Friction Compensation for an
Industrial Hydraulic Robot
P. Lischinsky, C. Canudas-de-Wit, and G. Morel
J
oint friction is one of the major limitations in performing high
precision manipulation tasks. It affects both static and dynamic performances, and may cause instability when coupled to
position or force feedback control. Thus, compensating for joint
friction has been one of the main research issues in robot design
and control over the years. The aim of this paper is to show how
friction compensation based on the LuGre (for Lund and Grenoble) dynamic model, [3], which was applied to an electric actuator in [4], can be successfully used for an hydraulically actuated
manipulator. Fig. 1 is a photograph of the Schilling Titan I1 manipulator used in this research.
Friction compensation is particularly important for hydraulic
manipulators. First, due to high supply pressure, tight sealing is
required to prevent the actuators from significant internal leaks.
This generates very high joint friction. As an example, the joint
friction of the Schilling Titan I1 manipulator can reach 30% of
the nominal actuator torque. Secondly, nonlinear Stribeck friction, a well known source of stick-and-slip oscillations, has a
particular importance in hydraulic systems [ 151. (Fig. 4 illustrates the Stribeck effect for the first joint of the Titan I1 robot. A
25% drop between the static friction torque and the minimum
torque is observed.)
While compensating for friction is specially important for hydraulic devices, it is also particularly difficult. There are several
ways to compensate for friction, basically divided into nonmodel based and model based compensation [ 11.Among the first
type there is, for example, classical dither noise, which consists
in adding a high frequency signal to the control signal. Another
possibility is to design a joint torque feedback, requiring extra
torque sensors to be mounted on the robot or on its base; see for
example [9]. In most cases (including our industrial application),
none of those sensors are available. Model-based friction compensation uses on-line friction torque estimation [2]. The estimated friction torque is added to the torque reference generated
by the position controller and gravity compensation. This kind of
compensation assumes that the actuator has a fast and accurate
torque response. This is generally verified with electric actuators. Nevertheless, most servovalves, which are the control devices of the hydraulic actuators, do not provide a sufficiently fast
and efficient torque response. Then an inner torque loop has to be
designed.
f! Lischinsky (pablo@ing.ula.ve) is with the Department of Automatic Control at the Systems Engineering School, Univer;vidadde
Los Andes, Mirida, Venezuela. C. Canudas-de-Wit is with the Department of Automatic Control, Polytechnic Institute of Crenoble,
St-Martin-d’Ht.re.7 Cedex, France. G. Morel is with the University of
Strasbourg/ENSPS LSIIT/GRAVIR, Illkirch, France.
Februav 1999
Fig. 1. Schilling Titan II manipulator during an assembly task in
teleoperation mode.
Another difficulty in applying friction compensation to hydraulic systems arises from the variation of operating conditions.
In particular, oil temperature affects its viscosity, bulk modulus
and compressibility. Actuator wear also influences friction. Furthermore, the nonlinear dynamics of these actuators are position
dependent (see (1) below). These variations significantly affect
the joint friction and the torque inner-loop characteristics during
a manipulation task. Adaptation is then required.
The LuGre friction model used in this paper fits the requirements for friction compensation of hydraulic systems because it
can describe complex friction behavior, such as stick-slip motion, presliding displacement, Dah1 and Stribeck effects and frictional lag. In addition, it can be coupled with a simple and robust
adaptation algorithm, as shown in [4]. This model has two kinds
of parameters. A first set of four static parameters are used to
characterize the steady state static map between velocity and
friction force or torque. This includes static, Coulomb, Stribeck
and viscous frictional effects. A second set of two dynamic parameters affects the dynamic friction response.
A two step off-line identification methodology of the LuGre
parameters has been proposed in [4]. First, closed-loop constant
velocity experiments are performed to identify the static velocity
to friction map. In a second step, stick slip motions are performed. For this kind of motions, which emphasizes the dynamic
friction effect, a simplified friction model is used in order to
identify the two dynamic parameters.
Finally, to cope with changes in friction characteristics, a single parameter adaptive scheme can be combined with the LuGre
observer-based friction compensation scheme.
