pres.1993.2.3.203.pdf

Robert N. Rohling
and
John M. Hollerbach
Biorobotics Laboratory
McGill University
Montreal, Quebec, Canada H3A 2B4
Stephen C. Jacobsen
Center for Engineering Design
University of Utah
Salt Lake City, Utah 841 12
Optimized Fingertip Mapping:
A General Algorithm for Robotic Hand
Teleoperation
Abstract
An optimized fingertip mapping (OFM) algorithm has been developed to transform hu-
man hand poses into robot hand poses. It has been implemented to teleoperate the
Utah/MIT Dextrous Hand by a new hand master: the Utah Dextrous Hand Master.
The keystone ofthe algorithm is the mapping of both the human fingertip positions and
orientations to the robot fingers. Robot hand poses are generated by minimizing the
errors between desired human fingertip positions and orientations and possible robot
fingertip positions and orientations. Differences in the fingertip workspaces that arise
from kinematic dissimilarities between the human and robot hands are accounted for by
the use of a priority based mapping strategy. The OFM gives first priority to the human
fingertip position goals and the second to orientation.
Introduction
PRESENCE, Vol. 2. No. 3. Summer 1993. 203-220
© / 994 The Massachusetts Institute of Technology
Hand masters are
being developed and applied for teleoperation of mul-
tifingered robot hands, control ofgraphics displays, and interfaces for computer
games (Eglowstein, 1990; Foley, 1987). Popular commercial hand masters
include the VPL DataGlove (VPL Research Inc., Redwood City, CA), the
Exos Dextrous Hand Master (Marcus, Lucas, & Churchill, 1989), and the Cy-
berGlove (Virtual Technologies, Stanford, CA). For more advanced applica-
tions, force-reflecting hand masters have been developed, including a
hydraulic-
powered system (Jacobsen, Iversen, Davis, Potter, & McLain, 1990), electric
drive systems (Iwata, 1990; Jau, 1992; Oomichi, Miyatake, Maekawa, & Haya-
shi, 1988), and pneumatic-powered systems (Burdea, Zhuang, Roskos, Silver,
&Langrana, 1992; Stone, 1991).
For some of the telemanipulator systems just cited, the hand master and the
robot hand have the same geometry, and so the kinematic mapping is direct.
Human finger motion is restricted to that allowed by the master's kinematics.
For other systems, there may be significant geometric differences between ro-
bot and hand master, especially for those hand masters that attempt to measure
directly the human finger joint angles. Direct measurement of the human joint
angles requires a model of the human hand kinematics to be derived when
implementing a teleoperation algorithm. Teleoperation of dextrous robot
hands then requires an
algorithm that performs transformations of human hand
poses to the robot hand.
This paper describes an
optimized fingertip mapping (OFM), which ad-
dresses kinematic dissimilarity via a
goal priority approach to fingertip control.
Rohling et al 203
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204 PRESENCE: VOLUME 2, NUMBER 3
Figure I. Utah/MIT Dextrous Hand.
The OFM has been implemented to teleoperate the
Utah/MIT Dextrous Hand by a new hand master, the
Utah Dextrous Hand Master.
2 Utah/MIT Dextrous Hand
The robot hand (Fig. 1) is a four fingered tendon
operated hand; it is similar in size to a human hand and
contains one finger (thumb) to oppose the other fingers
(Jacobsen, Iversen, Knutti, Johnson, & Biggers, 1986).
Figure 2 shows the overall kinematic structure ofthe
robot hand. A Denavit-Hartenberg (DH) coordinate
system (Denavit & Hartenberg, 1955 or Paul, 1981) has
been established to describe the kinematics of each finger
ofthe robot hand. Reference frames are also placed at
each fingertip, therefore the last DH parameters locate
the fingertip. The DH coordinate systems are
depicted
in Figure 3 and the DH parameters are located in
Table 1.
Common Reference Frame
Finger 1
Finger 0
Figure 2. Kinematic model ofthe Utah/MIT Dextrous Hand. The
model is shown in the zero-angle position. The common reference frame
is located at joint 2 offinger 2.
This paper adopts the following notation to identify
joints and coordinate systems:
•
joint ij (i =
0, 1, 2, 3 j =
1, 2, 3,4) refers to finger
i, joint ;'
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Rohling et al 205
Äooi
y0 |z0Zoo
«T*-
Yc
r-vz,
02
L20
^03
y—fZo4
-'04
v02
x03
04
X30T Z30
y3o
Palm View Side View of Palm
Figure 3. Coordinate description ofUtah/MIT Dextrous Hand shown
with fully extended fingers. Dashed lines indicate vectors not lying in
plane ofpage. Denovit-Hartenberg parameters ofVector,¡ (finger i, joint
j) are found in Table I.
• coordinate system ik (i =
0, 1, 2, 3 k =
0, 1, 2, 3, 4
k =
j —
1) refers to coordinate system axes labeled
ik. The labeling of coordinate systems k =j —
1 cor-
responds to the standard Denavit-Hartenberg con-
vention of labeling joint axes/ —
1 at joint/. An axis
system is also placed at the fingertip and corresponds
to k =
4.
• The base coordinate frame is labeled simply as sys-
tem 0.
A remote pneumatic actuator pack activates each fin-
ger joint movement via antagonistic tendons. Control is
provided by the CONDOR (Narasimhan, Siegal, &
Hollerbach, 1989) real-time control system by using
joint angle data and tendon tension data from Hall-effect
and strain-gauge sensors
respectively.
