Proceedings of the 2001 IEEE
International Conference on Robotics & Automation
Seoul, Korea • May 21-26, 2001
Robotic Mapping of Friction and Roughness
for Reality-based Modeling
John E. Lloyd and Dinesh K. Pai
Dept. of Computer Science, University of British Columbia
Vancouver, B.C., Canada
flloyd,[email protected]
Abstract
This paper discusses the robotic acquisition and characterization of surface friction and roughness for real-world
objects. Our motivation is the construction of detailed
“reality-based” models for existing objects that can be used
in haptic displays and other applications involving simulation. A key challenge addressed in this paper is the acquisition of these surface properties on real objects with
non-trivial shape, and registration of these properties with
respect to geometric models of the shape. We show how
Coulomb friction may be effectively estimated in the presence of variations in surface normal. We also show how
to estimate a stochastic process model of surface roughness. Finally, we demonstrate the robotic mapping of surface friction over an entire object, using the UBC Active
Measurement Facility (ACME).
1 Introduction
Friction and other surface properties, such as roughness,
figure prominently in the mechanics of contact and robotic
(as well as human) manipulation [1] ; knowledge of these
properties is important for predicting and simulating system behavior. In particular, models of friction and roughness are very important for the simulation of objects with
haptic displays, and are useful for other applications such
as fine motion and grasp planning in robotics.
Obtaining accurate surface models for real-world objects can be tedious, because such items often have intricate surface patterns and curved geometries and aren’t generally designed for ease of modeling. Friction, for instance,
can be accurately measured in a laboratory setting, but this
usually requires small flat samples of each type of surface
material.
By contrast, in the context of this paper, we are interested in acquiring, for arbitrary objects, approximate surface models that can be used effectively in applications
such as haptic simulation. Because this is a potentially
complicated task, we emphasize the use of robotic technology to acquire these models automatically.
Figure 1 shows our system. The surface of the bottle in
the center has different patches with different surface friction. Such a distribution of friction on the surface is very
difficult to map using existing methods. Our system ac-
0-7803-6475-9/01/$10.00© 2001 IEEE
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Figure 1: ACME facility being used to map surface characteristics of a bottle.
tively explores the surface of the bottle using the robot on
the right, adapting the sampling online based on the measurements, and constructs a map from surface points to surface characteristics.
This paper will discuss three principal issues required
for such a robotic system:
1. How to effectively measure Coulomb friction at arbitrary locations on a surface of uncertain geometry
using a robotic manipulator;
2. How to approximately characterize surface roughness in terms of a small set of parameters which
model the force profile obtained by dragging a probe
across the surface;
3. A case demonstration in which we use a robotic system to automatically map the surface friction of a test
object.
Surface roughness characterization will be demonstrated
for the materials shown in Fig. 2.
This work was undertaken as part of the development
of the UBC Active Measurement Facility (ACME) [2], a
system designed to rapidly (and semi-automatically) create comprehensive physical models of various artifacts (including shape, stiffness, surface reflectance, and acoustic
suring the variation of these properties over the surface of
existing objects. Demonstrating the ability to do so (using exploratory methods similar to those previously used
to estimate contact sound response over an object’s surface [21]), is a major focus of this paper. Similar issues
arise in estimating local properties of contact during teleoperation [18, 19, 20], though the models are designed for
recognition, rather than rendering, of the contact state. Estimation of the distribution of contact sound response over
the surface of an existing object was described in [21].
3 Measuring Coulomb Friction
Figure 2: Some materials whose surface properties are
studied in this work. From left to right: ribbon cable, masonite, and rubber gasket material.
properties), for use in such applications as robotics, teleprogramming, virtual reality and simulation and training environments.
2 Related Work
Traditionally, the study of friction lies within the field of tribology, a branch of mechanical engineering concerned with
friction, lubrication, and wear of machinery. There is a vast
literature on friction characteristics of engineering systems
such as robot joints, surveyed in [3]. The Coulomb model
of friction is by far the most widely used, though variants
have been proposed which more accurately account for observed phenomena (e.g., [4]), or are useful for haptic rendering (e.g., [5, 6]). While the traditional focus of friction estimation has been in improving the control of machines [3], there recently has been interest in estimating
friction for haptic rendering [7, 8, 9, 10]. However, in most
of this work friction was measured only on small samples,
and the issues in measuring friction over the surface of an
existing 3D object were not addressed.