0272- 1708/99/$10.00019991EEE
25
Torque Control
In order to compensate for friction torque, it is required to
provide the manipulator with the ability of accurately applying
the desired torque. This is generally not achieved in hydraulic
systems, as the servovalve (electro-hydraulic valve) controls the
flow rather than the pressure into the actuator. To provide the robot with torque control, two pressure sensors were installed at
each joint, one for each chamber of the actuator. Through differential pressure measurement it was possible to estimate the actual hydraulic torque applied by the actuators. Then, a torque
controller was designed based on the hydraulic actuators model.
In the context of the overall control problem, this torque controller constitutes an inner loop for the outer position controller.
Modeling a hydraulic actuator is quite complex, [ 6 ] ,[7].As
indicated in [ 111,in principle a hydraulic actuator consists of two
oil compartments or chambers, separated by a movable part. In
linear movement actuators, this part is a piston fixed to a shaft; in
the case of the rotary actuator this part is the vane, which is connected to the output shaft. The oil flows into and out of the chambers are provided by the servovalve.There are three main stages.
1. The input current u drives the position of the servovalve
spool with a fast second order linear transfer functionG,7(s).Because the bandwidth of the servovalve is well beyond that of the
actuator, these dynamics were neglected.
2. The servovalve spool position controls the oil flow into the
chambers of the actuator with a nonlinear map b(u,AP), which
depends on complex internal piping and geometry of the servovalve.
3. This flow, combined with disturbing flows due to both actuator motion and internal leaks, controls the variation of the differential pressure between the two compartments M = P, -P2
with nonlinear coupled dynamics. AP depends on the actuator
geometry and its position q.
This can be formally written using the continuity equations as
follows
the unknown disturbances, such as the leak flow (Dl, are
supposed to be rejected by a linear compensator H,(s).
The torque control law is then given by
(4)
where k' = APc - AP is the pressure error. AP, is the desired
value for the differential pressure that is directly computed from
the desired torque rcas AP' = (1I V,)
In order to achieve a
good rejection of the disturbances, including static and dynamic
leaks, the linear pressure controller H , ( s )has been designed to be
a Proportional plus Integral regulator. From (1) and (4) the closed
loop dynamics are given by
r,.
~
dAP
=BNq)[H,(s)LPdt
where the leak flow (Dl has been modeled as (Dl = K f A P , K, being a constant parameter. As shown by (S), the resulting closed
loop dynamics of the pressure subsystem does not depend anymore on the joint velocity 4. However,it still depends on the joint
position q. This is due to the non-compensated nonlinear term
qq)in (5). A stability analysis of the torque loop has shown that
the worst position for the joint was the one which maximizes N q )
and thus, the bandwidth of the closed loop (5). In practice, the PI
gains of H,(s) are tuned in this configuration, which is the mechanical limit of the actuator. The gains are adjusted in order to
provide a high inner loop bandwidth compared to the outer position loop. Experimental results presented later show that robustness of the nonlinear PI controller is good enough to provide
accurate torque control in other joint configurations. Also nonlinear PI control exhibits better closed loop response than a simple linear PI controller.
Friction Modeling and Compensation
where B is the oil bulk modulus parameter, represents the internal leakage flow between the two compartments, V, 4 models
the disturbing flow due to the actuator motion, Vrbeing the actuator displacement corresponding to piston area in linear actuators.
A fully developed model of the nonlinear terms b(u,AP) and
@(q)for the Schilling Titan I1 actuators based on [1 11 can be
found in [8]. A simplified form of this model is given by (1) with
b( U, AP) = Cd-
Friction is usually modeled as a discontinuous static map between velocity and friction torque which depends on the velocity's sign. It is often restricted to Coulomb and viscous friction
components. A more complete static model is shown in Fig. 2.
However,there are several interesting properties observed in systems with friction which cannot be explained only by static models. This is basically due to the fact that friction does not have an
t
Friction [Nm]
Viscous Friction
(2)
Multi-Valuated
Stribeck Effect
(3)
whereC is the servovalve constant gain, Pyis the supply pressure,
and 1 IS a constant depending on actuator geometry, with
P, > sign(u) AP and12 > q 2 .