The wrist of the robot hand is attached with a fixed
palmar orientation to a 3-DOF Cartesian robot. The
Cartesian robot follows the human operator's wrist mo-
tion through the use of a Bird position sensor (Ascen-
sion Technology Corp., Burlington, VT). The Bird sys-
Table I. Denavlt-hfartenberg Parameters for the Utah/MIT
Dextrous Hand
j a,}(mm) si} (mm) ot,; (deg) 6,y (deg)
Finger/ =
1,2,3
0 -18.0
1
2
3
4
15.2
43.2
33.0
18.7
Finger i
-
0
0
1
2
3
4
0
10.2
43.2
33.0
18.7
-17.7»
18.4
50.7
-53.6
0
0
0
0
0
0
0
0
90
90
0
0
0
90
-90
0
0
0
12
[-45,45]*
[-60,30]
[0,90]
[0,90]
0
[-45,45]
[-14,54]
[4,90]
[0,90]
aho^20,s30, respectively.
bA variable range.
Row/ =
0 corresponds to the transformation between
coordinate system 0 and system ¿0.
tern consists of a small electromagnetic receiver strapped
to the operator's wrist and a
remotely mounted trans-
mitter.
3 Utah Dextrous Hand Master
The hand master (Fig. 4) measures motion of the
thumb, index, middle, and ring fingers, via a carbon-
fiber exoskeleton attached to an elasticized glove. The
exoskeleton is comprised of three pairs of parallel-link
mechanisms spanning the length of each finger and at-
tached to an immobile base on the back of the hand.
Pads are adhered to the glove surface above the three
finger links of each finger and connected to the parallel
linkages. Rotation of adjacent pads or rotation of the
proximal pad with respect to the immobile base yields an
angular motion between pairs of parallel linkages (Fig.
5) and is measured by Hall-effect sensors. Abduction-
adduction of each finger rotates the series of parallel link-
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Figure 4. Utah Dextrous Hand Master.
ages about the perpendicular axis ofjoint 1 and is mea-
sured by Hall-effect sensors located in the base.
The first hand master, created by Ed Iversen and Steve
Jacobsen at the University of Utah, employed a
straight
linkage design in the exoskeleton and used Hall-effect
joint angle sensors. This design was later modified and
marketed as the EXOS Dextrous Hand Master. This first
design had the drawback of not measuring the finger
joint angles accurately, because of the kinematic mis-
match between the exoskeleton joints and the human
finger joints. This mismatch would also require the exo-
skeleton attachments to move
during finger flexion. The
first design gave readings, which were also sensitive to
how the glove was put on, because of a translation de-
pendence of the attachment points. That is to say, the
readings depended on the exact location ofthe attach-
ment bands on each finger segment.
To avoid this mismatch, the Utah Dextrous Hand
Master employs four bar linkage connections between
joints and measures the angle between the pads contact-
ing the human finger segments. If the pads are well ad-
hered to the finger segments and the soft tissue under
the pads undergoes negligible deformation, the finger
joint angles are
accurately measured. The Utah Dextrous
Hand Master is also translation invariant: the exact loca-
tion of the pads on the finger segments does not affect
the readings. Compared to the VPL Dataglove, an exo-
skeleton based hand master design offers the advantage
that the joints angles may be measured independently.
4 Previous Hand Teleoperation Algorithms
The VPL DataGlove and the EXOS Dextrous
Hand Master have been previously employed to operate
the Utah/MIT Dextrous Hand. Mappings developed for
the VPL Dataglove and EXOS Hand Master include (1)
linear joint angle mapping (Hong & Tan, 1989), (2)
pose mapping (Pao & Speeter, 1989), and (3) fingertip
position mapping (Speeter, 1992). These algorithms
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Rohling et al 207
Figure 5. Utah Dextrous Hand Master kinematics. Hall-effect sensors
are placed at each joint angle label in the top figure.
were
implemented with the Utah Dextrous Hand Mas-
ter to determine their ability to successfully teleoperate
the Utah/MIT Dextrous Hand.
4.1 Linear Joint Angle Mapping
Linear joint angle mapping is possible because the
robot hand and the hand master both contain four fin-
gers with four joints per finger. The intrinsic assumption
here is that the kinematics ofthe robot and human
hands are
nearly identical. The fingers of the robot hand
each have three parallel rotary joints and a
perpendicular
rotary base joint connecting the fingers to the palm base.
This structure is roughly equivalent to the human finger
joints. Yet there are
significant kinematic dissimilarities,
such as the direction and location ofthe finger base
joints as well as link length differences. Despite the kine-
matic differences, the 16 joint angles of the hand master
each has a
corresponding joint on the robot hand and a
linear function relating the robot hand and hand master
joints may be established:
e^obot =
mt}^" + bg
where 9(y°bot is the angle of finger ¿, joint/ ofthe robot
hand, 9"™"" is the angle offinger i, joint/ of the hand
master, and w,y and by are constants determined by com-
parison of the kinematics and trial and error
during
implementation.
This simple mapping generated roughly similar hu-
man and robot motions, but was unsatisfactory because
the kinematic dissimilarities between the human and
robot hands required the operator to make contorted
hand poses to achieve the desired robot hand motions.
