Proceedings of the ASME 2009 Dynamic Systems and Control Conference
DSCC2009
October 12-14, 2009, Hollywood, California, USA
DSCC2009-2751
PASSIVE BILATERAL TELE-OPERATION AND HUMAN POWER AMPLIFICATION
WITH PNEUMATIC ACTUATORS
Perry Y. Li∗
Center for Compact and Efficient Fluid Power
Department of Mechanical Engineering
University of Minnesota
Minneapolis, Minnesota, 55455
pli@me.umn.edu
Venkat Durbha
Center for Compact and Efficient Fluid Power
Department of Mechanical Engineering
University of Minnesota
Minneapolis, Minnesota 55455
Email: durbh002@umn.edu
ABSTRACT
In this paper a passive bilateral tele-operation between two
pneumatic actuators is presented. The co-ordinated system is
controlled to behave as a rigid mechanical tool that interacts
with the human and other environment inputs. The input human
forces when applied via a force sensor, can be amplified through
the tele-operator to provide assistance for the human operator
to perform the task either remotely or on-site. By ensuring that
the system is energetically passive, robust stability is gauranteed
during interaction with humans and various environments. Heat
transfer during actuation affects the force output of a pneumatic
actuator. The significance of this effect is studied by modeling the
actuator dynamics for isothermal and adiabatic process. Control
schemes for these two extreme cases of heat transfer are developed separately. Experimental evaluation of the controllers is
done on two single d.o.f. pneumatic actuators. Results show
good co-ordination between master and slave actuators, both in
free motion and during hard contact. The root mean square position co-ordination error for isothermal model is 1mm in free motion and 3.5mm during hard contact. The corresponding errors
for adiabatic model are 0.8mm and 2.5mm respectively. Human
force amplification, and force reflection during hard contact are
also experimentally demonstrated for both isothermal and adiabatic model. From these results it is apparent that the difference
between isothermal and adiabatic assumptions is not very significant.
∗ Address
Figure 1.
SCHEMATIC OF TELEOPERATION.
1
INTRODUCTION
Bilateral teleoperation enables humans to interact with remote environments. A schematic of tele-operation with causal
flow is shown in Fig.(1). The interaction dynamics between the
human, teleoperator and the environment poses interesting control problems. The closed loop interaction between a stable teleoperator and humans or environment is not always gauranteed to
be stable. This is very undesirable when interacting with fragile
environments and potentially dangerous with a tele-operator that
has the property of amplifying the human power input. From systems theory [1], it is known that closed loop interaction between
a passive system and a strictly passive system is always stable. It
has been shown in [2] that the human muscle dynamics are close
to passive, and most of the environments are passive. Thus, an
energetically passive teleoperator can gaurantee stable and safe
operation when interacting with broad range of environments.
The paper by Hokayem and Spong [3] provides a comprehensive
survey of different control schemes in bilateral tele-operation.
In much of the literature, a common objective for teleoperation is to achieve complete transparency while maintaining stability. However transparency eliminates the intervening
dynamics between human and the environment making the operation nonintuitive. A more intuitive approach is to enforce
all correspondence to this author.
1
Copyright © 2009 by ASME
a virtual rigid connection between the master and slave. This
will make the combination of master and slave robots behave
as a passive mechanical tool. In [4], this method is proposed
to achieve scaled telemanipulation with electromechanical actuators. A passive controller for following the desired dynamics of
a virtual rigid mechanical tool is implemented. This is achieved
by cancelling out the nonlinear dynamics. Robustness may become an issue in the absence of complete information about the
system dynamics. In [5], a passive controller for nonlinear bilateral tele-operation with electromechanical actuators is presented.
The co-ordinated system is controlled to follow the dynamics of
a desired rigid mechanical tool. However, unlike in [4], the nonlinear dynamics are not cancelled out. A major advantage of this
approach is that passivity can be enforced robustly, even with inadequate information from the sensors. However, human power
amplification was not considered in that paper.
Passive control of fluid-powered actuators presents unique
challenge as the acutator dynamics are inherently non-passive
[6]. In [7], a novel method for energetically passive human power
amplification with hydraulic actuators was presented. In this approach the compressible actuator is modeled as a combination
of an actuator with no compressibility and a nonlinear spring for
modeling the compressibility (Fig. (2)). By controlling the ideal
velocity as velocity of a virtual inertia, an energetically passive