By using this model, a torque controller has been designed in
[lo]. Both the servovalve input nonlinearity b(u,AP)and the disturbing flow V7qare compensated by this torque controller, while
26
'I
Coulomb Fricti
Constant Velocity [radk]
Static Friction Level
...
Fig. 2. Friction-(constant)
velocity description.
IEEE Control Systems
instantaneous response on a change of velocity, i.e., it has internal dynamics. Examples of these dynamic properties [ 11, [3] are:
stick-slip motion which consists of limit cycle oscillation at
low velocities, caused by the fact that friction is larger at
rest than during motion,
presliding displacement which shows that friction behaves
like a spring when the applied force is less than the static
friction break-away force,
frictional lag which means that there is an hysteresis in the
relationship between friction and velocity.
All these static and dynamic characteristics of friction are
captured by the dynamical and analytical model proposed in [3],
called LuGre, which is suitable for the design of model-based
friction compensation schemes. Experimental results on a D.C.
motor with constant parameters and adaptive compensation
schemes based on this model were reported in [4]. The LuGre
model is given by
whereh,,(q) is theithdiagonal term ofH(q),G,(q)is theithcomponent of G, rtis the torque applied to the ithjoint and F, is the ith
joint friction torque given by (6) and (7).
Parameter Estimation
Friction parameters are difficult to estimate since they appear
nonlinearly in the model, and the internal friction state is not
measurable.
The four static parameters can be estimated by the construction of the friction-velocity map measured during constant velocity motions. For constant velocity experiments, from (8) and
(10) and assuming exact gravity compensation, we have
In this work, closed-loop experiments under position PD control
with gravity compensation were performed over the six joints of
the robot. The friction-velocity data values are then obtained by
averaging the measured velocity and the input torque values.
Nonlinear optimization algorithms were used to fit the experimental data to equation (1 1) with the static parameters [4].
The estimation of the two dynamic parameters B,, and oItis
not
possible using linear estimation techniques due to the nonlindz
F =cT,z+cT,-+u~~,
ear dependence of friction with these two parameters, and to the
dt
(7) fact that the internal state z, is not measurable.
Nevertheless, an approximated estimation can be done. In orwhere q[rad I sec] is the angular velocity, and F[Nm] is the fric- der to estimate oat, a small magnitude, slowly varying torque intion torque. Equation (6) represents the dynamics of the friction put r, is applied in open loop. Assuming that it remains smaller
internal state z, which describes the average relative deflection of than the break-away torque, the system exhibits presliding mithe contact surfaces during the stiction phases. This state is not cro-displacements. In this case, it can be assumed that ij, = 0,
measurable. The function (CO > a, + a , 2 g(4) L a, > 0) de- 4, = 0 and 2, is constant. From (10) and (7)
scribes part of the "steady-state'' characteristics of the model for
constant velocity motions: v, [rad I sec] is the Stribeck velocity,
(a,+ a,)[Nm] is the static friction, and a, is the Coulomb friction. The steady-state friction characteristics (when the velocity Thus, from equations (6) and (12), we get
q is constant and dz I dt = 0) are given by
where a2[Nmsecl rad] represents the viscous friction. Thus,
the complete friction model is characterized by four static parameters a,, a , ,a2andv,, and two dynamic parameters on, 0,.
The parameter B, [Nm I rad] can be understood as a stiffness coefficient of the microscopic deformations of z [rad] during the
presliding displacement, while (T, [Nmsecl rad] is a damping
coefficient associated with dz I dt.
The dynamic equations of the robot without centripetal and
Coriolis terms are:
where H ( q ) is the inertia matrix, G ( q )is the gravity torque vector, F is the friction torque vector and l- is the applied hydraulic
torque. For each axis i, the locally decoupled dynamics become
February 1999
This equation can be explicitly integrated to obtain z , ( t )by using
an input ramp function S(t) = ct, c > 0. Assuming that the initial
configuration is ~ ~ (=00,) and also 4, > 0, it yields:
Therefore, from the actual measurement of q,(t) and the previously estimated values for a,, and a L, z,( t )can be computed during a time interval (0, T ) . An estimation for (T,! can be obtained
by fitting this data in the approximate linear relationship
S ( t ) = B",Z,(t).