4.2 Pose Mapping Algorithm
We also tested pose mapping, where the robot and
human hand were placed in a number of similar poses
and a
relationship between each robot angle and a sum
of 16 weighted hand master joint angles was found by a
least-squares fit. This relationship was found by manu-
ally manipulating the robot hand into a pose that mimics
the pose that the human operator was
assuming. The
hand master joint angles and the robot joint angles were
then recorded. This was
repeated for n poses and may be
put in matrix form:
AT = B
where A is a matrix of measured human hand poses of
dimension n
by 16 (number of measured hand master
angles), T is the 16 by 16 transformation matrix be-
tween hand master and robot joint angles, and B is a
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matrix ofmeasured robot hand poses ofdimension n
by
16 (number ofjoints of robot hand).
The T matrix was found through pseudoinversion
techniques after n =
20 poses were measured. The robot
joint angles may therefore be calculated from the trans-
formation of the hand master joint angles:
tlT =
£
where n is a row vector of hand master joint angles and £,
is a row vector of robot joint angles.
This method was also computationally simple but suf-
fered from a lack ofoperator confidence in controlling
the robot hand, particularly for delicate tasks where pre-
dictability is important. The relationship between robot
and human joint angles determined this way appears
unpredictable to the operator because movement ofonly
one human joint results in motion ofmany of the robot
joint angles. Modifying the algorithm to calculate each
robot joint angle from a weighted sum ofonly the four
joints of the corresponding human finger resulted in
little improvement. Further drawbacks include the need
to perform these pose mappings for each new
operator
and a lack of a clear definition ofwhat identical poses are
for kinematically dissimilar hands.
4.3 Synergistic Fingertip Mapping
Algorithm
Finally, we tested a
simple version offingertip po-
sition mapping, which did not address fingertip orienta-
tion, workspace differences, or make use of the robot
redundancy of fingertip position. The human fingertip
positions were calculated using a
simple model ofthe
human hand and the measured hand master joint angles.
Using a common reference frame located in the palm,
the inverse kinematics ofthe robot hand were solved and
implemented whenever the solutions were within the
joint limits. To resolve the fingertip position redun-
dancy, the algorithm simply set the angle ofjoint 3 equal
to the joint 4 angle for each finger:
6¿3obot =
ö,i4bot * =
0, 1> 2, 3
This synergistic relationship is reasonable for free human
finger motion.
The operator felt more comfortable during telema-
nipulation than with previous mappings, as direct con-
trol of the distance between fingertips appears to be es-
sential for performance ofgrasping tasks. Yet problems
were encountered similar to those discussed in previous
research (Speeter, 1992):
• Human-robot kinematic dissimilarities result in
only a
partial overlap of the fingertip workspaces.
• Errors are introduced by approximations of a sim-
plified model ofthe human hand and inaccuracy of
the hand master measurements.
• Each robot finger contains fewer than 6 degrees of
freedom (DOFs) to track the mapped human posi-
tion and orientation.
In response to these problems we
developed the Opti-
mized Fingertip Mapping (OFM), which differs from
previous work by (1) matching fingertip orientation as
well as Cartesian position, and (2) generating robot
poses when exact mapping is not possible due to work-
space dissimilarities. OFM minimizes the human-robot
fingertip position and orientation error within the con-
straints ofeach robot finger's workspace and available
DOFs. A priority scheme is implemented that favors
position over orientation.
At present the OFM algorithm has been implemented
only on the Utah/MIT Dextrous Hand and Utah Dex-
trous Hand Master master/slave combination. The
OFM idea may be applied, however, to any combina-
tions ofhand masters/slaves that have the same number
offingers.
5 Human Hand Model
The Utah Dextrous Hand Master contains a
large
number of sensors that allow a
sophisticated model of
the human hand to be used for OFM human fingertip
calculations.
The hand may be considered (Chao, An, Cooney, &
Linscheid, 1989) as a
linkage system of articulated bony
segments. These segments define the fingers and the
palm and allow motion through movement between
bone segments. Joint motion is produced by muscle
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Rohling et al 209
Index.Middle,Ring Finger
io^ x
{¿¡3 i ¿12 Un
y¡3 y¡2
DIP PIP
Thumb
Z03 1Z,
ym
MP
00.
|Zo3 |Z02 1Z01
X03 ^ ><02,. X01 I
d01
01 ^
-
'M>,
00
y00
yo3 yo2 y.01
MCP TMC
Figure 6. Side view ofhuman finger model. Alljoints are assumed to
rotate about fixed axes.
forces and constrained by both soft tissue (including
muscle and capsuloligamentous structure) and bone seg-
ment shape. These constraints allow simplifications to be
made about gross finger motion.
Human hand kinematic studies (Cooney, Lucca,
Chao, 8c Linscheid, 1981; Thompson & Giurintano,
1989) show at least 5 DOFs for each finger. A simplified
model is dictated by the 16 DOFs of the hand master.
The simplified model first approximates each joint as a
rotation about a fixed axis. The distal interphalangeal
(DIP) and proximal interphalangeal (PIP) joints ofthe
index, middle, and ring fingers, and the interphalangeal
(IP) and metacarpophalangeal (MCP) joints of the
thumb are assumed to have 1 DOF (Fig. 6). The meta-
carpal (MP) joint of the index, middle, and ring fingers,
and the trapeziometacarpal (TMC) joint of the thumb
are assumed to have 2 DOFs. Flexion extension ofthe
MP and TMC joints is assumed to be about an axis lo-
cated at the MP and TMC joints and parallel to the distal
joint axes.