structure is obtained. In [8], a general framework of this approach for both hydraulic and pneumatic actuators was developed using a storage function method. In the current paper, the
ideas proposed in [8] are extended to passive teleoperation with
human power amplification, of pneumatic actuators.
In our approach to bilateral tele-operation with fluid powered actuators, a common virtual inertia is used as a velocity
source for both master and slave actuators as shown in Fig. (3).
The advantage of this approach is that it can be easily extended to
co-ordination of multiple (more than 2) actuators by connecting
all of them to the same virtual inertia. In this paper for simplicity,
we consider only two actuators. Human power amplification is
achieved by sensing the applied human force and then applying
the required additional forces on the virtual inertia. The control
problem is then to achieve position and velocity co-ordination
between master, virtual mass and slave system, while amplifying
the human force input. Once the control objective is achieved,
the tele-operator will behave as a rigid mechanical tool interacting with amplified human force and environmental forces such
as friction, as shown in Fig. (4). It will interact with the environment with an amplified human force. A passive decomposition scheme as proposed in [5] is then used to transform the
system dynamics into individually passive shape system (relative
dynamics) and locked system (center of mass dynamics) dynamics. A backstepping controller and a method to ensure robust
closed loop passivity is proposed to regulate the shape system
dynamics. The scaling factor η can be appropriately selected to
ensure that the human operator has an intuitive feel of the task.
In order to understand the effect of heat transfer on actuator
performance, controller design for isothermal and adiabatic pro-
Figure 2. Master and slave system interacting with human force Fh and
environment forces Fem , Fes .
Figure 3. Problem reperensation with the two pneumatic actuators connected to a common virtual inertia with Fdes = ηFh .
Figure 4.
RIGID MECHANICAL TOOL.
cess are developed separately and compared experimentally. As
communication delay is not pertinent to the existing experimental setup, that issue is not addressed in this paper. Although we
focus on single d.o.f. teleoperation, the proposed method is generalizable to multi d.o.f. systems and to co-ordination of mutiple
agents.
In the next section, dynamics of the pneumatic actuator are
presented. In section 3, the desired open loop passivity problem
is presented. Passive decomposition and the desired closed loop
passivity are presented in sections 4 and 5. Backstepping controller design along with a method for obtaining robust passivity
is presented in section 6. Experimental results are presented in
section 7, followed by concluding remarks in section 8.
2
Actuator Dynamics
The dynamics of pneumatic actuators has been well studied and reported in literature. A common approach to controller
design is to assume that the thermodynamic process is isothermal. In this paper we model the process as both isothermal and
adiabatic, and present independant controller for both the models. For an adiabatic process, the pressure dynamics are obtained
as, [9],
γṁ1 RT1 γP1V˙1
−
V1
V1
γṁ2 RT2 γP2V˙2
Ṗ2 =
−
V2
V2
Ṗ1 =
2
(1)
Copyright © 2009 by ASME
ṁ = ΨC f Av
 Pu
if PPdu ≤ Pcr
 C1 √T
r
Ψ=
γ−1
 C2 √Pu ( Pd ) 1γ 1 − ( Pd ) γ Pd > Pcr
Pu
Pu
T Pu
where C1 =
Figure 5.
γ
2 γ+1/γ−1
,
R ( γ+1 )
C2 =
q
2γ
R(γ−1) ,
and Pcr =
2 γ/γ−1
)
.
( γ+1
Pu , Pd correspond to pressures upstream and downstream of the valve. Note that these pressures vary depending
on whether the chamber is charging or discharging. In the above
equation, C f Av is a measure of the flow area open in the valve
and is designated as the control input u to the actuator.
As stated earlier, the pneumatic actuator is modeled as combination of an ideal velocity source and a nonlinear spring. Equilibrium position of the spring is obtained by equating actuator
force to zero and is given by,
PNEUMATIC ACTUATOR.
where Pi , Vi , Ti and ṁi (i = 1, 2) indicate the pressure, volume,
temperature, and flow rate of the respective actuator chambers,
R is the universal gas constant and γ is the ratio of specific heats.
The temperature dynamics depend on whether the chamber is
charging(ṁi > 0) or discharging(ṁi < 0) and is given by Eq(2).
RTc
Tc
ṁin (γTin − Tc ) − (γ − 1)V̇c
PcVc
Vc
RTd2
Td
Ṫd = −
(γ − 1)ṁout − (γ − 1)V̇d
Pd Vd
Vd
q
(6)
Ṫc =
x̄ =
(2)
Fa = −K(m, x, T )(x − x̄(m, T ))
Ṫ1iso
T1iso
=
T2iso
(8)
R(m1 T1 +m2 T2 )
g
g
where K(m, x, T ) = (L +x)(L
is the nonlinear spring stiff1o
2o −x)
ness. From this expression it is clear that the stiffness is high
towards the beginning and end of the stroke length, and has a
minimum value at the middle of the stroke length. Energy stored
in the nonlinear spring can be written as,
Ṗ1iso =
Ṗ2iso
(7)
Using the above expression, the actuator force in Eq(5) can
be rewritten as,
where (.)c indicates charging chamber and (.)d indicates discharging chamber. The input temperature Tin is assumed to be
