An adaptive controller is developed for adjusting robot arm parameters while manipulating payloads of unknown mass and inertia. The controller is tested experimentally in a master/slave configuration where the adaptive slave arm is commanded via human operator inputs from a master. Kinematically similar six-joint master and slave arms are used with the last three joints locked for simplification. After a brief initial adaptation period for the unloaded arm, the slave arm retrieves different size payloads and maneuvers them about the workspace. Comparisons are then drawn with similar tasks where the adaptation is turned off. Several simplifications of the controller dynamics are also addressed and experimentally verified

Carignan, Craig R.

Mosier, Gary E.

Tarrant, Janice M.

English

NASA Technical Reports Server

:l
AN ADAPTIVE CONTROLLER FoR ENHANCING OPERATOR
PERFORMANCE DURING TELEOPERATION
Craig R. Carignan, Janice M. Tarrant
ST Systems Corp.
Lanham, MD
Gary E. Mosier
Goddard Space Flight Center
Greenbelt, MD
An adaptive controller is developed for adjusting robot
arm parameters while manipulating payload_of-unknown
moss and inertia. The controller is tested experimentally in a
masterlslave configuration where the adaptive slave arm is
commanded via human operator inputs from a master.
Kinematically similar six-joint master and slave arms are
used with the last three joints locked for simplification.
After a brief initial adaptation period for the unloaded arm,
the slave arm retrieves different size payloads and
maneuvers them about the workspace. Comparisons are
then drawn with similar tasks where the adaptution is turned
off. Several simplifications of the controller dynamics are
also addressed and experimentally verified.
1.0 INTRODUCTION
Whether working in space, undersea, or on the ground,
humans and robots must often contend with operating in an
uncertain environment. One key characteristic often left
unspecified is information about the object being
manipulated. In-the work presented here, a parameter
identificationscheme isused to estimatetheparameters of
the robot when maneuvering an unknown payload. The
effect on performance of the improved model in tracking
desired workspace trajectories is then examined.
The paper begins by giving the dynamics for the f'u'st
threelinksof a parallelinkagerobotarm. The parametersto
be used in the identificationalgorithmareformulated from
the link parameters. A parameter adaptive controlleris
developed for the slavearm which containsboth a model-
dependent fccdforwardterm and a posRion/vclocityfeedback
term. The master arm uses the same feedback as the slave
arm with a reversalin sign. The algorithmisthen tested
experimentallyon the teleoporatedsystem doing payload
retrievaltasks.
2.0 DYNAMICS
A set of minimaster hand controlle_nmnufactured by
Kraft Telerobotics Inc. was used in the teleoporation
experiments: the leftarm was used as the mastex and the
right arm as the slave. Except for the right/leR symmetry,
the two arms were identical. The Denavit-Hartcnberg "
Parameters (see Craig [I]) for the first three links of the
Kraft arm am given in Table 1.
Because of the parallellinkage used to drive the third
joint (see Fig. I),the Kraft arm dynamics could not be
derived using re.cursivealgorithmssuch as the Lagrangian
Method or Newton-Euler Method (seePaul [2]).Instead,
the method presentedin Asada and Youcef-Toumi [3]was
used,which isLagrangian-based but does not assume open
kinematicchains. Also pertinentto the development of the
dynamics is the use of actuator coordinates and joint
coordinateswhich need not be synonymous forparalleldrive
mechanisms. The reader is again referred to [3] for a
discussionon thistopic.
Following the procedureof Asada etal[3],thedynamics
for the arm is derived in the form
:_ = H_+C_+:Ig+Dcsgn(.0.) +Dt_ (I)
The matrixC isnot unique and ischosen m be
.Z.N_ + _H__ix._H___dk (2)½Cij
because of its unique property of yielding the skew
symmetric sum, H - 2C. This is important in the
formulation of the adaptive controller. IL C and gg for the
Kraft arm are given in the appendix. Dc and D_t are diagonal
matrices representing the magnitude of the coulomb friction
and viscous friction coefficients, respectively.
Table I: D-H Parameters for Kraft Mlnlmaster.
I al-1 (m) al ((leg)
I 0.000 0
2 0.0130 -90
3 0,180 (12) 0
d I (m) *
0`000
:t0.075
:t:0.055
* tim right m,m has positive offieLi in this colidlnie convention mid
tim left arm hits nc_ltlv¢ offsets (noic_ d2=bl mid d3=b2-bl in Fig. 1).
