SICE Annual Conference 2008
August 20-22, 2008, The University Electro-Communications, Japan

Mechanical Compliance Control System for A Pneumatic Robot Arm
Kouichi Watanabe1 , Hisashi Nagayasu1, Naoki Kawakami1 and Susumu Tachi1 ,1Department of Information Physics and Computing, The University of Tokyo, Tokyo, Japan(Tel : +81-3-5841-6917;
E-mail: {Kouichi Watanabe, Hisashi Nagayasu}@ipc.i.u-tokyo.ac.jp{kawakami, tachi}@star.t.u-tokyo.ac.jp)

Abstract: The design and control of robots from the perspective of human safety is desired. We propose a MechanicalCompliance Control System as a new pneumatic arm control system. However, safety against collisions with obstacles inan unpredictable environment is difﬁcult to insure in previous system. The main feature of the proposed system is that thetwo desired pressure values are calculated by using two other desired values, the end compliance of the arm and the end
position and posture of the arm.
Keywords: Pneumatic actuator, Humanoid robot arm, Compliance control

1. INTRODUCTION
Many human coexistence-type robots are being developed in order to achieve a human-robot coexistence society. In particular, robots that interact with humans actively, such as AIBO or ASIMO, are emerging. Therefore, the design and control of robots from the perspectiveof human safety is desired.
As a control system for robots actuated by motors forthe purpose of safety, an impedance control system had
been proposed [1]. However, safety against collisions
with obstacles in an unpredictable environment is difﬁcult to insure in this system. In addition, the size andweight of robots increases because the ratio of the output power to the weight of the motor is small. Therefore, the safety of this system is inadequate. We propose a “Mechanical Compliance Control System” as a
new pneumatic arm control system to solve the abovementioned problems. Consequently, we have focused ona pneumatic actuator as a robot actuator.
The pneumatic actuator’s safety is intrinsic because of
it being passive compliant due to the compressibility of
air and being explosion proof, and possessing high backdrivability. In addition, this actuator can exert enoughdriving power despite being lightweight and having asmall size because the ratio of its output power to its
weight is large. An avoidance motion when a collisionoccurs is an important function for human-robot interaction. Therefore, the pneumatic actuator having theseproperties is available for human coexistence-type robots.
Various types of pneumatic actuators such as a pneumatic rubber artiﬁcial muscle and a pneumatic cylinder
have been developed, and their features and characteristics are different in several respects. (Fig. 1 shows
an example of the latter). The pneumatic actuators havestarted gaining attention as robot actuators. We focusedon the robot arm using a pneumatic cylinder because of
its high power, high stiffness, small size, simple conﬁguration, and ease of modeling.
There exist many researches regarding the position
control of a robot arm using the pneumatic actuators. On
the other hand, there exists little research for compliance

control using aggressively properties of air pressures. In
the ﬁeld of industrial robots, the compliance control ofa robot arm is either passive control-type or feedback
control-type. On the other hand, in human life space,
the compliance control should both be active control-type
and real-time control-type. In general, a pneumatic cylinder servo system can achieve the desired compliance easily because it can change its compliance just by changing
the pressure. Thus, we have considered controlling thecompliance of a humanoid arm using a pneumatic cylinder servo system.
In this paper, we present an overview of the system andexplain the control section of the system. The pneumatic
arm used in this paper is virtually identical to mentionedin [2] in terms of conﬁguration and performance. However, control law and system as satisfying desired position and posture and desired compliance is not proposedin [2]. Model-based control should be used in proposedsystem to control the compliance before collision withobstacles. Therefore, we propose not only MechanicalCompliance Control System and also the modeling of apneumatic arm for real.

- 2789 -Fig. 1 Robot arm using pneumatic cylinder.