290K. The state dynamics for isothermal process can be obtained
from ideal gas law as,
ṁ1 RT P1V̇1
−
V1
V1
ṁ2 RT P2V̇2
−
=
V2
V2
= Ṫ2iso = 0
m1g T1
Lo − L1o
m1g T1 + m2g T2
(3)
(4)
=T
Z x
Wsp =
Note that pressure dynamics in isothermal and adiabatic processess differ by the factor γ. Using the ideal gas law, the net
force exerted by the actuator can be rewritten as,
Fa (m, x, T ) = γR(
m1g T1
m2g T2
−
)
L1o + x L2o − x
x̄
Fa (m, l, T )dl
(9)
For the adiabatic process, using the ideal gas relationship
TV (γ−1) = constant, we get the following expression for energy
stored in spring,
(5)
Wadb = m1Cv (T1 − T1re f ) + m2Cv (T2 − T2re f ) − Patm A p (x̄ − x)
(10)
where Cv is the specific heat of air at constant volume and Tire f
is the temperature of the respective chamber at x = x̄. The above
expression essentially says that the energy stored in the sping
is equal to the change in internal energy and work done against
atmospheric pressure. For an isothermal process where the temperature remains constant, the following expression is obtained
for the energy stored,
where mig , Pig Vi /RTi , Pig corresponds to the gauge pressure
and A1 , A2 are the areas on either side of the piston, x is position of the piston, L1o , L2o correspond to the dead volume
of respective chambers and are obtained as L1o = V1o /A1 and
L2o = Lo +V2o /A2 and Lo is the stroke length.
The force output can be controlled by modulating the mass
flow into the respective chambers. The mass flow rate through
the valve is obtained as,
3
Copyright © 2009 by ASME
Thus, the teleoperator is said to be energetically passive with
scaling of human power if the supply rate satisfies the following
condition,
L1o + x̄ p
L2o − x̄ p
)+m2g RT ln(
)−Patm A p (x̄−x)
L1o + x p
L2o − x p
(11)
In passive controller design we are interested in modulating
the power flow in the system. Power in the spring(actuator) is
given by,
Wiso = m1 RT ln(
∂Wsp
1
Ẇsp = Fa (−ẋ + ( )(−
)Ψ u)
F
∂m
}
| a {z
Z T
s p :=
((η1 + 1)Fh + Fem )ẋm + ((η − η1 )Fh + Fes )ẋs > −d 2
(17)
where d is a measure of the maximum energy that can be extracted from the system. The factor η provides the desired power
amplification from the human operator to the co-ordinated system. The control objective is then to achieve co-ordination between master and slave robots while gauranteeing the passivity
condition in Eq(17).
(12)
γ1 (x,m,T )
where, Wsp is Wadb or Wiso depending on the assumptions of the
underlying process and Ψ = [Ψ1 ; Ψ2 ]. The affect of control input
on force dynamics is given by the following equation. In a teleoperation scheme with two pneumatic actuators, we would have
two such decoupled equations.
Ḟa = −K(m, x, T )ẋ + K(m, x, T )γ3 (m, x, T )u
0
qE (xm , xs ) := xm − xs → 0
(18)
To achieve the stated control objective in Eq(18) we would
have to ensure velocity co-ordination between master, slave and
virtual inertias
(13)
VE1 (ẋm , ẋv ) := ẋm − ẋv → 0
3
Problem Formulation
The dynamics of inertia connected to the two single d.o.f
actuators are given by the following equations,
VE2 (ẋs , ẋv ) := ẋs − ẋv → 0
Thus the conditions in Eq(18) and Eq(19) subject to the passivity condition in Eq(17) constitute the desired control objective. Once co-ordination is achieved, i.e., ẋm = ẋs = ẋv = VL , the
co-ordinated system dynamics from Eq(14, 15) are obtained as,
Mm ẍm = Fh + Fem + Fam
Ms ẍs = Fes + Fas
(14)
MLV̇L = ((η + 1)Fh + Fem ) + Fes
where (.)m,s refer to master, and slave systems respectively. Fh
is the human force acting on the master via a force sensor, Fa is
the force exerted by the actuators and Fe is the external environmental forces like friction, gravity, etc. From Fig.(3), the virtual
mass dynamics can then be written as,
Mv ẍv = Fdes − Fam − Fas
Z T
0
((η1 + 1)Fh + Fem )ẋm + ((η − η1 )Fh + Fes )ẋs
(20)
where ML = Mm + Mv + Ms is the total inertia of the system and
VL is the co-ordinated system velocity. Thus the co-ordinated
system interacts with the external environment with an amplified
human force.
4
Passive Decomposition
A passive transformation is proposed to decouple the current state space [ẋm , ẋv , ẋs ] into shape system describing relative
dynamics and locked system describing the overall dynamics of
the two actuators [5]. The transformation matrix is designed such
that the scaled kinetic energy in current co-ordinates is the same
as sum of kinetic energies of shape system and locked system.
Consequently, passivity results obtained in the transformed coordinates hold in the actual state space.
(15)
Let Fdes = F̄d + F̃d , where F̄d = η1 Fh and F̃d = (η − η1 )Fh .
In the context of human force amplification, F̄d is defined to be
the desired force from master actuator and F̃d is the desired force
from slave actuator.
Thus the desired supply rate for the master and slave systems
is given by,
s p :=
(19)
1
1
1
1
1
2
Mm ẋm
+ Ms ẋs2 + Mv ẋv2 = MLVL2 + ME VE2
2
2
2
2
2
(16)
4
(21)
Copyright © 2009 by ASME
where Mi , Vi with i = (L, E) correspond to inertia and velocities of locked and shape system respectively. The transformation
matrix S is given by,
um
us
1
γ1m
=
0

