low-pressure air motor for wall-climbing

Low-pressure air motor for wall-climbingrobot actuation

Yi Zhang a,*, Akira Nishi b,1

a Center for Manufacturing Research, Tennessee Technological University, Box 5077, Cookeville,

TN 38505-0001, USAb Miyazaki Study Center, The University of the Air, 11-11 Hyuga, Miyazaki 883-8510, Japan

Received 3 July 2000; accepted 20 June 2001

Abstract

A low-pressure rotary-type air motor is suitable to use for a wall-climbing robot, as it has

good performances and lightweight and so on. The prototype of the low-pressure air motor

has been developed in Miyazaki University, Japan. It is mainly composed of a pair of impellers

and the corresponding casings, a switching valve and a shaft. The two impeller-casing pairs are

designed to drive the motor shaft to turn in opposite directions. The input airflow is derived

with the switching valve to drive one of the two impellers, and thus by alternating the valve

position the rotational direction of the air motor shaft can be reversed. This paper presents the

mechanism, the static and dynamic characteristics of the air motor, as well as the velocity and

position controls in actuating systems.

� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Air motor; Rotary-type air motor; Pneumatic actuator; Wall-climbing robot; Robot control

1. Introduction

Many types of wall-climbing robots have been developed for the purposes of

inspecting, cleaning, fire fighting on wall surfaces [1–4]. If a robot is required to work

in a large area, it is desirable that the robot is self-powered. The most commonly

used power plant is the DC power source, in which case the trade-off betweenthe weight and the sustainable time of battery exists. For a wall-climbing robot

Mechatronics 13 (2003) 377–392

*Corresponding author. Tel.: +1-931-372-3133; fax: +1-931-372-6345.

E-mail addresses: [email protected] (Y. Zhang), [email protected] (A. Nishi).1 Tel.: +81-982-53-1893; fax: +81-982-53-1898.

0957-4158/03/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

PII: S0957-4158 (01 )00047-2

mail to: [email protected]

employing suction cups to attach itself on a wall [1] as shown in Fig. 1, one or two

blowers are employed to produce negative air pressures inside the cups. For these

kinds of robot, low-pressure air from the blower driving with small engine carried by

the robot is a power source that can be utilized for pneumatic drive.

Nomenclature

a constant used in the PI-controller

c constant used in the adaptive controller

eðtÞ voltage induced in the DC motor

En Laplace transform of the rotational-speed error

Et Laplace transform of the angular-position error

GAðsÞ transfer function of the air motor

i current passing through the generator (DC motor)J moment of inertia

k steady-state gain

Kb second constant of proportionality of the DC motor

Km torque constant of the DC motor

Kn slope of the approximating line in the T–n diagram of the air motor

Kp proportional constant of T0 and pKs constant gain of the PI-controller

Kt constant gain of the adaptive controllerKv constant gain of the butterfly valve

L output power of the air motor

n rotational speed of the air motor

N Laplace transform of rotational speed of the air motor

ni ideal rotational speed of the air motor

Ni Laplace transform of the ideal rotational speed of the air motor

p inlet air pressure of the air motor

Q air volume flow rateRs armature resistance

R resistance of the variable electric resistor

s operator of Laplace transform

t time

T output torque of the air motor

T0 linearly approximated torque of the air motor when n ¼ 0

Ti torque generated by the current through the generator

v input voltage of the servo unit of the butterfly valvea butterfly valve angle

h angular position

hi ideal angular position

g efficiency of the air motor

s time constant

378 Y. Zhang, A. Nishi / Mechatronics 13 (2003) 377–392

Air-powered motors generally have the advantages of low cost, good power-

to-weight ratio, and intrinsically safe operation [5]. These characteristics are very

suitable and important to be applied as a standard in selecting the driving compo-

nents of a wall-climbing robot, especially for the self-powered walking types. Note

that when a motor is used on a self-powered robot, not only the weight of the motor

but also that of the power supplier of the motor must be taken into account in

evaluating the power plant. The well-known types of air motors are vane motors [6]and radial piston motors [7,8], which usually consume high-pressure compressed air.