Another way of estimating (T,, is to directly use the measures
of the micro pre-sliding displacement A q c :
27
Friction Compensation
Tracking Reference
5
0
10
15
20
25
30
The estimation of friction parameters allows fixed and adaptive friction compensation of the robot, see the complete analysis
in [3], [4], and [5].Other friction compensation schemes based
on the LuGre model were presented in [ 121 and [131.
Fixed friction compensation. Fixed friction compensation
consists of designing a friction observer for the system for each
joint i. Here, for the sake of readability, the subscript i is omitted.
From the friction model given by equations (lo), (6)-(7) the observer is:
20
25
30
141 z - k e , k > 0
z =q-o, 7
Reference Toraue
5
0
10
100
15
Torque Error
A
gGQ
fi=o,;+o,i + a , q ,
2
0
5
10
15
Time [SI
20
25
30
Fig. 3. Experimental comparison of torque controllers on joint 1:
position reference, torque reference, and torque erro'oI:
I
Static Friction Estimation : Axe 1
j
._.
: *-.-.'.-'-'
.
150 _.......... i ........... I ........... i...........
p.+.-.-+
,
0
._
....... j ........... j ........... i.......................
50
0 - .......... i ........... i.......................
where e = q -q7 is the tracking error, H ( s ) is the position controller, ? and F are the estimated internal state z and friction
torque F , respectively; k is the observer gain and h the linearized
joint inertia. The torque reference r, is the input to the inner
torque loop presented previously. The closed loop error dynamics are given by the loop interconnection of two systems
0
..; ........... ;........... :
100 _ .......... i ........... j ........... j ........... i ........... k ........... ;........... + ..........
z
(17)
and adding it to the position controller we obtain
-1 00
0
-E
.
e=
~
-
h ( s 2+ H ( s ) )
(-F)=
0, s
+ 0,
(-Z)
h(s2+H(s))
= G ( s )(-Z)
(19)
i........... i .......... :_........
;........... ;........... ;........... :
_ .......... j ........... j ........... j ........... i........... i........... j............ i........
-1 00 - ...................... i........... ...........................................................
I
$
-50
.
whereF = F - F a n d ? =z -z^.IfH(s)ischosensuchth_atG(s)is
strictly positive real (SPR) then the observer error, F - F , and the
position error, e, will asymptotically converge to zero.
To prove it let's introduce a state space representation of G ( s )
-1 50 - .............................................................................................
e-,+.-.-.-.?'-'
-200
I
I:
....... i.0.........j ........... i..
-0.2
-0.15 -0.1
..............................................
-0.05
0
0.05
0.1
Static Velocity [radisec]
0.15
0.2
= A(
dt
Fig. 4. Experimental friction-(constant) velocity curve
corresponding to joint 1.
e=C(
where Art = $( T ) - r,(O)is the differential torque value required to obtain a presliding differential micro-displacement
Aqz = q , ( T )-4,(O).
we used the linearized deFinally, in order to estimate o,,,
scription of the system (6)-(7) in the stiction phase (4,=O,
z,= 0) given by
4, 4,+(Oh + a,, 1 4, + 0 0 , 4, = l-;
'
(16)
Here, o ,, is determined such that this system has near critical damping, i.e., 0.8 < 6< 1, using the expression o,,=2 6 d c -a,i.
This condition was found to be necessary to achieve a damped
transient response of the friction observer used for compensation
purposes.
28
+ B(-z")
and a Lyapunov function
v = ('P<+ -.z",
k
Since G ( s ) is SPR, it follows from the Kalman-Yakubovich
Lemma, [16], thatthereexistmatricesp =PT> OandQ =QT> 0
such that
A~P+PA=-Q
PB = C T .
