of the prototype for different frequencies[7].

Fig. 11 Bounding prototype with the power supply circuit on board.

Fig. 12 Motion of the self-contained quadruped robot.

Ho and Lee: Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot

4 Conclusion

discussions.

The design, analysis, prototype, and experimental results of an LIPCA-actuated self-contained quadruped robot are reported in this paper. The key feature of the robot is that it is actuated by a smart material, LIPCA, without any conventional actuators. The design of the robot leg is inspired by the leg structure of biological creatures in a simplified way. Since each leg is designed to have only one DOF, the robot has a simpler mechanism and the power of actuators is used efficiently. The most general locomotion type of quadrupeds, bounding is employed in the prototype. In addition to design characteristics, a small power supply and control circuit is developed that is fit for the robots. The experiments on the self-contained prototype show a clear feasibility toward an LIPCA-actuated autonomous legged robot. This success can also extend the possibilities of LIPCA in other applications. However some weak points need to be improved to achieve the goal: first the speed of the robot is still slow, second the five minute working time of battery is short for a mobile robot to perform useful missions, and third the bounding robot does not possess the ability of turning motion due to the symmetric configuration. Hence as our future work, we consider the application of more biomimetic ideas to the robot design for a better performance and also consider the change of the material into lightweight and strong composites. In addition we are planning to optimize the design by doing parametric analysis in a similar way as in Ref. [15]. Since the bounding prototype cannot move backward, the turning ability should be essential for obstacle avoidance. We expect that a minor design change in the body and legs can provide the robot with the turning ability. As the actuator LIPCA is in the process of downscaling, we also expect the development of a smaller version of LIPCA-actuated legged robot. Overall the bounding prototype can be considered as an important step toward building a fully autonomous mobile robot actuated by unconventional actuators.

References

Acknowledgements This work was supported by Korea Research Foundation grant (KRF-2006-005-J03303) and Seoul R&BD Program. The authors are grateful to Prof. Kwang-Joon Yoon and Prof. Tae-Sam Kang for helpful

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