Surface roughness also has a long history in engineering metrology [11]; roughness is viewed as the small scale
geometry of a surface which can be measured using profilometers. Roughness is also a very important component of haptic texture perception in humans [12, 13], and
recent interest has been motivated by the requirements of
rendering rough surfaces using force feedback haptic devices [14]. A method for detecting fine surface features is
described in [9]. Stochastic models of surface roughness
have been used both in metrology [11] and for fast haptic
rendering [15, 16, 8].
All of the above work has been primarily concerned with
estimating surface properties of small samples of material.
There has been little previous work in automatically mea1885
In Coulomb’s model of dry sliding friction for point contacts, the tangential frictional force ff during sliding is proportional to the contact normal force fn, according to
ff =
,fn u
(1)
where is the coefficient of friction and u is a unit vector
in the direction of motion. The normal force fn, and hence
ff , varies depending on the dynamics of contact.
The Coulomb friction model, along with other friction
models, is a coarse description of microscopic surface interactions between bodies, and so tends to have a fair amount
of variability associated with it. The friction coefficient is itself a function of a given pair of interacting materials,
and will also change somewhat depending on the geometry
and surface area of contact.
In a tightly controlled setting determining is straightforward: one places the two materials in contact with a normal force fn, slides them with respect to each each other,
measures the resulting frictional force ff in the direction of
motion, and then computes = kff k=kfnk.
However, in the setting of this paper, we need to obtain a
large number of friction measurements over the surface of
an arbitrary object. To reach the various points on the object’s surface, we use a robot equipped with a special probe
(Fig. 3). The probe has a spherical tip made of a specific
material (presently steel). It is brought into contact with
the object, and then pulled across the object’s surface using a compliant motion to ensure contact is maintained. Resulting forces are then measured and used to estimate between the probe material and a local region of the object’s
surface.
The measurement process is trickier than in the laboratory setting:
The direction of the surface normal may be known
only approximately, and may also vary as the probe
is pulled across the surface.
The force and position measurements from the robotic
manipulator are noisy due to structural vibrations,
“stick-slip” effects on smooth surfaces, and the surface texture.
n
f
f
=2
ff
ff
Figure 3: Measuring Coulomb surface friction of an object
using a robot equipped with a probe.
Figure 4: Forces associated with motion in two different directions along an object surface.
4
We address both these problems using a differential measurement approach, in which the probe is passed along a
short path segment on the surface, and then passed over the
same segment again in the opposite direction.
Force measurements made during this process are collated so that for each point along the path, the forces f and
f associated with the forward and reverse motions are both
known. Now referring to Fig. 4, f and f each have a normal component parallel to the surface normal n, and a friction component (denoted by ff and ff , respectively) which
lies opposite to the direction of motion and is perpendicular
to n.
Now even if n is unknown, and the magnitudes of f and
f differ, we can still estimate by calculating the angle between f and f :
= tan(=2):
:
k^f + ^f k
^
f +^
f
reverse motion data
forward motion data
−2
−4
−6
fz
−8
0
50
100
150
200
250
300
350
400
450
500
Figure 5: Force profile for a straight line segment on glass.
(3)
By averaging the values of obtained at various points
along the path, a reasonable estimate of the Coulomb friction coefficient may be obtained.
3.1
fx
0
(2)
Note that this calculation is ideally independent of the speed
of travel, the force of the probe against the surface (in either direction), the orientation of the probe, and of course
the surface normal itself. If ^f and ^f denote the normalized
values of f and f , we can calculate the surface normal from
n =
2
Example measurement results
Some of the force profiles associated with the above procedure are now shown.
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For the force data shown in Fig. 5, the probe was drawn
back and forth along a 20 mm line segment, parallel to the
x axis, with a speed of 10 mm/s and an applied pressure of
5 Newtons. Data was sampled at 100 Hz, and there was a
.5 second pause between the forward and reverse motions.
The top and bottom traces correspond to the force components fx and fz , which are parallel to the motion direction and the anticipated surface normal, respectively. fz
roughly tracks the desired 5 Newton tracking force, while
the effect of the friction is apparent in the sign change of fx
after the motion changes direction. To eliminate the effect
of transients at the beginning and end of the motions, we restricted our computation to data windows which were well
within the motions themselves; these are indicated by the
labels “forward motion data” and “reverse motion data”. was calculated to be 0:106, with standard deviation 0:004.
0.5
4
0.45
2
0.4
rubber
fx
0.35
0
0.3
0.25
−2
reverse motion data
forward motion data
0.2
−4
0.15
0.1
glass bottle
−6
0.05
fz
−8
0
0
50
100
150
200
250
300
350
400
450
500
Figure 6: Force profile for a straight line segment on rubber.