3.0 CONTROLLER
The adaptive controllerused in thisstudy is the one
developed by Slotineand Li [4].As in thecomputed torque
scheme, itcontainsfeedforward terms tocompensate for the
-I _L r ',_-_ _,..: I_: _ (:.: c #,._b,,,:is { or:_.) ", i_
t. "_L
N<_U-i_ _.>
I _T un,:1 . :
https://ntrs.nasa.gov/search.jsp?R=19900001122 2020-03-20T01:06:19+00:00Z
Zi
x: i,
E
' 2
i i ...... r-
' ' I_I I Z! I ! t t 1i._ ................... _........ _..., ........ ,.........
(b)
Figure 1: Kinematics for first three links of Kraft arm
showing (a) side view and (13)top view.
dynamics, but it also has feedback terms to compensate for
modelinguncertainty:
+ i_csgn(_ + _l_-t - K[_ (3)
5=O-ed
and _d(t) is the desired trajectory. The feedforward is
adjustable through model updates, and the feedback, KD_
through trajectory updates if KD is constant. A block
diagram depicting the control scheme is shown in Fig. 2.
The only requirement on KD is that it be positive definite.
One desirable choice for KD is _1 (see Slotiue and Li [5])
which produces a feedback which deponds on the model
updatesas well as the commanded trajectory. This yields a
control law of the form
= +
whichisapproximatelythesame asa computedtorquewith
criticallydamped errordynamics.
The robot model, encompassedby Athe "^" terms in (3),
is linear in the model parameters 1l. g is updated so as to
ensure that the derivative of the Lyapunov function
v(t)=½FH +½ rr (s)
^
is negative definite, where 11--R-11,is the parametric error.
The positive definite weighting matrix, F, is usually chosen
to be diagonal. The parameter update law
= _F 4 yT_ (6)
where
Y _ = (_I-H)_.r + (_-C)_.r + dg-:Ig) (7)
yields aLyapunov derivative
V(t) I= - gT KD ¢ (8)
thus ensuring stability for a positive defmite choice of KD.
Because of their simpler form, the friction parameters have
been omitted from (6) and (7) and are updated according to
the analogous law
f)ck =" "l"J ek sgn(EhO (9)
_k -1= -y_ ek{)rk (10)
where k denotes the kthjoint, and Dck is the (k,k) element of
De. If KD is chosen to be _L_I,then _r must be replaced by
_r-_.e in (7) to account for the possibility that _1 is not
positive definite, r can be viewed as a gain which
determines how quickly the parameters will adapt and is
largely chosen heuristically.
Though this formulation ensures stability of the tracking
algorithm for correct model structures,it saysrelativelyLittle
about the convergence of the model parameters; it does,
however, guarantee convergence for "persistendyexciting"
trajectories.What thisterminologymeans inthenonlinear
caseisanareaofongoingresearch,althoughinanintuitive
sense,itmeans thetrajectorymust excitethedynamicsin
such a way that incorrect parameters will produce significant
differences between the modeled and observed dynamics.
In the linear case, persistent excitation depends on the
number of input frequencies used and how that relates to the
order of the system. However, in tests where the number of
input frequencies were varied, the convergence of the model
parameters did not appear to be significantly effected in a one
minute trial. It is possible that the speed of convergence
depends more on other factors such as the number of
parameters than on the degree of persistent excitation.
-=- !......... _ r-'L'_-- --_2"2_-,
2: 8chenmlk: of amter/slavu teleopemlor wtt_ (llim:t ac_onve contmner.
Q ;
t
3Asymptotic convergence is only guaranteed when the
parameters appear explicitly in the Lyapunov derivative. In
"composite" control formulations, both state feedback and
torque feedback are used and the model parameters appear
explicitly in V(t), However, improved convergence was not
apparent for this scenario and was computationally
expensive; thus the experiments performed here used the
simpler, noncomposite form of control. For more on this
topic, the reader is referred to Slotlne and Li [6].
4.0 EXPERIMENTS
A photograph of the Kraft "slave" arm used in the
telcoperation tasks is shown in Figure 3. Both arms are
clamped at the wrist so that only the fu'st three degrees of
freedom in the base are active. A hook was attached to the
clamp on the right arm enabling it to retrieve weights during
the tests. The AC motors were driven by control units that
were supplied by the arm manufacturer.