Now evaluating the time-derivative of V along the solutions
of the closed-loop system
IEEE Control Systems
2 dz"
dV
dt
- =-<'Q<-2<TPBz"+-z"-
=
-c7 Q<
-
k
2ez"+ -?(
2
k
dt
141 ? +
7
ke)
g(q)
where the last inequality comes from the fact that g(4) > 0. The
radial unboundedness of V together with the semi-definiteness of
dV / dt implies that the states are bounded. In the regulation case
( 9 , constant), we can apply LaSalle's theorem-to prove that
5 -+ 0 and + 0 which means that both e and F converge towards zero and the global asymptotic stability is proven. See [ 141
for the stability proof of the general tracking case.
This result can also be understood from the fact that the observer error dynamics (20) correspond to a dissipative map from
e to Z (see [3] for details). By adding the friction estimate to the
control signal, the position error will be the output of a linear system operating on 2. This means that we have an interconnection
of a dissipative system with a linear SPR system. Such a system
is known to be asymptotically stable.
The SPR condition on G ( s ) excludes the use of a pure PID
compensator for H ( s). If H( s) is chosen as a PD controller, then
the second order closed loop function is G ( s ) = I (
),
z
where, z,:= us -af with the following filtered signals of the velocity and the applied torque
hs
a
f'-
6:zi+K,,
...
.
...
.
0,s
+ 0" 4
...
.
...
.
(27)
...
.........................
.. ...
where K P and Kd are the proportional and derivative gains, respectively. Thus, the SPR condition on G ( s )yields:
0
5
10
15
20
25
..
..
................
...
<
..
..
35
40
45
50
.
.
.
30
35
40
45
50
30
Position of Axe 1
0
Kd >=.
In practice, this condition was found to be too restrictive due
to the high frequency zero of (19). The estimated values for
CT,, / (J,are between 100 and 2000 [ r a d s ]for the different robot
joints, which results in high gains. In [4] it was experimentally
shown that the SPR requirements are too restrictive and do not
give rise to a sharp stability condition.
Adaptive friction compensation. Friction can change for
different reasons, such as oil temperature variations and actuator
wear. Two adaptive schemes were presented in [4] based on the
adaptation of only one parameter, and using the previously estimated nominal friction model. The first of them is given by
where the nominal value of the parameter 0 = 1.
Here, we assume that the six nominal friction parameters and
the linearized joint inertia h are known, the dynamic friction parameters are invariant, and the variation of the static friction parameters are captured by the model (21)-(22), where 0 is
assumed to be unknown and bounded as 0 < 0 4 m. Then the following adaptive controller is used:
6
m
I
5
0
10
15
20
25
Fig. 5. Presliding micro-displacement onjoint 1 for estimation of 0,.
Fixed Friction ComPensation
I
0
5
10
15
20 25
Time [SI
30
35
40
45
Fig. 6. Tracking error without and with friction compensation on
joint 5.
February 1999
29
This controller, when applied to system (lo), (6)-(7) for each
joint i yields global asymptotic stability, if a linear operator H ( s )
can be found so that the closed loop linear mapG(s) in (19) satisfies the SPR condition.
To prove this result let's introduce "e= 0 - 6. The closed loop
equations are:
where G ( s )is defined as above. We then assume that the triplet
(A, B, C) and the vector [describe a minimal state representation
for the mapping above. Then, if the stable map G ( s ) is SPR, a
unique matrix P = P T > 0 satisfyingPA + ATP = -I and PB = C ,
exists. We can thus define the following Lyapunov function
From the filters introduced above (27)-(28), we can check
that Z also satisfies:
Now evaluating the time-derivative of V along the solutions of
the closed-loop system and neglecting O( exp(-pt)), we obtain:
Z = z,,, - i + O(exp(-pt)); p = -,0 0
0,
where the first two terms in the right-hand side of this expression
are measurable and the last one is derived from the non-zero initial conditions of q and r.In addition, the following holds:
Fixed Friction Compensation
Therefore all the internal system signals remain bounded, and
the "output" e = C jtends asymptotically to zero. See [4] for details and another adaptive scheme based on a different parameterization.
Experimental Results
V"
0
5
10
15
20
25
Time [SI
30
35
40
45
Fig. 7. Friction estimation on joint 5.