In Fig. 6, the same experiment is repeated, only this time
using the rubber material shown in Fig. 2. The larger coefficient of friction is apparent in the fx data. was calculated to be 0:305, with standard deviation 0:018.
Finally, in Fig. 7, the experiment is repeated on the
curved surface of the glass bottle used in Section 5. Now,
the force components vary considerably, due to the variation in the normal caused by the bottle’s surface. A reasonably good estimate of is still obtained, however: 0:13
with standard deviation :008.
4
2
fx
0
−2
reverse motion data
forward motion data
−4
−6
fz
−8
0
50
100
150
200
250
300
350
400
450
500
Figure 7: Force profile along the curved surface of a glass
bottle.
In all of the above calculations, the computed value of
was quite stable all along the data window, regardless of
variations in the surface normal. This can be seen in Fig.
8, which shows the computed value of over the data window, for the rubber and curved bottle examples.
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0
20
40
60
80
100
120
140
160
Figure 8: Computed values of at different points in the
data window, for the examples of Figs. 6 and 7.
4
Roughness Characterization
The glass and rubber surfaces described in the above section are both relatively smooth, but when we repeat the
same experiments on the masonite and ribbon cable shown
in Fig. 2, much rougher force profiles are obtained (Figs. 9
and 10).
We would like to characterize this roughness with a
model suitable for fast simulation, with a small number
of parameters. Several models of roughness are used in
the engineering metrology literature; most are designed for
evaluating the “quality” of a surface produced by a manufacturing process. The most relevant for our purposes are
statistical models which characterize the surface variations
as the spatial equivalent of a time series. Based on this, we
choose to model the variation in observed forces (with respect to the nominal forces induced by the surface normal
and friction) as a stochastic process. We prefer to model
force variations rather than geometric variations because
the former are more directly connected with what the user
of a haptic display will actually “feel”. Moreover, geometric variations will be correlated with force variations within
regions where the coefficient of friction is approximately
constant and the normal force is fixed.
How should we model this stochastic process? In previous work, [15, 16, 8] have modeled frictional forces as
an IID sequence, where the mean corresponds to frictional
force and the variance is a measure of roughness. However, this does not capture the rapidity of variation in the
force data: the profiles in Figs. 9 and 10 have similar amplitudes but the former obviously varies more slowly than
the latter.
One way to assess the rapidity in variation of a random
process is to examine it’s autocorrelation function fac : a
1
4
1
0.8
2
0.6
fx
0.5
0
0.4
0.2
−2
0
reverse motion data
forward motion data
0
−4
−0.2
−6
−0.4
fz
−8
0
50
100
150
200
250
300
350
400
450
50
100
150
200
−0.5
0
50
100
150
200
Figure 11: Autocorrelation functions of fx for the rubber
(left) and masonite (right) experiments.
500
Figure 9: Force profile for the masonite in Fig. 2.
We can in fact encapsulate these quantities by using an autoregressive model of order 2, denoted AR(2), so that the
force variation f (x) observed along the surface is given by
4
f (x) = f (kL) def
= f(k ) a1 f(k ,1) + a2 f(k ,2) + (k )
2
(4)
fx
0
where k is the sample index, L is the spatial discretization,
a1 and a2 are the model coefficients, is the standard deviation of the input noise, and (k) is a zero-meaned noise
input with standard deviation of one.
The quantities a1 , a2, and provide a compact set of parameters to characterize surface roughness, for a model that
is very easy to simulate. Higher order models could also be
used (for instance, if the roughness data exhibited several
different spatial frequencies), but an AR(2) model seems
to be broadly useful: Figs. 12 and 13 show a portion of the
force data for the rubber and masonite experiments, along
with a simulation of this data using the estimated AR(2) parameters.
−2
reverse motion data
forward motion data
−4
−6
fz
−8
0
0
50
100
150
200
250
300
350
400
450
500
Figure 10: Force profile for the ribbon cable in Fig. 2.
rapidly varying process will produce an fac which quickly
decays to zero. Fig. 11 shows the autocorrelation functions
of the forward motion fx data (after de-trending) for the
rubber and masonite experiments depicted in Figs. 6 and 9.
fac decays more quickly for the rubber data, implying less
short-term correlation and “tighter” spatial variation. Both
data sets also exhibit true periodicity, which is also visible
in the fac (since periodicity in a series maps into an equivalent periodicity in its autocorrelation function). This is
not surprising, since surface textures, particularly for manmade objects, are likely to exhibit periodic behavior due to
either the manufacturing process or functionality (e.g., the
ribbon cable) or even aesthetics.