Mv Ms
ML ML ML
 Mm

(22)
The inertia matrix is transformed as,
(23)
−Wt (0) ≤
+
The locked system dynamics are obtained as shown in
Eq(20). The shape system dynamics are given by,
Mm (Ms +Mv )
s
− MMm M
ML
L
(Mm +Mv )Ms
Mm Ms
− ML
ML
|
{z
ME
=
Vv
(27)
u1
Γ−1
3
On integrating both sides of Eq(28) the following condition
is obtained,

Mm 0 0
ML 01X2
S−T  0 Mv 0  S−1 =
02X1 ME
0 0 Ms
!
1
0
ẋv
u1m
γ3m
+
ẋv
u1s
0 γ13s
{z
}
|
}
| {z } | {z }
By factoring the Fdes as shown in section 3, we get
γ1
Ẇt = (Fh + Fem + F̄d )ẋm + (F̃d + Fes )ẋs + ( m Fam u1m − F̄d VE1 )
γ3m
γ1s
+ ( Fas u1s − F̃d VE2 ) (28)
γ3s
S

Γ−1
1

ẋm
VL
 VE1  =  1 0 −1   ẋv 
ẋs
VE2
1 −1 0
{z
}
|
1
γ1s
{z
|

!
0
Z t
(((η1 + 1)Fh + Fem )ẋm + ((η − η1 )Fh + Fes )ẋs
0
γ1m
γ3m
Fam u1m − F̄d VE1 − F̃d VE2 +
γ1s
Fa u1 )dτ (29)
γ3s s s
Thus to obtain the desired passivity condition in Eq(17), the
following condition on inputs needs to be satisfied,
!
V̇E1
V̇E2
} | {z }
Z t
γ1m
(
V̇E
Ms +Mv
Mm
ML ((Fh + Fem )) − ML (Fes + Fd )
M2
Mm +Mv
ML Fes − ML ((Fh + Fem ) + Fd )
0
!
γ3m
Fam u1m − F̄d VE1 − F̃d VE2 +
γ1s
Fa u1 ) ≤ d02
γ3s s s
(30)
Fa1
+
(24)
Fa
| {z2 }
6
Controller Design
The shape system dynamics are given by Eq(24). With the
above mentioned factoring of Fdes , the shape system dynamics
can be expressed as,
Fa
5
Closed Loop Passivity
With a passive controller, there should be net dissipation of
energy from the system. Total energy of the system is given by,
Mm (Ms +Mv )
s
− MMm M
ML
L
(Mm +Mv )Ms
Mm Ms
− ML
ML
|
1
1
1
2
+ Mv ẋv2 + Ms ẋs2
Wt = Wsm +Wss + Mm ẋm
2
2
2
{z
ME
(25)
V̇E1
V̇E2
} | {z }
V̇E
Ms +Mv
Mm
ML ((Fh + Fem ) + F̄d ) − ML (Fes + F̄d )
M2
Mm +Mv
ML (Fes + F̃d ) − ML ((Fh + Fem ) + F̄d )
=
where, Wsm ,Wss are the energies stored in both the springs and
other terms are the kinetic energies of master, slave and virtual system respectively. After some rearrangement, the rate of
change in total energy can be written as,
!
|
{z
! Fa1
+
Fa2
} | {z }
Fa
Fex1
−
F̄d
F̃d
| {z }
(31)
Fd
Thus the equations of interest for the co-ordination problem
Ẇt = (Fh + Fem + Fdes )ẋm + Fes ẋs + Fa1 (γ1m um − ẋv )
are,
+ Fa2 (γ1s us − ẋv ) + Fdes (ẋv − ẋm ) (26)
q̇E = VE
ME V̇E = Fex1 + Fa − Fd
Ḟa = −KmVE + Km ũ1
To maintain power continuity, the control input is defined as,
5
(32)
Copyright © 2009 by ASME
where ũ1 , u1 − (Γ3 Γ−1
1 − I)Vv , and u1 , Vv , Γ1 and Γ3 are as
shown in Eq(27). Once co-ordination is achieved V̇E = 0, VE = 0,
depending on the external forces, Fex1 , the actuator forces satisfy
the following force amplification relationship,