Figure 3: Photo o! Knit am #anipmltfltl payletd.
The only sensor information available was the position
of the finks supplied by potentiometers geared to the motor
shafts. Velocity and acceleration information were obtained
through differentiation and extensive filtering of the
potentiometer .data. A Compaq 386/20 equipped with
coprocessor was used to derive the control laws and transfer
data back and forth to the control unit. The experiments
were run at 81 Hz, the maximum rate achievable with the
current software. The control bandwidth, _., was chosen to
he I/2 Hz, just slightly below the natural frequencies of the
drive systems.
In all tests, the subjects were asked to move the arm to
pick up the weight from a table, move the arm back to its
initial position, sequentially move the shoulder azimuth (01),
shoulder elevation (02), and elbow (03) back and forth
several times, and then to return the weight to the table,. For
each weight tested, the controller was first tried with the
adaptation turned on and then turned off. Prior to running
all the tests, one adaptive run was made without a payload to
obtain initial values for the arm paratmtm_. These values
were used in all subsequent runs as the starting parameters.
The master and slave joint positions for one set of tests
run with the 0.5 kg weight are plotted in Pigs. 4 and 5. For
the adaptive results shown in Fig. 4, the master and slave
_les were nearly indistinguishable. In the nonadaptive
plots, however, the master and slave shoulder elevations and
elbow angles differed a great deal. This is because of the
increasing effect of gravity on the loaded arm as one
progresses toward the payload. Since the gravity parameters
are nonadaptive and the gravity forces dominate the inertial
forces for moderate speeds, joint 3 differed greatly from the
commanded angle, whereas joint 1, whose axis was parallel
to gravity, was relatively unaffected.
It is almost possible to track the progress of the
experiment simply by looking at Fig. 5: at 7 sec, the slave
arm reaches the payload and begins pushing down on it
(slave arm is impeded by the object so that 03 for the slave <
03 of the master -- pitch down produces positive 03); at 17
sec, the arm starts lifting the payload and at 20 sec, the
payload clears the table (the slave cannot lift the payload as
high as the master arm so that now 03 for the slave > 03 of
the master). Beginning at 23, 35, and 45 sec, respectively,
joints 1, 2, and 3 are moved back and forth, and at 57 sec,
the payload is returned to the table.
Although the joint angle errors provide a fairly good
measure of the tracking performance, the tracking error
provides the true measure of the control system
performance. Figure 6 plots the tracking errors for these
two tests on the same graphs. These plots reaffirm the
conclusions reached earlier from observations of the joint
angles. In the adaptive case, it is difficult to discern when
the payload is picked up, whereas for the nonadaptive case,.
this is relatively easy: at t=-Tsec, s3 begins rising rapidly, and
at t=17sec, s2 also begins to rise as the payload is lifted from
the table.
The same experiments were repeated for retrieving a 1 kg
wei._ht, and reaults for joint 3 in the adaptive case are shown
in Fig. 7. Even with a payload twice as large, the tracing
errors are not significantly different from those of the 0.3 Kg
case in Fig. 6. This illustrates the ability of the tracker to
maintain controlperformance when the ann'scharacteristics
are being significantly altered through interaction with the
environment.
As a final test, several adaptive runs were made with
structural simplifications in the model used by the controller.
Figure 8 shows joint 3 results for a trial in which the velocity
dependent terms, i.e. _ 6. f_c, and f_, were ignored. In
comparing Fig. 8 with s3 in Fig. 6, one can discern little
degradation in going to the less accurate model. This is
probably due to one of two reasons: the tracker was able to
compensate for this inaccuracy through the adaptation of
other parameters (for the friction parameters) or further
modification of already existent parameters (for the Coriolis
terms), or the neglected terms were insignificant for the
particular tests which were run. The latter case seems
unlikely for the friction parameters at least, since the
coulomb friction forces were found to account for about
20% of the peak torque. Whatever the case, ignoring these
terms can tagnificantly reduce the amount of computation
and is a possibility which should not he overlooked for more
complex systems.
5.0 CONCLUSIONS
This effort applied a parameter adaptive controller to a
parallel linkage arm and tested the controller on a
teleoperatesl - _stem. One purpose of this task was to verify
BLACK
i
ORIGINAL PAGE
AND WHITE PHOTCN3RAPH
Q J
t
ut
i
i t
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(l_U) ae
8
o ........ _,,,_, o
ORIGINAL PAGE IS
OF POOR QUALITY
t
5that the adaptation algorithm would work even ff the
commanded inputs were provided by a human operator.