Task Space Tracking Experiment
1.18
Fig. 8. Tracking reference and robot position without and with
friction compensation in the task space.
30
In order to validate our approach, experiments were performed with an hydraulic Schilling Titan I1 manipulator.
The overall real time controller uses three CPU boards connected through a VME bus. Two 68030 boards supporting
VxWorks run generic software for remote teleoperation. This
software includes external sensor based control, drivers for various interfaces with human operators, and generic models for direct and inverse robot kinematics. It provides a desired joint
position of the robot at a sampling rate of 500 Hz. The desired position is fed, through the VME bus, to the third CPU board, based
on a 8 6 0 processor, which runs the joint control algorithms presented in this paper. The whole control algorithm for the six
joints, including friction compensation and adaptation, runs at a
500 Hz sampling frequency. The VME bus also hosts high resolution input/output boards in order to drive the servovalve current and to read the resolver signal at each joint.
In a first step, experiments were performed to evaluate the efficiency of the nonlinear PI inner torque loop. Fig. 3 shows a position tracking experiment on the first joint of the robot. Here we
are interested in the inner torque loop performance rather than in
position tracking performance. The figure shows the tracking position reference, the torque reference resulting from the position
controller, and the torque error. From 0 to 15 seconds, a conventional linear PI torque controller is used. Then, from 15 seconds
to the end of the experiment, the nonlinear PI torque controller
(4) is applied. The torque error plot clearly shows a better performance of the proposed nonlinear controller.
The second experimental step was the identification of the
friction model for each joint of the robot. First, constant velocities experiments were performed to provide static friction-velocity plots. Fig. 4 shows the resulting plot for the joint I,
emphasizing a significant Stribeck effect at low velocities. Four
IEEE Control Systems
static friction model parameters were then estimated by fitting
this curve to (1 1).
For estimation of the dynamic parameter CY(],, the experiment
shown in Fig. 5 was used, where a presliding micro-motion is
produced using a slow input ramp function. Finally, the last dynamic parameter (5, was determined in order to provide a critical
damping in the stiction phase, as described earlier in the paper.
The third experimental step was to implement the friction observer given by (17), using the previously estimated static and
dynamic parameters. Here, a difficulty came from numerical stability. Trapezoidal approximation of integration was used. From
(17) the observer sampled equation becomes:
Task Space Tracking Experiment
,
0
u
u
0
5
10
15
20
25
30
35
5
10
15
20
Temps [SI
25
30
35
Fig. 9. Tracking endpoint position error norm and orientation error
norm without und with friction compensation.
where T = 2 ms was the sampling period used.
Figs. 6 and 7show the results obtained for fixed friction compensation on the joint 5 of the robot. The position controller H ( s )
is a PD compensator. The position reference is a 20 degrees, 0.1
Hz sine wave. A very important improvementin the tracking error
is noticed when the friction compensation is applied, at t = 24 s.
The same improvement is observed at the end-effector level.
Fig. 8 shows the results for Cartesian space tracking experiments
using the fixed friction compensation on all the manipulator
joints. The desired trajectory consists of following a straight line
to reach an intermediate point, and then coming back to the starting point. The experiment was done twice, without and with
fixed friction compensation. Both results are shown in Fig. 8.
The straight line corresponds to the tracking reference between
points A and B. The dash-dot curve corresponds to the experiment without friction compensation. The continuous curve corresponds to the experiment with fixed friction compensation.
Compensating for friction reduces the tracking error by a factor
of four for this experiment. In particular, as Fig. 9 shows, the position error norm of the end effector is about 2-3 cm without friction compensation, and about 0.5-1 cm when the friction
compensation is applied, at t = 175 s. Similarly, the orientation
error norm of the end effector decreases from 0.12 rad to 0.02 rad
with friction compensation.
The last experimental investigations concerned adaptive friction compensation. Here, adaptation is optionally used as a tuning process over a finite time interval, in order to adapt the
friction model to the current robot working confiitions. After a
short adapting period, the adaptation parameter 9 is frozen. This
allows a re-tuning of the friction model, mainly the Coulomb parameter a,. Fig. 10 shows the efficiency of the adaptive process.