Some wall-climbing robots employ artificial muscles which also consume high-

pressure air power [4]. If these kinds of motors or actuators are adopted on a

self-powered robot, the robot will have to carry an air compressor to provide high-

pressure air to the motors or actuators. Due to the heavy weight of the air

compressor, these kinds of air motors are not suitable to drive a self-powered wall-

climbing robot.

The lower-pressure air motor introduced in this paper has the advantage of beingable to utilize the power of the airflow from the blower vacuuming the suction cups

so that it does not require additional power suppliers. The prototype of the air motor

was developed in Miyazaki University, Japan, and its debut was on a poster session

of the JSME Annual Conference on Robotics and Mechatronics in 1997 [9]. Since

then, the performance of the air motor has been assessed with experimental methods

in our studies. A computer-integrated test-bed has been established to perform the

experiments. Similar to other studies of air motors [8], step and sinusoidal input

signals were used to evaluate the dynamic characteristics. In the velocity control, thecommonly used PI algorithm [10] has been applied and proved to be adequate.

Position-control experiment has been carried out on a test-bed being composed of a

single-degree-of-freedom (1-DOF) arm and its adaptive control system using the air

motor.

Fig. 1. An air powered wall-climbing robot.

Y. Zhang, A. Nishi / Mechatronics 13 (2003) 377–392 379

The following sections of this paper address the mechanism, the static and dy-

namic characteristics, and the velocity and position controls of the air motor in

actuating systems. The experimental results will also be given.

2. Low-pressure air motor and its static characteristics

2.1. The structure and features of the air motor

Fig. 2 is the sketch diagram of the low-pressure air motor. It is mainly composed

of a pair of impellers and the corresponding casings, a switching valve and a shaft.

The two impeller-casing pairs are designed to drive the motor shaft to turn in op-

posite directions. The input airflow is derived with the switching valve to drive one of

the two impellers, and thus by alternating the valve position the turning direction of

the shaft can be reversed. Several different sizes of impellers and casings, and dif-

ferent shapes and sizes of the blades of the impellers have been fabricated and tested.

The influences of these factors on the static characteristics of the motor have beeninvestigated. In selecting the air motors, higher maximum efficiency and appropriate

inlet air pressure to obtain the required output torque and rotational speed are the

main criteria. Based on the experimental results, the suitable dimensions of the

Fig. 2. Air motor.


impellers, blades, and the casings were selected as follows to drive a biped wall-

climbing robot model which was originally driven by DC motors [1]:

• The inlet radius and the outlet radius of the impellers are 50 and 16 mm, respec-

tively.

• There are 12 blades on each impeller, and each of them has a plane trapezoidal

shape whose dimensions are 10 (top width)� 20 (bottom width)� 40 (height)

(mm). Then they are curved to a 25 mm radius on the surface of a cylinder.

• The dimensions of the air motor case are 120 (width)� 170 (height)� 62 (thick-

ness) (mm).

• The weight of the air motor depends on the dimensions and materials of the airmotor. The weight of the air motor introduced in this paper is 576 g. Currently,

the impeller is made up of aluminum, and the casing is made up of carved wood

blocks and polycarbonate plates.

• The volute curve of the casing is Archimedes’s spiral.

Sizes can be varied to fit the available air pressure and the required output-power.

2.2. Static characteristics

A test-bed shown in Fig. 3 was constructed to test the static and dynamic char-

acteristics of the air motor. A DC motor acting as an electric generator was used to

exert a torque load on the air motor. During the experiments, the torque load T

applied to the air motor was adjusted by adjusting the variable electric resistor

connected to the generator. The torque T and the corresponding rotational speed n

were measured with a strain gauge and a tachometer, respectively. Pressure sensor 1

was used to measure the inlet pressure of the blower for the purpose of calculating

the volume flow rate. Pressure sensor 2 was used to measure the inlet pressure of the

Fig. 3. A test-bed of air motor.


air motor, which could be adjusted with the butterfly valve controlled by servo motor