To achieve stability, define the input signal and force estimation error dynamics as,
Ks ũ1 = Ḟd − F̂˙ex1 − Lz εqE − (Lz − K p − Ks )VE − Kd ME−1 Fζ
− Kz Z − Kd ME−1 F̂ex1
Fam ≈ F̄d = η1 Fh
F̃˙ex1 = Λ−1 (−ME−T KdT Lz−T Z − (VE + εqE ))
Fas ≈ F̃d = (η − η1 )Fh
ηFh ≈ Fam + Fas
(41)
The second stage Lyapunov function reduces to,

 
Kd − εME 0
0
VE
0
εK p 0   qE  (42)
V̇2 = − VET qTE Z T 
Z
0
0 Lz−1 Kz
(33)
6.1
Backstepping controller design
Many different controllers can be designed to regulate shape
system dynamics. In this paper controller obtained by backstepping is presented. The cascade structure of the dynamics in
Eq(32) makes them amenable for backstepping controller design.
Define the following Lyapunov function for the inertia dynamics,
ME
1
εME
VE
T
T
VE qE
V1 =
εM
K
+
εK
qE
2
E p
d
(40)
Since all the diagonal enteries are positive, V̇2 is negative
semi-definite. As all the signals are bounded, it can be shown
that V̈2 is bounded. Thus, using barbalat’s lemma it can be shown
that V̇2 approaches zero asymptotically, which implies that the
co-ordination errors qE and VE are regulated.
(34)
6.2
Robust Passivity
In order to limit the energy requirements of the controller,
and to satisfy the passivity condition in (Eq(17)), a fictitious energy element called flywheel is defined [5]. The dynamics of the
flywheel is given by,
The desired pseudo control input at this step of backstepping
is defined as,
Fζd = −K p qE − Kd VE − F̂ex1
(35)
where Fζ = Fa − Fd , and F̂ex1 is the estimate of Fex1 . The derivative of Lyapunov function is obtained as,
VET
V̇1 = −
|
qTE
M f ẍ f = T f
A vitual connection between the controller and flywheel is
established such that the velocity of the flywheel depends on the
energy demands of the controller. The objective is to ensure that
energy in the flywheel is never depleted. Thus different modes of
operation can be defined depending on the velocity of flywheel.
Including the flywheel, total energy of the system is given by,
Kd − εME 0
VE
+(VET +εqTE )(Z + F̃ex1 )
0
εK p
qE
{z
}
Vg
(36)
where Z = Fζ − Fζd is the difference between actual and desired
1
Wtot = Wt + M f ẋ2f
2
psuedo control and F̃ex1 = Fex1 − F̂ex1 is the error in estimating
Fex1 . The dynamics of Z are given by,
Z t
γ1m
Define the Lyapunov function for the second stage as,
1
1 T
V2 = V1 + Z T Lz−1 Z + F̃ex1
ΛF̃ex1
(38)
2
2
ex1
E
E
ex1
ex1
Fam u1m +
γ1m
γ1s
Fam û1m + Fas û1s − F̄ˆd VE1 − F̃ˆd VE2 )g(ẋ f )
γ3m
γ3s
(46)
where û1m,s , g(ẋ f ), and F̂des depend on flywheel velocity as,