A short list of parameters that we could use to model the
roughness force data could then be (a) amplitude, (b) decay
rate of the fac , and (c) the frequency of the dominant mode.
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5 Automated Measurement with ACME
The above techniques can be used to build a map of surface
characteristics over an entire object. We do this using the
ACME facility [2], a robotic system with a variety of sensors designed to automatically acquire physical models of
real-world objects.
At present, ACME consists of a time-of-flight laser range
finder; a Triclops trinocular stereo vision system, and a
high resolution RGB camera (both mounted on a 5 DOF
positioning gantry); a Puma 260 robot equipped with a
force/torque sensor, mounted on a linear stage; and a 3 DOF
planar positioning stage which serves as a platform for objects being measured. A partial view of the ACME set up
is shown in Fig. 1. See [2] for more details.
Surface properties are mapped with ACME in the following way. First, the object is mounted on the stage, and
4
Details of the motion planner are omitted here due to
space limitations. Briefly, we use an adaptive sampling
scheme for exploring the surface [21]. The robot first measures the friction (or more generally, surface texture) at the
vertices of the coarsest mesh. Texture parameters at adjacent sample points are compared, using a distance metric defined over the texture parameters. If this distance exceeds a prescribed threshold, then an additional sample is
taken in between, at a vertex of the next finer resolution
mesh. By tightening the sample spacing in areas where surface characteristics differ, we are better able to localize the
boundaries between regions of different surface properties.
3.5
3
2.5
2
1.5
1
0.5
0
0
20
40
60
80
100
120
140
160
180
2
1.5
1
0.5
0
−0.5
−1
5.1
−1.5
−2
0
20
40
60
80
100
120
140
160
180
Figure 12: Close up of data for the rubber experiment (top),
and a simulation of the data (below) using the estimated parameters a1 = 0:60, a2 = 0:25, and = 0:11.
4
3.5
3
2.5
2
1.5
1
0.5
0
0
20
40
60
80
100
120
140
160
Case study: friction on a bottle
200
180
2
1.5
1
0.5
0
As a case study, we have mapped the friction of a glass bottle, to which we have applied several patches of fine-grit
sandpaper (Fig. 14) to create regions of high friction. The
resulting friction map is shown using a grey-scale image on
the right of Fig. 14, in which higher friction regions appear
whiter. Note that the different friction regions are clearly
visible.
The entire friction map shown was constructed with a total of 153 sample measurements (each indicated by a line
segment in the friction map image). About half of these
were from uniform sampling at the coarsest level, while
the rest were taken from higher resolution meshes in places
where the planner detected variations in the data. Notice
that the planner correctly clusters the samples at the boundaries between areas of constant friction.
Note also that there is some blurring of the image in the
figure because of the interpolation algorithm we used to display the data — optimal interpolation of such scattered data
is a topic of current research.
−0.5
−1
6
−1.5
−2
0
20
40
60
80
100
120
140
160
180
200
Figure 13: Close up of data for the masonite experiment
(top), and a simulation of the data (below) using the estimated parameters a1 = 1:61, a2 = ,0:73, and = 0:16.
the range sensors are used to build a triangular mesh representing the object’s surface. The mesh is used to define
the control polyhedron of a Loop subdivision surface [22].
This gives us a multiresolution surface of arbitrary topological type that approximates the boundary and associated
normals well. The robotic system plans a sequence of probing operations to acquire surface information over a representative sample of surface locations.
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Conclusions and Future Work
We have shown how we can construct a map of friction
and roughness on the surface of existing objects. We also
showed how the coefficient of friction can be robustly estimated in the presence of variation in surface normal, and
how surface roughness can be efficiently represented using
a statistical model amenable to fast simulation.
Real objects usually are made of different materials with
different frictional and roughness properties. The work reported in this paper makes it possible to simulate contact
with such objects more accurately. The distribution of texture over the surface of the object can be mapped far more
easily than before, using active measurement techniques
and the ACME facility. We anticipate that such detailed
models of surface texture will be useful for haptic interaction. We are currently developing such haptic simulations
for the PHANToM haptic interface.
Figure 14: Mapping the friction of a bottle. Left frame
shows the bottle itself and the applied sandpaper patches.
Right frame shows a grey-scale representation of the resulting friction map, where black indicates the lowest friction
( 0:13 for the glass), and the lightest shade indicates
the high friction ( 0:5) of the sandpaper. Line segments
show the sampling points, whose density increases near the
patch boundaries.
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