From t = 0 to t = 18 s, friction is not compensated. A fixed friction compensation based on previously estimated parameters is
then used, fromt = 18 s tot = 37 s. Finally, fromt = 37 s, the adaptation algorithm is run. Fig. 11 shows that the inverse of th,e adaptation parameter decreases from the nominal value 1 I 0 = 1 to
1I 0 = 0.8. This shows that friction was overcompensated when
using the previously-estimated friction parameters. Thus, the adaptation process results in decreasing the estimated friction, as
depicted in Fig. 10. The re-estimation of a,,can beAcarriedout
multiplying its previous value by the final value of 1 I 8 = 0.8. The
February 1999
-
Fixed and Adaptative Friction Compensation
,
2.5
U
2
1.5
2
1
P
n K
"'"0
g
L
g
10
50
60
....
.
...
..;.............;.......................
............................................................................................
0
E
40
0.;
-0.5
-1
w
g
30
20
10
20
30
40
50
60
10
20
30
40
Time [SI
50
60
100
s o
._
._ -100
-200
0
Fig. IO. Tracking experiment on joint I . Position reference, tracking
erroc and friction estimation.
1.1
I
0
2
& 0.95
c
Eg
m
0.9
a
L
0.85
(1
-J
8
!
!
!
!
!
!
...................................... ......................... ............. ....................................................
1
8 1.05
._
I
_ ......................................................................................-
0.8
o,75
1
^
(.
{
1
(.
.............................................
_ ...........................
_ ................................................
i
I
_ ............:.............:........
.a...:
..........
_ ............i.............i.............i..........
"
.........................:............. .............:............. ............. .........i
i
i
i
Fig. I I . Adaptation parameter 1 I 0 corresponding to experiment
of' Fig. IO.
31
friction asymmetry for positive and negative velocity produce
the oscillation of the adaptation parameter after t = 40 S.
Conclusions
A model based friction compensation scheme using a novel
dynamical friction model was implemented on an industrial
Schilling Titan I1 hydraulic robot. Off line estimation of parameters was carried out, using the results o f two kinds of experiments. These experiments were done independently at each
joint. A nonlinear PI type controller was used in the inner torque
loop to improve its performance. The complete control scheme
has shown to substantially improve the position precision in regulation and tracking. Higher precision applications can be performed by the hydraulic robot with this controller.
Acknowledgment
This work was done under contract EP 663 2L3074 between
the LAG-INPG and the Teleoperation and Robotics group o f the
Direction d’Etudes et Recherches-ElectricitCDe France Chatou,
France.
References
[l] B. Armstrong-Helouvry, P. Dupont, and C. Canudas de Wit, “A survey of
analysis tools and compensation methods for the control of machines with
friction,” Automatica, vol. 30, pp. 1083-1 138, 1994.
[2]C. Canudas de Wit, K.J. Astrom, and K. Braun, “Adaptive friction compensation in DC motor drives,” IEEE Trans. Robot. Automat.,vol. RA-3, no.
6, pp. 681-685, 1987.
[3] C. Canudas de Wit, H. Olsson, K.J. .&trom, and P. Lischinsky, “A new
model for control of systems with friction,” IEEE Trans. Automat. Contr:,
vol. 40, no. 3, pp. 419-425, 1995.
[4] C. Canudas de Wit, P. Lischinsky, “Adaptive friction compensation with
partially known dynamic friction model,” Int. J. Adaptive Control andSignal
Processing, vol. 11, pp. 65-80, 1997.
[5] C. Canudas de Wit and R. Kelly, “Passivity-based control design for robots with dynamic friction,” Fifth IASTED Int. Con$ Robotics and Manufacturing, May 29-31, 1997, Canccen, Mexico, pp. 84-87.
[6] Herbert E. Merrit. Hydraulic Control Systems, John Wiley & Sons, 1967.
[7j T.J. Viersma, Analysis, Synthesis and Design of Hydraulic Servosystems
and Pipelines, Delft University of Technology, 1990.