The ¿0 coordinate system ofthe hand master (the co-
ordinate system located at the exoskeleton insertion
point into the base) is not coincident with the MP and
Table 2. Human Parameters (ofRNR) ofthe Simplified Human
Hand Model: /, = Human Finger Link Length, ,0d,, = Vector
from Coordinate System ¡0 to i I (mm)
Finger i
0 12 3
4
'Mi
50.8
31.7
25.4
12.7
0
-38.1
45.7
30.5
19.0
33.0
0
-40.6
50.8
31.7
19.0
34.9
0
33.0
45.7
30.5
19.0
28.6
0
-30.5
y
Zio
'At*0
10 A20 X3C
Master Base
~
x 00
Zoo *y00
Figure 7. Back view ofthe insertion points of
each finger into the hand master base. Dashed
lines indicate vectors not lying in the plane ofthe
page.
TMC joints, but is displaced by vector ,0d,i (Fig. 6) and
is located a short distance above the middle of the back
ofthe hand. Thus abduction-adduction is only approxi-
mately measured by rotation about z,0, and this approxi-
mation is incorporated into the simplified model.
The simplified model is therefore comprised ofboth
human parameters and hand master parameters. The
human parameters describe the finger link lengths and
the translation between coordinate systems ¿0 and ¿1
(Table 2). The hand master parameters describe the
transformations between each of the ¿0 coordinate sys-
tems (Fig. 7 and Table 3).
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Table 3. Hand Master Parameters ofthe Simplified Human
Hand Model0
Finger i 20R,o
0.766
0.260
-0.601
1
0
0
1
0
0
-0.434
-0.485
-0.765
0
0.981
-0.196
0
0.981
0.196
-0.488
0.840
-0.255
0
0.196
0.981
0
-0.196
0.981
20, d»
-56.3
42.7
-57.5
0
28.8
-2.5
0
-28.8
-2.5
transformations of each ¿0 coordinate system are
represented with respect to the 20 coordinate system.
20R,o =
rotation matrix describing coordinate system 20
with respect to ¿0. 20d¿0 =
vector from coordinate system
20 to¿0 (mm).
120
100
80
60
40
20
0
-20
-40
-60
Common Reference Frame Origin
dashedline =
humMfingertip workspace
solid line =
robot fingertip workspace
-50 0 50
x tip position (mm)
100
Figure 8. Workspace boundaries for robot finger 2 forjoint 21=0°
and for human finger 2 forjoint 21 = 0°. Both fingers are shown with
respect to the common reference frames.
Amplified Hall-effect sensor
voltages from the hand
master are read through an A/D converter by CON-
DOR. Resolution of the measured angles is ±0.1° on
average, and is limited by Hall-effect sensor noise. All
Hall-effect sensors and linkages have an
angular range of
90° to measure
unobtrusively almost the entire range of
human joint motions. Located on the backside of the
hand, the exoskeleton partially inhibits finger crossing
but does not inhibit hand motion for most tasks.
6 Human-Robot Kinematic Differences
The most important kinematic differences between
the human hand model and the robot hand are the struc-
ture of the finger base joints and the location of the
thumb. The robot finger base joints 1 lie at an
angle
tilted 30° above the palmar plane. The human model
joint 1 lies nearly perpendicular to the palm. The differ-
ence in the orientation of these axes results in a differ-
ence in the abduction-adduction motion of the robot
and human fingers. The robot fingers abduct-adduct in a
rolling motion with respect to the palm whereas the hu-
man fingers abduct-adduct in a yaw motion with respect
to the palm.
The robot thumb is located in the palm equidistant
from fingers 1 and 2. The human thumb is located along
axis z0o of the simplified model, which intersects the
palm near the TMC joint at the edge of the palm. Fur-
thermore, the orientation ofthe base joint of the robot
thumb lies parallel to the palm whereas the human
thumb rotates about a joint axis at approximately 45° to
the palm.
All four of the robot fingers have equal total finger
lengths. Human finger lengths exhibit a
length variance
among fingers that depends on each person. Most com-
monly, total finger length decreases from thumb to
middle finger to approximately equal index and ring fin-
gers.
The combined kinematic differences result in different
fingertip workspaces. Figure 8 shows the difference in a
planar section ofthe workspace that arises from the kine-
matic dissimilarity of the middle fingers (using one of
the author's (RNR) middle finger). The workspaces in
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Rohlingetal 211
Human Fingertip Colculotlons
Kead joint angles from
master glove and calculate
forward kinematics of fingers
¡-0.1,2,3
Express each finger's position
and orientation w.r.t. common
reference frame
Robot Finger Joint Calculations
Find finger 2 joint 1 angle"
Express finger ¡=0,1,2,3 position
and orientation w.r.t. system Î0
I
Find finger ¡=0,1,3 joint 1 angle
Solve Planar Finger Problem
For finger 1=0,1,2,3 express positior
and orientation w.r.t. system i1
Extract [xta»yd«.] from position
and 4frw from orientation_
Branch 1
Attempt to match [xd(
within joint limits
•yd«.] ond *<!< Unsuccessful
Branch 2
Attempt to match[xdM,ydet] within
joint limits
Unsuccessful
Successful
Branch 3
Place robot fingertip position
where error from [xd--,yd„jl ¡e
minimized and is within joint
limits
Successful If more than one solution is found
then choose solution whose
orientation is closest to 4> ^
Successful
Implement calculated joint
angles on robot hand_
Figure 9. OFM algorithm. The three branches are shown.