1. Servo motor 2 was used to drive the switching valve.

Fig. 4(a)–(c) show the characteristics of the torque T, power L and efficiency g of

the air motor, respectively. Note that the plots presented in Fig. 4(c) are also basedon the same amount of data from the experiments as that in Fig. 4(a) and (b). As

shown in Fig. 4(a), the T–n relations can be approximately represented by a set of

straight lines corresponding to a set of constant air pressures. Each line can be ex-

pressed with an equation in the following form:

T ¼ T0 � Knn; ð1Þin which Kn corresponds to the slope of the line and is almost the same for eachapproximating line, and T0 is the torque corresponding to the point of intersection of

the approximating line with the T axis. T0 varies with the static pressure p at the inlet

of the air motor, and their relation can be approximately described as

T0 ¼ Kpp; ð2Þin which Kp is a proportional constant. This tendency is almost the same as a DC

motor, and it is suitable for a robot actuator. The output power L of the air motor is

calculated by

L ¼ pnT=30: ð3Þ

%

(a) (b)

(c)

Fig. 4. Static characteristics: (a) torque; (b) output power; (c) efficiency.


The efficiency of the air motor is evaluated with

g ¼ ðL=pQÞ � 100%; ð4Þwhere Q is the volume flow rate of the air supplied to the motor.

Experimental results show the maximum efficiency of 32% and the maximum

output power of 32 W when the input air pressure is 650 mm Aq (see Fig. 4(b) and

(c)). Therefore, the power-to-weight ratio is 32 W=0:576 kg ¼ 55 W=kg. Higher

power-to-weight ratio may be obtained by manufacturing the higher-efficiency

motor with lighter-weight casing. This issue will be discussed more in Section 6.

3. Dynamic characteristics of the air motor

3.1. Equation of motion of the system consisting of the air motor and its loading device

The test-bed shown in Fig. 3 was also used to test the dynamic characteristics of

the air motor. Suppose the generator (a DC motor) is driven by the air motor at

rotational speed n, voltage e and current i will be induced correspondingly in thecircuit being composed of the generator and the resistor [10]

eðtÞ ¼ KbnðtÞ; ð5Þin which Kb is a second constant of proportionality of the generator [10]. n and e are

the functions of time t because of their dynamic status, and

iðtÞ ¼ eðtÞ=ðRþ RsÞ; ð6Þwhere Rs is the armature resistance, and R is the resistance of the variable electric

resistor. The corresponding torque generated due to the current iðtÞ is [11]TiðtÞ ¼ KmiðtÞ ¼ KmKbnðtÞ=ðRþ RsÞ; ð7Þ

in which Km is the torque constant of the generator. Assuming negligible friction, the

equation of motion of the rotating part of the system can be obtained as followsaccording to Euler’s equation [12]

p30

� J dnðtÞdt

þ KmKbnðtÞRþ Rs

¼ KppðtÞ � KnnðtÞ ð8Þ

or

p30

� J dnðtÞdt

þ KmKb

Rþ Rs

�þ Kn

�nðtÞ ¼ KppðtÞ; ð9Þ

where J is the total moment of inertia of the rotating parts of both the air motor and

generator. pðtÞ, nðtÞ, T ðtÞ are used instead of p, n, T for the reason that they vary with

time t in the dynamic state. Eq. (9) is a first-order differential equation relating ac-

tuator input pðtÞ and output nðtÞ. Its time constant s is [13]

s ¼ p30

JKmKb

Rþ Rs

��þ Kn

�ð10Þ


The steady-state gain [13] of the system is

k ¼ Kp

KmKb

Rþ Rs

��þ Kn

�: ð11Þ

Eq. (9) can be expressed in a standard form as

sdnðtÞdt

þ nðtÞ ¼ kpðtÞ: ð12Þ

Eq. (12) establishes a relationship between the air pressure and the rotational speed

of the air motor. It also provides us with the equation describing the input–output

relation of the plant for the control of the air motor. It is not difficult to prove thatthe form of this equation is also suitable when a mechanical load is applied to the air

motor instead of the electric loading device, though the time constant and steady-

state gain may be different.