Another was to investigate the differences, in terms of
improved manipulation ability, between a controller with
invariant characteristics and one which azcomodates external
perturbations.
In experimental tests, the adaptive tracking algorithm
was found to converge within several seconds following
picking up or putting down a payload. This was an
improvement over the nonadaptive controller where the
errors built up considerably because of the inability of the
feedforward to correctly compensate for the added
gravitational forces on the arm due to picking up a payload.
While this limitation did not unduly impede the operator in
these tests, a more precise task would force the operator into
moving the master arm along a "false" trajectory to achieve
the desired motion in the slave arm. In a scenario dominated
by inertial rather than gravitational forces, this inability
would be manifested as large overshoots for the slave arm.
In either situation, the range of motion for the slave arm may
become severely restricted compared to the master.
The only way to reduce the error without modifying the
feedforward in the nonadaptive case would be to increase the
feedback gains on the position and velocity errors. These
gains can only be increased to a certain extent, however,
befme the natural frequencies of the arm are excited (-1 Hz).
By contrast, the adaptive controller is able to maintain the
same errors before and after a payload is picked up without
changing the bandwidth.
_o IO ,IO 4o
t (see)
Figure7: Joint3 trackingerror duringadaptive manlpulMlon
of 1.0 kg payload.
1.4
1.
0.6
0.4°
G.Io
"_.I •
t0 I I _
t _)
FigureS: Joint3 trackingerrordudng _ maniptdmion
of O.Skg payloadwithoutvelocityfeldforwlvd.
Because the gravity forces dominated the arm torques in
these experiments, the desired trajectory played only a minor
role in the parameter adaptation. This is born out by
observing that the joint 1 errors for the adaptive case
decreased little if any over those for the nonadaptive case.
(Joint 1 torques had no direct dependence on gravity.) For
the trajectory to play a more important role, the inertial forces
would have to be much higher relative to gravity. Thus it is
not possible to extend all the conclusions drawn here on
tracking convergence to a gravity-free environment.
One drawback worth mentioning in using this approach
for teleoperation occurs during contact of the robot arm with
immobile objects. When the progress of the robot arm is
impeded by an object such as a table surface, the adaptive
controller begins modifying the arm parameters to reflect an
increase in the mass of the arm which could account for the
inability of the arm to continue along its path. As the arm is
commanded away from the surface, the movement is delayed
as the arm parameters readjust to the newly found freedom
of motion. If the exact position and orientation of the ....
surface were known (such as in a completely automated
setting), then the arm-environment interaction could be
modeled and the contact could be taken into account in the
tracking errors and the false modification of the arm
parameters would not take place (see Niemeyer and Siotine
[7]). Thus during compliant motion, the adaptation should
be turned off to prevent their adjustment during this
interaction.
ACKNOWLEDGMENTS
The authors would liketo express theirappreciationto the
Space StationProjectOffice (Code 400.6),NASA Goddard
Space Flight Center for theirsupport of thisresearch.
Thanks alsogo to Rick Schnurr (Code 712.3)for providing
the communications software for the Kxaft/Compaq
interface.
I°
2.
REFERENCES
Craig, J. J., Introduction to Robotics, Addison-Wesley,
Menlo Park, Calif., © 1986
Paul, R. P., Robot Manipulators: Mathematics.
Programmine. and Control, MIT Press, Cambridge,
Mass., © 1981
3. Asada, H., and Youcef-Toumi, K.,
Robots. MIT Press,Cambridge, Mass., © 1987
4. Slotine,J-J.E., and Li, W., "On the Adaptive Control
of Robot Manii_ulators,"Int.J.Robotics Research,Vol.
6, No. 3, 1987
.
.
.
Slotine,
Control:
Control,
J-J. E., and Li, W., "Adaptive Manipulator
A Case Study," IEEE Trans. on Automatic
Vol. 33, No. 11, 1988
Slotine, I-J. E., and Li, W., "Composite Adaptive
Control of Robot Manipulators," Automatica, Vol. 25,
No. 4, 1989
Niemeyer, G., and Slotine, J-J. E., "Computational
Algorithms for Adaptive Compliant Motion," Proc.