Figure 8 overlap well because the robot and human fin-
gers have almost equal total lengths. The robot fingers 1
and 3 have a smaller intersection ofworkspace volume
with human fingers 1 and 3 because of a greater differ-
ence in finger lengths. The workspace intersection of the
thumbs is very small because of the large relative posi-
tion difference of base joint locations and the difference
in thumb link lengths.
7 Optimized Fingertip Mapping
OFM proceeds by (1) calculating the forward kine-
matics of the human hand, (2) mapping the fingertip
positions and orientations to the robot hand via a com-
mon reference frame, and (3) generating robot inverse
kinematic solutions. For human hand poses where fin-
gertip position and orientation mapping are not pos-
sible, approximate solutions must be generated without
introducing discontinuities between exact and approxi-
mate mapping. The OFM algorithm continuously gen-
erates exact and approximate fingertip poses throughout
the robot workspace by prioritizing the position and
orientation goals and minimizing the errors. The algo-
rithm is shown in Figure 9.
7.1 Forward Kinematics
The forward kinematics are calculated from hand
master joint angle data using the simplified human hand
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model. First the forward kinematics of each finger are
calculated with respect to coordinate system ¿0.
'l22 COS GST" + ¿23 COS (%%"" + *T")'
+ i2i cos (esf^ + e5fter + 92n4astcr)
0
l22 sin 8¡T" + l23 sin (Q?rKr + eg"")
_i_ / «¿m /û master _i_ a master _i_ omasterx
+ ¿24 sin (ü22 + H23 + H24 )
ilYhuman
_
/0Yhuman
iO"D human
.Inhuman + ,0^
R v,n(e«
master . a master _i_ omaster
2 + ö,3 + ö<4 )
where '¿xi111™11 is the human fingertip position vector
with respect to coordinate system ik, <*R^uman is the
3-by-3 human fingertip orientation matrix; it represents
X-T-Z fixed angle rotations about the coordinate sys-
tem ik, lij is the human finger link length, 9,y,astcr is the
hand master joint angle, RV/i(9) is the 3-by-3 rotation
matrix describing a rotation 9 about ylh, and ,0d¿i is the
vector from coordinate system ¿0 to ¿1. The forward ki-
nematics of each finger is completed by including abduc-
tion-adduction, which consists of a rotation ofthe fin-
gertip position and orientation vectors about the axis z,0.
baseurhuman
_
n /amaster i'0vhuman
base<T> human
R /û master ¿Ou human
zi0 (Ö«I ) K>
where base
chuman and baselRhuman are thc fingertip posi.
tions and orientations after abduction-adduction.
7.2 Scaling of Human Hand Parameters
Scaling of the human hand model parameters dur-
ing forward kinematics calculations to more
closely
match the robot parameters was
investigated to address
the fact that human hand sizes vary significantly. Hands
of different sizes placed in the same type of pose produce
slightly different robot hand poses if a scale factor is not
used. A scaling factor was introduced to scale the human
hand to have the same average finger length as the robot
fingers. The scaling factor did make the robot attain
poses that were more aesthetically similar to the human
poses and did not depend on human hand size.
7.3 Common Reference Frame
Mapping fingertip positions and orientations re-
quires a common reference frame on the human and ro-
bot hands. Previous fingertip mapping research (Hong
&Tan, 1989; Speeter, 1992) placed the common ori-
gins at the base of the thumbs. The base ofthe thumb is
not a
good location for the common reference frame
between the robot hand and the human hand for finger-
tip mapping. The kinematic differences previously cited
result in a very small overlap ofthe robot and human
workspaces because the thumbs are the most kinemati-
cally dissimilar fingers of the robot and human hands.
Furthermore, the human thumb base is difficult to locate
because of a lack of bony landmarks. The OFM algo-
rithm uses common reference frames located at the MP
joint of the middle human finger and joint 2 of the robot
finger 2. These locations were chosen because they lie at
locations of high kinematic similarity.
Specifically, the human reference frame is located at
the middle of the MP joint ofthe middle finger oriented
along the finger. The position and orientation of each
human finger are transformed to the common
origin MP
by first transforming from coordinate system ¿0 to 20,
then transforming to MP by a rotation of -
9™ster about
z20 and translation by —
20d2i.
MP „human =
RZ2o(-Q^ri[20R,0b-'x,human + 20d,0] -
20d21
MP T> human
_
1} / a master 20"D baseiü human
The robot reference frame is located at joint 2 offin-
ger 2, rotated 60° from the 21 coordinate system (Fig.
2) so that it points along the finger similar to the human
reference frame. The mapped position and orientation of
each robot finger with respect to coordinate system 21
are therefore
21« robot
_
=
Rz„ (-60°)
,° MPvhuman
21t> robot _
Rz„ (-60°)MPR
o MPtj human
In other words, the human fingertip positions and
orientations that were written with respect to the immo-
bile base are first transformed to the common reference
frame pointing along the human middle finger with an
origin at the MP joint. This is then the desired position
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Rohlingetal 213
and orientation for the robot hand with respect to a
similar reference frame located at joint 2 of finger 2
pointing along the robot finger. The nearest robot DH
coordinate system is system 21 so the desired robot posi-
tion and orientation are then expressed with respect to
system 21 by rotating by 60°.