3.2. Step response

As shown in Fig. 3, a butterfly valve was used as the pressure control mechanism

in the test-bed. Its performance-test results show that it has the advantages of being

easily driven with a micro servo motor and being approximately linear in a wide

range of about 50� about the butterfly axis. Since there is a total of 90� between the

opened and closed positions of the valve, there are another 40� remaining outside the

linear range. However, the variation of the air pressure within the nonlinear regions

of the valve is negligible, and only the approximate linear region was used in theexperiments. With this valve and its controlling servo motor, the air pressure can be

controlled.

In the step-response experiment, the butterfly valve was turned on at the moment

when t ¼ 0 to generate an approximate step input of the air pressure. The corre-

sponding step responses of rotational speed n and torque T are displayed in Fig. 5(a)

and (b), respectively. In the experiment, the resistance of the variable electric resistor

was fixed to be constant, so that the torque load exerted on the air motor was

generally proportional to the rotational speed of the air motor. The same loadcondition will be applied in the following sections in the cases where the same

loading device is used.

A time lag of about 0.2 s can be found near t ¼ 0 in Fig. 5(a) and (b), and it is

caused partly by the time needed to establish a constant air pressure powering the

motor. The actual air pressures were measured and are shown in Fig. 5(c). Theo-

retically, the step response of the system described by Eq. (12) which is a first-order

differential equation should be [13]

nðtÞ ¼ kð1� e�t=sÞ: ð13Þ

Hence, we can estimate the time constant s and the steady-state gain k of the system

from the experimental results of step responses. However, it has been found to be

difficult to make an accurate estimation because the input actuating air pressures

were not exact step signals.


3.3. Frequency response

The butterfly valve made the sinusoidal fluctuations in the experiment of the

frequency response. The same loading device introduced in Section 3.2 was used to

apply a torque load on the air motor. The steady-state responses of the rotational

speed n and torque T were recorded. Fig. 6(a) and (b) show the frequency responses

corresponding to the sinusoidal inputs with frequencies of 2 and 1 Hz, respectively.

Note that the curves in Fig. 6 were plotted faithfully according to the massive dataobtained in the experiment. We can find from either Fig. 6(a) or (b) that the air

pressure p at the inlet of the air motor approximately follows the sinusoidal function

with a small phase lag. Obvious phase delays and steady-state gain variations can be

found from both of the speed and torque responses. The time constant s and steady-

state gain k of the system can be estimated from the two sets of responses given in

Fig. 6.

As shown by Eq. (10), the time constant is determined by the parameters of both

the air motor and its loading device, such as the moment of inertia. Loads withdifferent moment of inertia will result in different time constants of the system. In the

experiment, a time constant as small as 0.13 s was obtained, and a 2 Hz sinusoidal

velocity was easily practiced, as shown in Fig. 6(a).

3.4. Inverse response

In the inverse-response experiments, while the shaft of the air motor was rotat-

ing at a constant speed, the angle of the switching valve was alternated and the

Fig. 5. Step responses of the air motor: (a) rotational speed; (b) torque; (c) inlet air pressure.


corresponding moment was taken as t ¼ 0. Thus, the airflow was conducted to drivethe impeller on the opposite side of the originally driven one. As a result, the ro-

tational speed of the air motor gradually dropped down to 0 and then began to

rotate inversely. In about one second, the transient response of the speed variation

(a)

(b)

Fig. 6. Frequency response of the air motor: (a) 2 Hz; (b) 1 Hz.

0 0.5 1 1.5 2

-3000

-2000

-1000

0

1000

2000

3000

1000 rpm.

1500 rpm.

2000 rpm.

2500 rpm.

3000 rpm.

t (s)

n (r

pm

.)

Fig. 7. Inverse responses of the rotational speed.


completed and the motor rotated at a constant inverse velocity. In the experiment,

the same loading device being introduced in Section 3.2 was employed. A set of

corresponding inverse responses of the rotational speed is shown in Fig. 7.