[8] P. Lischinsky, “Compensation de frottement et commande en position
d’un robot hydraulique industriel,” PhD. thesis, Laboratoire d’Automatique
de Grenoble, INPG, 1997.
[9] G. Morel and S. Duhowsky, “The precise control of manipulators with
joint friction : abase force torque sensor method,” IEEEInr. Con5 Robot. Automat., Apr. 1996, Minneapolis, MN, pp. 360-365.
[IO] J. Heintze and A.J.J. van der Weiden, “Inner loop design and analysis for
hydraulic actuators with application to impedance control,” Proc. 4th. IFAC
Symp. Robot Control, Capri, Italy, Sep. 1994, pp. 401-406.
[ l I] J. Heintze, G. van Schothorst, A.J.J. van der Weiden, and P.C. Teerhuis,
“Modeling and control of an industrial hydraulic rotary vane actuator,” Proc.
32
32nd. Con$ Decision and Control, San Antonio, Texas, Dec. 1993, pp.
1913-1918.
[I21 P. Vedagarbha, D. Dawson, and M. Feemster, “Tracking control in the
presence of nonlinear dynamic friction effects,” Proc. Amer: Contr: Conf, Albuquerque, NM, June 1997, pp. 2284-2288.
[I31 S. Jain, E Khorrami, N. Ahmad, and S. Sankaranarayanan, “Friction
compensation for drives with and without transmission compliance,” Proc.
Amer: Contr: Cor$, Albuquerque, NM, June 1997, pp. 2925-2929.
[14j C. Canudas de Wit. Comments on “A new model for control of systems
with friction,” IEEE Trans. Auto. Contr:,vol. 43, no. 8, pp. 1189, 1998.
[ 151S. Ananthakrishnan and R.M. Fullmer, “Experimental Adaptive Control
of aFour-Axis Hydraulically Actuated Robot,”Int J. Robot. Automat., vol. 6,
no. 4, 1991, pp. 210-219.
[ 161 H.K. Khalil, Nonlinear Systems, 2nd ed., Prentice Hall, NJ, 1996
Pablo Arnold0 Lischinsky was horn in Montevideo,
Uruguay, in 1960 He received his B Sc (1985) degree
in systems engineering and his M Sc (1990) degree in
control engineering from the Universidad de Los Andes, Merida, Venezuela Since then he has been an associate professor with the Department of Automatic
Control at the Systems Engineering School, Universidad de Los Andes In 1993 and 1997 he received
his M Sc and Ph D in automatic control from the Polytechnic Institute of Grenohle, Department of Automatic Control, France His
current research interests are in adaptive control, system identification and
computer control.
Carlos Canudas de Wit received his B S c degree in
electronics and communications from the Technologic
of Monterrey, Mexico, in 1980 From 1981 to 1982 he
worked as a revearch engineer at the CONVESTAV-IPN
in Mexico City. He received the M Sc and Ph D at the
Polytechnic Institute of Grenoble, Department of Automatic Control, Grenoble, France, in 1984 and 1987, respectively He was a visiting researcher in 1985 at Lund
Institute of Technology, Sweden Since that time he has
been an associate professor in the Department of Automatic Control, Polytechnic Institute of Grenoble, where he teaches and conducts research in the
area of adaptive and robot control In 1988 he authored Adaptive Control of
Partially Known Systems. Theory and Applications (Elsevier) He is also the
editor of Advanced Robot Control (Springer-Verlag, 1991) He is currently
an associate editor of IEEE Transactions on Automatic Control
Guillaume Morel graduated from IST, University of
Paris VI, in 1990 He conducted his Ph D research at the
Laboratoire de Robotique de Pans, and received his Doctorate degree in Robotics from the University of Paris VI
In 1994 After a two-year postdoc at the Massachusetts
Institute of Technology, and a period with the research
department at Electricit6 de France, he joined the Laboratom des Scienceb de I’Image, de I’Informatlque et de la
TelBdktection at the University of Strasbourg in 1997, as
an assistant professor His research concerns robotics and control, with a particular focus on vision-based control and force control
IEEE Control Systems