PR0001/08/0000-2789 ¥400 © 2008 SICE

2. MECHANICAL COMPLIANCE
CONTROL SYSTEMf∗ (P1 , P2 ) = F − F ∗= A1 P1 − A2 P2 − Ar PA − F ∗ = 0,(2)� tF ∗ � −Kp x + KI(x∗ − x) dτ2.1 Overview of System
Our proposed control system can determine the adequate inner pressures of pneumatic chambers when thedesired end compliance and the desired end position andposture of the arm have been speciﬁed. Fig. illustratesa system diagram of the proposed system. As shown in
Fig. , there are two main control ﬂows –compliance control ﬂow and position control ﬂow– in this system. The
main feature of this system is that the two desired pressure values can be calculated by using the two desiredvalues –the end compliance and end position and postureof the arm. Although we should consider seven degreesof freedom under normal condition, we consider only one
degree of freedom because extension of degrees of freedom is easy.
Note that we deﬁne a measure of compliance as reciprocal of spring stiffness. The compliance C is represented by following equation.
dx
C�dF

�
�dθ
C�
dM

τ =0dx− KDdt(3)where x is end position of piston with direction to piston rod from lower limit of cylinder. Fig. 3 shows therelation of each parameters of the pnneumatic cylinder.

PAFA2P2lx(1)A1where dF is external force (dM is moment) and dx
is displacement caused by dF (dθ is each joint displacement).
2.2 Deﬁnition of Parameters
In this subsection, we deﬁne any parameters using following sections.
(x∗ , y∗ ) is Cartesian coordinates.
l∗ is rod length.
P1 , P2 are pressures.
A1 , Ar are cross section of piston and rod.
θ, φ, η are angles.
τ is torque.
F is inner force of pneumatic cylinder.
r is screw radius.
Cjnt , Ccyl are compliance of each joints and eachpneumatic cylinders, respectively.
2.3 Position Control Flow
In the position control ﬂow, the desired joint angles areobtained by inverse kinematics from the desired end position and posture of the arm. The desired joint angles arethen translated to the desired cylinder position by using atransform function (Tp ). They are used as the input dataof the position control block, and a relational expression(f ∗ = 0) of the pneumatic chamber pressure is generated.
In Fig. 2, while the position control block represents anI-PD control system, any position control law such as an
adaptive control law can be applied to this block if only it
generates a relational expression of the pneumatic chamber pressures.

P1Fig. 3 Pneumatic cylinder model. .
2.4 Compliance Control Flow
In the compliance control ﬂow, Direct ComplianceControl (DCC) [3] converts the desired end complianceof the arm to the desired joint compliance. The desired
joint compliance is then translated to the desired cylinder compliance by using a transform function. The relational expression of the pneumatic chamber pressures are
obtained from the desired cylinder compliance using anappropriate model-based control law (G).
2.5 Proposed Cylinder Compliance Control
Next, we present a relational equation for determining
the desired pneumatic chamber pressures in the compliance control ﬂow. It is desirable to be able to control thecompliance before collision with obstacles for this arm.
Therefore, it should be used a model-based control, andmodeling of the pneumatic arm is needed. As mentionedin Section 1, the conﬁguration of pneumatic arm is simple
and modeling is easy. Then, we control cylinder compliance by using the model-based control law.
NORITSUGU et al. have proposed the relational
equation of cylinder compliance as follows [4].
��P1P2f (P1 , P2 ) = κCcyl A1+ A2+1=0xl−x(4)∗∗where l is cylinder length and κ is ratio of speciﬁc heat.

- 2790 -DCC
SimultaneousEquation

Pneumatic
Arm

Position Control
InverseKinematics+-I-PD

Fig. 2 Mechanical Compliance Control System diagram.
Here, it is assumed that a pneumatic cylinder is ina closed equilibrium and that the state variation of thepneumatic chamber is an adiabatic change.
However, inspired and exhaust air and change of air
density are neglected. We consider that applying this control law to the pneumatic arm system is not appropriate.
Therefore, we propose new relational equation for determining the desired pneumatic chamber pressures considering the inﬂuence of inspired and exhaust air and changeof air density.
First, a relational equation of cylinder pressres,

where we use following assumption.
dρi � pi dPi , pi � 273

A2 � A1 − Ar

(5)
(6)

P2 ∗ =

equations of continuity
nRT1
nP1 A1dm1 −dx,
V1V1nRT2nP2 A2dm2 +dx,
dP2 =V2V2dmi = dρi Vi + ρi dVi (i = 1, 2),

1(A1 P1 ∗ − F ∗ − Ar PA )A2T MP3 + T MP4,nl(r − 1)A1 Ccyl ∗1P2 ∗ =(A1 P1 ∗ − F ∗ − Ar PA )A2
P1 ∗ =(7)(8)