4. Rotational-speed control of the air motor

4.1. Control strategy

Based on the test-bed in Fig. 3, a rotational-speed control system was imple-

mented together with a computer. Fig. 8 shows the block diagram of the system.

When an ideal rotational speed ni of the air motor is designated through the key-

board input, the computer calculates the suitable valve angle of the servo valve (the

butterfly valve), which controls the inlet air pressure of the air motor. According to

the calculated valve angle, the computer sends a voltage signal v to the valve control

unit, which is a (Futaba) micro servo motor adjusting the angle of the servo valve.The actual rotational speed n of the air motor is measured by a tachometer whose

output is in the form of pulse signal, and the result is fed back to the computer

through a PIO board. Then, the computer calculates the difference between the

actual rotational speed n and the ideal rotational speed ni, and decides the new valve

angle by following the PI control law. The block diagram showing the PI control

algorithm is displayed in Fig. 9.

Fig. 8. Rotational-speed control of the air motor.

+

Fig. 9. PI control of motor speed.


4.2. Experimental results

Fig. 10(a)–(d) show a group of experimental results of constant, sinusoidal and

trapezoidal rotational-speed controls. Generally, constant, sinusoidal and trapezoi-

dal velocities were traced successfully. However, we should also indicate that:

(a) in constant speed control, it takes obviously different amounts of time ð0–6 sÞto follow different constant targets from a stationary state (Fig. 10(a));

(b) suitable sinusoidal speed control can only be realized when the frequency ofthe target is low, such as 0.2 Hz (Fig. 10(b));

(c) obvious disturbance exists in the results.

5. Position control of a 1-DOF arm

A further experiment was carried out on a 1-DOF arm and its control units. Asshown in Fig. 11, the air motor was used to drive the 1-DOF robot arm through a

reduction gearbox including a worm gear set with self-locking property. The re-

duction ratio from the motor shaft to the arm shaft is 14 400. Control signals were

originated from a computer and sent to a transmitter through a D/A converter. The

Fig. 10. Speed control of the air motor: (a) constant speed; (b) 0.05 Hz sinusoidal speed; (c) 0.2 Hz

sinusoidal speed; (d) trapezoidal speed.


signals were received by a receiver and sent to the two micro servo motors driving the

butterfly valve and the switching valve, respectively. The angular position of the arm

was measured with a potentiometer and sent to the computer through an A/D

converter as feedback. The angular velocity was calculated on the computer and used

as additional feedback.

An adaptive control technique was used in the angular-position control of the

arm. Fig. 12 shows its block diagram. Gain Kt between the angular-position error Et

and the valve angle a is constant, while gain ‘‘c=n’’ is an inverse proportion of theangular velocity of the arm. The switching valve alternates whenever the angular

error varies from plus to minus or from minus to plus. Fig. 13 shows the results of

the experiments in which the robot arm moved from an initial position to three

different target positions when the payload was set to 3.0 kg at the distance of 0.8 m

from the fixed pivot of the arm. It can be observed that less than 5 s is needed in the

Fig. 12. Angular-position control strategy.

Fig. 11. A 1-DOF arm and its control units.


adjustment of the arm to stop at the target position from the moment when it sur-

passes the target position for the first time.

Note that by using a worm gear set with self-locking property in the power

transmission train from the motor shaft to the arm shaft, the position control can be

realized with a simple adaptive control algorithm based on the proportional control

law as shown in Fig. 9. This is because the self-locking property of the worm gear set

ensures that the direction of the power transmission is from the air motor to the arm,so that the arm position can be kept even if the airflow to the motor is cut off.