WEE Conf. on Robotics and Automation, Scottsdale,
Ariz., May 1989
|
gAPPENDIX: KRAFT ARM DYNAMICS
X =H_.+C_)+Ig
where
a --
p0+2p Ic3s3+p3s22+p4s32+p5c22 p12s2 P2C3-p9s3
+p7C32-2p I012c2s3+2p I IC2C3
P12S2 136 -P1012t32+p1163
P2c3-P9S3 -P1012$32+PlIC32
I 10H11_. I aHl1.,
_-:"_ 2 +_ --'_3
'_ae2 z ao3
C = - _ a0 2 1
" 2 a03 l
°]:_g = -Pl3C2 gPlOS3-Pl4C3
002 I a02 2 _ a03 t a03 3
0 _-_s
ae3
aH •
= 2(133-P5)S2C2+2p 1012s2s3-2p I1s2c3
ao2
= 2(p4-P7)S3C3+2p 14-2p lS_-2p 1012c2c3-2p i 1c2s3
a03
_H23 = P1012c32+P 1lS32
a02
= P12C2
a02
= -p2s3-p9c3
a03
_H23= .P1012c32_PllS32
ae3
model parameters:
p0=Ilzz
pl=I3xy
p2=13yz
p3=I24xx
p4=I35xx
p5=I_yy+m31_
p6=ITAzz+m31,_
p7=I35yy+m4L_
p8=135zz+m41_
p9=I3xz-m415b 1-m5x5b3
Pl0=m3Y3
Pl l=m3x312+m4x415
P 12--m2x2 bl+m4x4bl+m3]2(b2 +z3)
P13=m2x2+m312+m4x4
P14=m3x3+m415+m5x5
*si=-sin0i and ci!ecos0i, s32=-sin(03-02) and c32m_of_03-02)
The capital 'T' 's are combinations of link incrtias and mass
x CM 2 terms:
Ilzz = ilzz+mlYl 2
• 2
I2zz = 12zz+m2x 2
• 2 2I3xx = 13xx+m3Y3+m3(z3+b2)
I3yy = i3yy+m3x_+m3(z3+b2) 2
• 2 2
I3zz = ]3zz+m3x3+m3Y3
I4xx = i4xx+m4b_
• 2 2
I4yy = 14yy+m4x4+m4b 1
• 2
[4zz = 14zz+m4x 4
I35xx = I3xx+I5xx
I35D, = I3yy+I5yy
I35zz = I3zz+I5zz
• 2
I2xx = 12xx+m2b 1
• 2 2
I2yy = 12yy+m2x2+m2b]
I3xy = i3xy-m3x3y 3
I3xz = i3xz-m3x3(z3+b2)
I3yz = i3yz+m3Y3(z3+b2)
• 2
I5xx -- 15xx+m5b 3
I5yy = iSyy+msx_+msb32
• 2
ISzz = 15zz+m5x 5
I24xx = 12xx+14xx
24yy =:2yy+I4yy
24zz = 12zz+14z.z
The CM positions in the local coordinate frames are:
= , , -- Y3 ,X_ml Yl /_cm2 = xrm3
Zl z3
Xrm4 = , /_cm5 =
The link inertia tensors about the CM in the local coordinate
frames are:
o] ,i.oo]I]=[ 0 ilyY_ilyz"ilyz ' I_2=L 0i2YYilzz 0 i2zz '
,x,,.] 013 =/-i3_y i3yy-i3yz , _ = hi. ,
L-i3xz-i3yz i3zz 0 i4zz
[- i5xx 0 0 ]
o°i,.o l0 iSzz
where the elements of I arc moments of inertia about various
axes. e.g. ixx'=_(y2+z2)dm and ixyEJJxydm.
The initial parameter values used in all the experiments were:
p0--0.0489 p5=0.0973 P10--0.0523
p 1=0.0021 p6--0.3449 P ! 1-..-0.0827
p2=-0.0214 p7=O.3999 P12=0.0088
p3=0.0521 PS=0.5819 P_3=0.0650
i)4=0.0807 p9=-0.0209 p 14=0.0996
P15=0.0228 (coulomb,I)
pl-r=O.0536(coulomb,2)
P19=0.0500 (coulomb,3)
P16=0.0302 (viscous, l)
P18=0.0392 (viscous,2)
p20--0.0248 (viscous,3)
t


An adaptive controller for enhancing operator performance during teleoperation

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