273 Pi − 0.378 × 6.11 × 10τi +2 Hi,Ti
PA
7.5(Ti − 273)
(i = 1, 2)(9)τi �Ti − 35.7ρ i = ρo(13)
(14)

(10)

are derived.
From these equation, relational equations of pneumatic cylinder pressures are obtained�(r − 1)P1 − crΓ1nCcyl ∗ A1nr − 1x�(r − 1)P2 − crΓ2+1+ A2
l−x=0(11)

(15)
(16)

whereT M P 3 = −(nr − 1)x(l − x)(17)
+ n(r − 1)Ccyl ∗ (F ∗ + Ar PA ) x,
∗T M P 4 = cnrCcyl {A1 Γ1 (l − x) + A2 Γ2 x} (18)and a relational equation of volumef ∗ (P1 , P2 ) ={−(l − x) + κCcyl ∗ (F ∗ + Ar PA )} x,
κlA1 Ccyl ∗In proposed method, they are

dP1 =V1 = A1 x, V2 = A2 (l − x)(12)

From two relational equations of pneumatic cylinderpressure (2), (4) and (2), (11), pneumatic cylinder pressures P1 ∗ , P2 ∗ are obtained as results of simultaneousequations.
In conventional method, pneumatic cylinder pressures
areP1 ∗ =F (P1 , P2 ) = A1 P1 − A2 P2 − Ar PA ,ρoTi P A

In general pneumatic actuator system, a negative pressure can not treat. In conventional method, when theend position of piston come at the lower limit of cylinder (x = 0) P1 ∗ equals zero from the equation (13). Inaddition, by the constraint P2 ∗ � 0, the end position ofpiston is locked at the lower limit of cylinder.
On the other hand, in proposed method when the end
position of piston come at the lower limit of cylinder, lockphenomenon is avoided by following equation.

- 2791 -P1 ∗ =crΓ1
r−1(19)

Table 1 Link parameter of Denavit-Hartenberg
notation(right arm)

The desired pneumatic chamber pressures are determined from a solution of the simultaneous equations ()and ()obtained in Section 2.2 and 2.4, respectively.
By using this control method the compliance can bechanged in real-time before a collision with obstacles occurs. Furthermore, the proposed system can be applied tothe pneumatic robot arms if only the general information(position, posture, and pressures) of the robot arms can beacquired. Consequently, it is considered that the application of the proposed system to a real system is possible.

3. MODELING OF PNEUMATIC ARM
3.1 Overview of Pneumatic Arm
In this Section, we use the pneumatic arm actuallyconstructed and modeling of this arm and develop the expression for transform function.
We use the pneumatic arm shown in Fig. 1. Joint
mechanism of the robot arm using pneumatic actuators
is generally complication as compared with a robot arm
using DC motors. However, in all of pneumatic actuators
the pneumatic cylinder has simple mechanism comparedwith other pneumatic actuators. Therefore, modeling of it
can obtain geometrically. In following sections, we construct the model of pneumatic arm and propose that theresult of modeling is obtained relatively easy. This mechanism is one of examples, other pneumatic cylinder arm
will be obtained geometrically as well.
3.2 Frame arrangement and DH Parameters
Joint motion ranges of pneumatic arm and arrangement of link frames xi -yi -zi are shown in Fig. 4. Weuse DH parameters notation as the manner of frame arrangement. In this notation, we arrange the origin of baseframe X-Y -Z on the shoulder. Table 1 shows DH parameters.

frame[{i}]ai−1 [m]di [m]

10020030Lupper

40050

Lfore

600700end effector

La endLd endαi−1 [rad]π−2π2π2π2π−2π2π2Aα end

θi [rad]
θ1π2π
θ3 +2θ4θ2 +θ5θ6 +π2θ7Aθ end

3.3 Joint Classiﬁcation and Modeling
We divide the seven joints of the pneumatic arm into
three types of mechanisms; 3 link + 4 link mechanism,screw mechanism and 3 link mechanism. Joint 1, 2, and4 are classiﬁed into 3 link + 4 link mechanism, Joint 3 and5 are screw mechanism and Joint 6 and 7 are 3 link mechanism. In following subsections, we present the modelingof these link mechanisms and transform functions. Transform functions consist of four functions; transform fromjoint compliance to cylinder compliance Tc , from joint
angle to cylinder position Tp , from joint angular velocity
to cylinder velocity Tv and from joint torque to cylinderpressure Tf .
3.3.1 3 link + 4 link mechanism

Fig. 5 .
From Fig. 5, next equations are obtained geometrically.