6. Discussions

Initiated from the idea of driving the biped wall-climbing robot with low-pressure

air motors, a rotary-type air motor has been developed. Experimental results show

the maximum efficiency of 32% and the maximum output power of 32 W when the

input air pressure is 650 mm Aq (Fig. 4(b) and (c)). According to these properties, we

can conclude that the power of the air motor is sufficient to be used on the robot

presented in [1] instead of the original 12 W DC motor. However, there still remainsthe possibility of acquiring higher efficiency and larger output power by improving

either the design or the fabrication. According to the maximum output power of 32

W at the input air pressure of 650 mm Aq, the current power-to-weight ratio can be

calculated to be 55 W/kg. It was obtained based on the prototype whose impeller

material was aluminum, and the casing was made up of carved wood blocks and

polycarbonate plates. Note that the power-to-weight ratio may be significantly in-

creased for this kind of air motors by using lighter materials such as plastics and

thinner casing wall by improving the manufacturing process. We may expect that theweight can be reduced to 1

3of the current value. Besides, there remains room of

acquiring higher efficiency and thus larger output power, as being mentioned above.

Hence, the power-to-weight ratio can be increased to at least three times as that of

the current model.

Fig. 13. Angular-position control of a 1-DOF arm.


A test-bed for the performance test of the air motor was established, and the

equation of motion of the system containing the air motor and its loading device is a

first-order differential equation as shown in Eq. (12). Eq. (12) is also applicable incase a practical mechanical load is actuated, although different load may result in

different time constant and steady-state gain. A small time lag of about 0.2 s has been

found in the step response (Fig. 5(a) and (b)) and it was caused partially by the time

needed to establish a step air pressure at the inlet of the air motor (Fig. 5(c)). This

characteristic makes it difficult to create a fast actuation. However, it is applicable in

situations where such amount of time lag in step response is acceptable, such as for

the biped wall-climbing robot [1].

Fortunately, there is no obvious time lag if the air pressure is adjusted continu-ously, such as in sinusoidal responses. A time constant of 0.13 s for the air motor and

its loading device shown in Fig. 3 can be estimated according to the frequency re-

sponse in Fig. 6. As shown in Eq. (10), the time constant is determined by the pa-

rameters of both the air motor and its loading device, such as the moment of inertia.

Loads with different moments of inertia will result in different time constants of the

system. In the test-bed, a time constant as small as 0.13 s was acquired, and a 2 Hz

sinusoidal velocity was easily realized (Fig. 6(a)).

PI control strategy was used in the velocity control carried out on the test-bedshown in Fig. 3 with a computer being integrated additionally into the control

system. Although constant, sinusoidal and trapezoidal velocities were traced suc-

cessfully even with this simple control strategy, other control strategies should be

explored in the future for better results.

The air motor was also used to drive a 1-DOF arm in its position control. A

simple adaptive control algorithm based on the proportional control law was used.

Although there was a considerable payload of 3.0 kg at the distance of 0.8 m from

the fixed pivot of the arm, less than 5 s was needed to adjust the arm to stop at thecorrect position from the moment when it surpassed its objective. There remains the

possibility of getting a faster response in position control. Generally, the response

time of the 1-DOF arm depends on the system’s time constant shown in Eq. (10). We

may find that it is proportional to the total moment of inertia J. In the case of the 1-

DOF arm, the moment of inertia J largely depends on the moment of inertia of the

arm. To raise the velocity of the robot, we need to reduce the response time of the

system, which requires less moment of inertia. Therefore, efforts should be made to

reduce the weight of the robot. Besides, further study on the control strategies isnecessary for robust control over the 1-DOF arm.

7. Conclusion

A low-pressure air motor has been developed for the purpose of actuating the

wall-climbing robot. Its static characteristics show that it holds adequate power and

practicable efficiency. The studies on its dynamic characteristics show that it can be

applied in the situations where the requirement of response speed is not very fast.

Actually, it should be decided according to both the time constant of the system


being composed of the air motor and its load, and the required response speed. The

constant, sinusoidal and trapezoidal rotational-speed controls have been realized by

PI control strategy. Furthermore, position control has been realized on a 1-DOF

arm.Further research directions are suggested as follows:

1. Developing air motors with higher efficiency and larger output power.

2. More robust control strategies for velocity control and position control.

3. Modeling method and control algorithms of multiple air motors powered by one

blower.

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low-pressure air motor for wall-climbing

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