7.4 Inverse Kinematics
The OFM algorithm inverse kinematics consider
the desired fingertip position 21x!robot as the first priority
goal, and fingertip orientation 21Rfobot as the second pri-
ority goal.
7.4.1 Simulations of Planar Finger Motion. Ini-
tially simulations of planar finger movement were per-
formed by two implementations of the goal prioritiza-
tion method. The first simulations were
composed in the
velocity domain (Nakamura, Hanafusa, & Yoshikawa,
1987) where Jacobian matrices were written to describe
each goal and inverse kinematics performed through
pseudoinversion techniques.
While easy to formulate, the drawbacks to this ap-
proach include being computationally intensive. A fast
servo rate between human and robot motion is necessary
during teleoperation. It is also difficult to incorporate
joint limits. Furthermore, for large differences in robot-
human hand positions, such as
during start-up, the solu-
tion will "overshoot" before settling down.
There are other inverse kinematics strategies to do
redundancy resolution (such as Pohl & Lipkin, 1990),
but it was found that solutions could be found directly
by a geometric analysis. The geometric analysis can be
performed at considerably lower computational cost and
yields robot joint angle solutions without derivatives. It
encompasses joint limits in the priority scheme and cal-
culates the optimum robot pose in one step. A second
set of simulations verified the practicality of the geomet-
ric analysis approach (Fig. 10).
7.4.2 Optimized Fingertip Mapping. Each robot
finger is redundant with respect to fingertip position.
For a
given robot fingertip position, orientation is fixed
except within the plane determined by the three parallel
100 r
50
Oh
-50
Robot Workspace Boundary
Branch 3 Branch 1
Branch 2
Branch 3
Branch 2
+
Desired Trajectory Position
o Actual Robot Fingertip Position
-50 0 50
x tip position (mm)
100
Figure 10. Simulation ofa robot finger tracking a linear trajectory
within its plane with a desired orientation of 185°. All three branches of
the OFM tree are traversed during tracking.
Table 4. OFM Structure
1 Achieve desired position and projected orientation
2 Achieve desired position and minimum error from
projected orientation
3 Achieve minimum error from desired position
distal joints. The desired robot orientation is therefore
the projection of the human orientation into the plane of
the robot finger. The goal prioritization results in a three
branched algorithm for each fingertip (Table 4). The
solution will fall into one of these three categories with
highest priority on the first category.
OFM Joint Angle Calculations. A three-dimen-
sional drawing of a projected position into the plane of
the finger (Fig. 11) may be useful as a reference when
following the detailed OFM calculations.
1. The common robot reference frame, as
previously
described, is attached to joint 2 of finger 2. Joint 1
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Palm Base
Plane of Finger
''Rotation Axis
-Desired Position, Orientation
-Projected Position, Orientation
Fingertip Workspace Boundary
Figure II. Projection ofdesired fingertip position
and orientation onto the plane offinger I. Joint I of
finger I is shown rotated to the limit of —45°. This
situation corresponds to item 3a or 3b in the
Summary ofOFM Calculations and the Criteria for
Success.
offinger 2 cannot therefore be calculated from po-
sition or orientation data. Joint 1 offinger 2 is cal-
culated by equating the distance swept out by the
human base joint movement from its middle posi-
tion to the distance swept out by the robot base
joint movement from its middle position.
e™bot =
r/22 cos e^*" +1
>2
s~rxc /Qmastcr _i_ «master
23 COS (922 + ö23
_i_ / ^^r. /omaster _i_ Amaster _i_ omastem
+ *24 cos ("22 + H23 + ö24 )J
x 92n1astcr/[21^obot + J21]
This angle is clipped to be within the joint limits of
±45°. If the common reference frame was located
at a fixed position in the palm, joint 1 of all fingers
could be determined from fingertip position data.
The fingertip position and orientation with respect
to the base would then be slightly different than
the OFM method. The fingertip position and ori-
entation with respect to each other, however, are
identical. The OFM common reference frame
placement, as
previously described, has the advan-
tage of lying at a location ofhigh kinematic simi-
larity and therefore has a
large overlap of the hu-
man and robot finger workspaces.
2. The position and orientation of fingers 0, 1, and 3
are transformed from coordinate system 21 to each
finger base ¿0:
iOvrobot
„„.„„„.
_
>(m 21vrobot i iOJ
X¿ —
JV2i X,- -r Q2i
iOji robot
_
¿0"D 21TJ robot
R2i21Rf
3. The joint 1 angle for fingers 0, 1, and 3 is calcu-
lated from desired position data:
9,rS>bot =
atan2(!'°yirobot, «»j^*«)
The angle is clipped to within the joint limits of
±45°. The joint 1 angle determines the plane of
each finger.
4. The position and orientation are transformed into
the plane of the finger.