g(ẋ f ) = ẋ1f
 ˆ



Regular mode :  F̄d = F̄d 
if ẋ f ≥ fo
(47)
 F̃ˆ = F̃ 
V̇2 = Vg + Z T Lz−1 (Lz (VE + εqE ) − KsVE + Ks ũ1 + K pVE
+ K M −1 (F + F ) + F̂˙ ) + (V T + εqT )F̃ + F̃ T ΛF̃˙
ζ
γ3m
T f = −(
On differentiating this Lyapunov function we get,
ex1
γ1s
Fa u1 − F̄d VE1 − F̃d VE2 + T f ẋ f )dτ < d02
γ3s s s
(45)
Define the input torque to the flywheel as,
(
0
Kd ME−1 (Fζ + Fex1 ) (37)
E
(44)
The passivity condition is then obtained as,
Ż = −K(m, x, T )VE + K(m, x, T )ũ1 − Ḟdes + K pVE +
d
(43)
ex1
d
(39)
d
û1m,s = u1m,s
6
Copyright © 2009 by ASME

g(ẋ f ) = f1o
F̄ˆd = 0
F̃ˆ = 0







Emergency mode : 

d


 û1m = −Fam 
û1s = −Fas
if ẋ f < fo
(48)
In regular mode of operation the passivity condition in
Eq(17) is trivially satisfied. In emergency mode, control adds
energy back into the flywheel thus maintaing passivity. It is usually advisable to remain in emergency mode till ẋ f > f1 > fo ,
where f1 is selected by the user.
7
Results
The controller was implemented on two vertically mounted,
single d.o.f pneumatic actuators with position feedback. The experimental setup is as shown in Fig. (6). All the experiments are
conducted at a supply pressure of 90psi. Both the actuators have
similar specifications of 0.0508m (2”) bore and 0.3048m (12”)
stroke length. A MLP-50 force sensor from Transducer Techniques is used to measure the input human force and is attached
on the master actuator as shown in Fig. (6). The actuator force is
calculated using SDET-22T-D16 pressure sensors from FESTO.
A pair of FESTO MPYE-5-LF010 proportional servo valves are
used for metering the flow to the two actuators. Performance of
the controller in tracking an arbitrary position profile is shown in
Fig’s. (7 and 8). The controller achieves good position and velocity coordination for arbtrary input profiles. The position tracking
plots also show the response of the system when it encounters
a hard contact. In this experiment the obstacle was placed in
the path of slave actuator. From the plots it is evident that no
contact instabilities are induced. The plots also reveal no clear
differences in the performance of the controller for isothermal
and adiabatic processes. The root mean square error in position
tracking for the isothermal process is obtained as 1mm in free
motion and 3.5mm during hard contact. For the adiabatic process the numbers are 0.8mm in free motion and 2.5mm during
hard contact. These error values are too close to conclude accuracy of one model over the other.
The desired force output from the actuators is as given in
Eq(33). From Eq(33), for small accelerations, the following relationship should be satisfied,
(η + 1)Fh ≈
η+1
(Fam + Fas )
η
Figure 6.
Figure 7.
POSITION TRACKING WITH ISOTHERMAL ASSUMPTION
As the constraint is placed in the path of slave actuator, during hard contact the contact force is same as the slave actuator
force i.e. Fas = Fes . Force amplification and force reflection as
given by Eq(49 and 50) respectively, are experiemntally verified
for both isothermal and adiabatic models and are shown in Fig.
(9 and 10). For these plots, the amplification factor η equals 10.
The presented formulation of the controller is independant of the
actuator orientation. It should be noted however that no gravity
compensation is provided. Consequently, in the absence of human force input and sufficiently large weights to overcome the