Fig. 4 Range of movement and frame arrangement (rightarm).

x1 = l1 cos(θ + φ),
y1 = l1 sin(θ + φ),�22
la = (x2 − x4 ) + (y2 − y4 )From these equation, Tp is�
la = {T M P 1}2 + {T M P 2}2
� Tp (θ) ,- 2792 -(20)
(21)
(22)

(23)
(24)

where TMP1 and TMP2 arela =T M P 1 = x1 + q2 (x3 − x1 ) − q3 (y3 − y1 ) − x4 ,T M P 2 = y1 + q2 (y3 − y1 ) + q3 (x3 − x1 ) − y42(33)� Tp (θ)

2l2 − l3 + q1,
(25)
2q1
� �
�2
�
�
− l2 2 − l3 2 + 2 l2 2 + l3 2 q1 − q1 2q3 �
4q1 2(26)

q2 �

2πr2
θ + la op(34)where la o is la in condition of θ = 0.
Also, from Fig. 6, Tf is
Tf (P1 , P2 , τ ) � A1 P1 − A2 P2 − Ar PA −=0

From derivation of Tp , Tv isdla
1= �dt2 (x2 − x4 )2 + (y2 − y4 )2��
dx2
dy2+ 2(y2 − y4 )2(x2 − x4 )
dtdt
�
�dθ
� Tv θ,dt

is(28)

From equilibrium of force and torque, Tf is1
τ
Tf (P1 , P2 , τ, θ) � A1 P1 − A2 P2 − Ar PA −R(θ)=0(29)In addition, from the force relation in the cylinder, Tc
1dFp 2πr2dτ=R==Cjntdθdθ
2π pCcyl
2r=Ccyl

(27)

1τR
(35)

Ccyl = r2 Cjnt � TC (Cjnt )

(36)
(37)

(38)

3.3.3 3 link mechanism

In addition, Tc is
Ccyl =R(θ)lθ (θ)
1dR(θ)(A1 P1 − A2 P2 − Ar PA )−Cjntdθ� TC (θ, P1 , P2 , Cjnt )(30)
Fig. 7 .

3.3.2 Screw mechanism

From Fig.7, next equations are obtained geometrically.
x1 = l1 cos(θ + φ),
y1 = l1 sin(θ + φ)

(39)
(40)

Therefore, Tp isFig. 6 .
From Fig. 6, next equations are obtained geometrically.
p dladθ=r2πr dt
dt

(31)

Thus, Tv is
2πr2 dθdla=� Tvdt
p dt

�dθdt

�

�
22(x1 − x2 ) + (y1 − y2 )(41)�= {l1 cos(θ + φ) − x2 }2 + {l1 sin(θ + φ) − y2 }2(42)la =(32)

Therefore, Tp is- 2793 -� Tp (θ)(43)

From derivation of Tp , Tv isdla
1= �dt2 (x1 − x2 )2 + (y1 − y2 )2��dx1
dy1+ 2(y1 − y2 )2(x1 − x2 )
dtdt�
�dθ
� Tv θ,dt

(44)
(45)

Also, from Fig. 6, Tf is
Tf (P1 , P2 , τ, θ) � A1 P1 − A2 P2 − Ar PA −
=0is

1
τR(θ)
(46)

In addition, from the force relation in the cylinder, Tc
Ccyl =R(θ)lθ (θ)dR(θ)
1(A1 P1 − A2 P2 − Ar PA )−Cjntdθ� TC (θ, P1 , P2 , Cjnt )(47)

4. CONCLUSION
We propose a ”Mechanical Compliance Control System” as a new pneumatic arm control system. The mainfeature of the proposed system is that the two desiredpressure values are calculated by using two desired values –the end compliance and the end position and postureof the arm.
In this paper, it is important to have indicated theframework of the pneumatic arm control system using
pneumatic cylinders. In next step, we should present thequantitative result of simulation and real evaluation.

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1990- 2794 -