¿l-v-robot
_
¡I'D ¿O-v-robot i il J
robot
¿iRfbot =
''1R.0'0R,r
The remaining jointsj =
2, 3, 4 for fingers i =
0,
1, 2, 3 form a three-link planar problem with re-
spect to each coordinate system »1. The three-link
planar problem is solved using the x,y elements of
liebelt as t^e desired position and the desired ori-
entation cpdes is extracted from !lRir°b°t- The z ele-
ment of '1xJrobot will equal zero if the joint 1 angle
has not been clipped. Ifjoint 1 has been clipped,
thcx,y elements of ,1xIrobot represent the projection
of ,0-iç:ohoc onto the plane of the finger. The desired
fingertip position is labeled [x^, ydcs].
4a. Calculate an inverse kinematic solution to the
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Rohlingetal 215
3-link planar problem using both the desired po-
sition and orientation.
9™bot = acos
[(4, + yis -
a22 -
a2,)/(2a,2al3)]
atan2(ydes, x^)
+ atan2 (ai3 sin 9£bot, a,2
+ al3 cos 9,r3obot)
9robot
_
a -
6robot
_
± a robot
¿4
_
«Pdes
"
ö(3 6robot
a
The solution is successful if 9$**, 9£bot, and 9£bot
are within the joint limits as found in Table 1.
4b. If solution 4a cannot be found within the joint
limits calculate an inverse kinematic solution that
achieves desired position and minimizes orienta-
tion error. This entails placing one ofthe joints at
one of its limits and solving for the other two
joint angles to achieve the desired position. This
procedure is repeated for all three joints at both
ofeach joint's limits for a total ofsix possible
pose solutions. An example ofthe equations for
one of the six calculated poses is given below and
is shown in Figure 12. The other equations are
easily derived in a similar manner.
a robot
__
=
0 (joint limit)
«robot _
acos
xL + Ydes -
«a -
(«¿s + *rt):
9robot
_
a -
2a,2(ai3 + ai4)
atan2(ydes, x^)
+ atan2 [(ai3 + ai4) sin 9£bot,
+ (al3 + ati) cos 9£bot]
6robot n
¿3
~
°<2
robot I
_.
_
ii Arobot
e
-
I <Pdes _
"¡4
The solution is successful if 9£bot, 9;3obot, and 9J°bot
are within the joint limits. Ifmore than one pose
is successful, the solution chosen is the one that
obtains the minimum orientation error e.
4c. Ifsolution 4b cannot be found within the joint
limits then calculate an inverse kinematic solution
minimizing the error between the robot fingertip
L^les^des J
Figure 12. One ofsix possible finger poses when one
joint angle is set to a limit.
0 50
x tip position (mm)
Figure 13. The region outside the workspace boundary for fingers 1,2,
and 3 is segmented into six regions. Vertices are labeled A, B, C, and D.
and the desired position. The area outside the
workspace is divided into separate regions (Figs.
13 and 14). Equations are written for each region
that determine the location along the workspace
boundary that minimizes the position error from
the desired position. First each defined region is
checked to determine ifthe region contains the
desired position and the fingertip is placed at the
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-50 0 50 100
x tip position (mm)
Figure 14. The region outside the workspace boundary for the thumb
is segmented into six regions. Vertices are labeled A, B, C, and D.
position of minimum distance error. The mini-
mum distance error occurs when the robot is
placed at the workspace boundary whose perpen-
dicular intersects [x^, ydes]. As an
example of the
finger 1 calculations, the equations representing
region 1 of Figure 13 are:
criteria for position within region 1 :
[Xdes + (Ydes -
0,2)2] > («i3 + ^
Xdcs < 0 and ydes > ai2
ifcriteria is satisfied:
erobot =
90o
9;30bot =
atan2(|xdes|,ydes-«l2)
9£bot =
0
Equations of region determination and joint
angle solutions are
easily derived in a similar man-
ner for the other regions. Regions are defined
only for the sections that have a smooth work-
space boundary. When the [x^,, ydes] is nearest to
a vertex of the workspace boundary a separate
calculation must be made. If [x¿es, ydes] is not
found in one of the six described regions then the
robot fingertip is placed at the vertex closest to
[xdes, ydcs]. The closest vertex is found by calculat-
ing the distances to each vertex A, B, C, and D.
Great care must be taken to ensure
continuity of the
joint angle solutions when changing branches. The opti-
mizing nature of the branches produces continuity of the
robot joint angles but the continuity may be lost if for
example orientation jumps from —10° to 350° because
of a
change oftrigonometric equations between
branches. Standardizing the orientation range reduces
the possibility of introducing program-generated discon-
tinuities.
The OFM algorithm contains the goal priority gener-
ated branches within the solution of the planar finger
problem—after the joint 1 angle has been calculated.
Success in branch 1 of achieving the desired projected
position and orientation in the plane does not indicate
that the desired position is necessarily matched in three-
space unless joint 1 has not been clipped to its joint
limit. The three-branched OFM structure contains three
subbranches from branch 3. The subbranches arise when
fingertip position is not achievable because of the joint 1
range limit but redundancy ofjoints 2, 3, and 4 still al-
lows orientation consideration within the plane ofthe
finger.
Summary ofOFM Calculations and the Criteriafor
Success
1. Achieve desired position and projected orienta-
tion:
a. joint 1 calculation lies within joint range and
b. position and projected orientation within finger
plane are achievable within joints 2, 3, and 4
ranges.
2. Achieve desired position and minimum error from
projected orientation:
a. joint 1 calculation lies within joint range and
b. position within finger plane is achievable and
errors from projected orientation are minimized
within ranges ofjoints 2, 3, and 4.