friction force, the actuators will move down for a vertical configuration shown in Fig. (6). Such would not be the case for
horizontal arrangement of the actuators.
(49)
The reaction force at the hard contact must be the same as
the input forces. Assuming that the friction forces are small, the
following condition should be satisfied,
Fes ≈ (η + 1)Fh
EXPERIMENTAL SETUP
8
Conclusion
A passive scheme for bilateral tele-operation with human
power amplification of pneumatic actuators has been presented
(50)
7
Copyright © 2009 by ASME
Figure 8.
in this paper. Novelty of the current approach is that the actuator is modeled as a combination of an ideal velocity source and
a nonlinear spring modeling the compressibility. In this paper,
the actuator dynamics were obtained based on the assumptions
that the thermodynamic process in the actuator chamber is either isothermal or adiabatic. A passive decomposition is used
to obtain coordination error dynamics(shape system). A backstepping controller is implemented to regulate the co-ordination
error dynamics to zero. Human force amplification, and force
reflection at hard contact were experimentally verified. Experimental results have shown that there is not much difference in
the performance of either isothermal or adiabatic models. Further work is being done to understand the effect of heat transfer
on the actuation dynamics. Current work includes incorporating
guidance schemes discussed in [5], [10], for multi d.o.f pneumatic systems. This would be implemented on a six d.o.f robotic
rescue crawler test bed.
POSITION TRACKING WITH ADIABATIC ASSUMPTION
ACKNOWLEDGMENT
This research is supported by the NSF through their funding
to Center for Compact and Efficient Fluid Power under the grant
EEC-0540834. We would like to thank Enfield Technologies and
FESTO for donating the hardware for the experiments.
REFERENCES
Figure 9.
Figure 10.
[1] H.Khalil, 1995. Nonlinear Systems. Prentice Hall.
[2] Hogan, N., 1989. “Controlling impedance at the man/machine
interface”. Proc. IEEE Int. Conf. on Robotics and Auto., 1989.,
pp. 1626–1631.
[3] F.Hokayem, P., and W.Spong, M., 2006. “Bilateral teleoperation: An historical survey”. Automatica(42), September, pp. 2035–
2057.
[4] T.Itoh, K., and T.Fukuda, 2000. “Human-machine cooperative telemanipulation with motion and force scaling using taskoriented virtual tool dynamics”. IEEE Trans. on Robotics and Automation, 16(5), October, pp. 505–516.
[5] D.Lee, and P.Li, 2005. “Passive bilateral control of nonlinear mechanical teleoperator”. IEEE Trans. on Robotics, 21(5), October,
pp. 936–951.
[6] P.Y.Li, 2000. “Towards safe and human friendly hydraulics: the
passive valve”. ASME Journal Dyn. Sys. Meas. and Control, 122,
pp. 402–409.
[7] Li, P., 2006. “A new passive controller for a hydraulic human
power amplifier”. In IMECE, ASME, pp. 1–11.
[8] P.Y.Li, and V.Durbha, 2008. “Passive control of fluid powered
human power amplifiers”. In Japan Fluid Power Symp., Int. Fluid
Power Symp., pp. –.
[9] Carneiro, J. F., and de Almeida, F., 2006. “Reduced-order thermodynamic models for servo-pneumatic actuator chambers”. In
IMECE J. Sys. Control Engg., ASME, pp. 301–314.
[10] Li, P., and Horowitz, R., 1999. “Passive velocity field control of
mechanical manipulators”. IEEE Transactions on Robotics and
Automation, 15(4), pp. 751–763.
ACTUATOR FORCES WITH ISOTHERMAL ASSUMPTION.
ACTUATOR FORCES WITH ADIABATIC ASSUMPTION.
8
Copyright © 2009 by ASME