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Rohling et al 217
Figure 15. Teleoperation ofthe Utah/MIT Dextrous Hand with the Utah Dextrous Hand Master in conjunction with the Bird
position sensor and the wrist positioning robot.
3. Achieve minimum error from desired position:
i. projected orientation is achievable:
a. joint 1 is clipped to a joint limit
b. both projected position and projected orien-
tation within finger plane are achievable within
ranges ofjoints 2, 3, and 4.
ii. closest to projected orientation:
a. joint 1 is clipped to a joint limit
b. projected position is achievable and error
from projected orientation within finger plane is
minimized within ranges ofjoints 2, 3, and 4.
iii. no orientation consideration: position lies out-
side finger workspace:
a. always successful by placing fingertip at
workspace boundary.
For any given continuous trajectory of desired posi-
tions and orientations the OFM algorithm generates a
continuous robot trajectory. It can be easily shown that
the algorithm—whereby the position and orientation are
projected into the plane ofthe finger and then opti-
mized—achieves the best three-space optimization of
position and orientation. By inspection ofgeometry it is
apparent that if the position in three-space is projected
onto the finger plane and the planar distance error is
minimized then the three-space distance error is also
minimized. With only 1 DOF of redundancy, two of the
three orientation variables are fixed and the third orien-
tation may be adjusted for minimum error from its de-
sired value and, therefore, orientation error in three-
space is also minimized.
8 Results
8.1 Remarks on Implementation
Teleoperation using the OFM algorithm (Fig. 15)
resulted in graceful human-like robot motion. The algo-
rithm maintains a servo rate of 25 Hz while operating
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on a
single 68020 processor. The servo rate was accept-
able for normal hand motion but may be increased by
introducing additional or faster processors to aid com-
putation. The nature ofthe priority-based algorithm is
transparent: the switching of branches goes unnoticed.
Picking up small objects with a low force grip was ac-
complished with much greater ease than with non-fin-
gertip-mapping algorithms. Successful grasping of ob-
jects was achieved without much practice.
The thumb motion was
remarkably improved over
previous algorithms. The thumb motion is important to
observe for two reasons. The first is that the thumb is
important for virtually every grasping and manipulation
task. Second, the thumb is the finger whose kinematics
differ the most from its human counterpart. This is the
situation where the OFM algorithm clearly shows its
advantage over other algorithms. The ever-present kine-
matic dissimilarity between the robot and human hands
does not hinder the human control over the robot finger
placement and orientation because OFM generates exact
fingertip mapping when the robot fingertip workspace
overlaps the human fingertip's workspace, and the clos-
est mapping when they do not overlap.
For the index, middle, and ring fingers the operator is
able to control the robot fingers very predictably. The
algorithm becomes completely transparent when the
robot and human kinematics are nearly identical. The
three distal joints ofthe index, middle, and ring robot
fingers are
kinematically very similar to the correspond-
ing human fingers joints so the fingertip workspaces
overlap well. The operator therefore appears to have di-
rect joint mapping throughout much of the workspace
because movement of one human joint angle results in
similar movement ofonly the corresponding robot joint.
To demonstrate the OFM algorithm accuracy with
different operators, a second operator was selected to
perform teleoperation tasks using the OFM algorithm.
The second operator has a hand that has human param-
eters 20% smaller on average than the first operator's
(RNR) hand. With approximately the same
practice
time, the second operator was able to perform the tasks
in the same time as RNR.
One type of motion that generates some unhuman-
100 h
a.
a.
0 50
x tip position (mm)
Figure 16. Robot finger tracking a shorter human finger during curling
motion.
like motion of the robot fingers occurs when the opera-
tor curls in the ring finger from the fully extended posi-
tion. In particular, when the operator's ring finger is
considerably shorter than the robot finger, the robot
finger will attempt to track the human finger by flexing
only the distal joint as shown in Figure 16. The algo-
rithm attempts to minimize the position error (Branch
3) when the fingers are
nearly extended, thereby rotating
only the distal joint. Because humans generally cannot
flex the distal DIP joint without flexing the PIP or MP
joints the robot motion appears unhuman-like. This
generated robot motion, although aesthetically odd, is
simply a characteristic ofthe priority-based algorithm.
8.2 Limitations
Even when both fingertip position and orientation
mapping are
possible, errors from the human hand
model, hand master data, robot hand model, and robot
joint controller reduce the mapping accuracy. The main
source oferror comes from human hand model limita-
tions and are centered mainly around determination of
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Rohlingetal 219
the human parameters. Measurement ofthe human
model parameters is presently performed through use of
calipers and bony landmarks. Measurement by this
method is limited by the difficulty of determining the
joint centers with respect to the bony landmarks.
Limitations also arise from the inability of the hand
master to measure all of the DOFs of the human hand.
It has been shown (Cooney et al., 1981) that the MCP
joint possesses abduction-adduction and axial rotation
movement in addition to the measured flexion-exten-
sion movement. Other unmeasured joint movements
and palm shape changes also limit the accuracy ofthe
fingertip calculations.
The 16 DOFs that are measured contain small errors
that arise when the linkage pads and glove material lift
away from the skin surface during some
large flexion
hand movements. The soft nature of the finger surface
itselfalso introduces pad movement with respect to the
hand skeleton. The Hall-effect sensors themselves exhibit
some drift and need occasional calibration for best re-
sults.
The robot joint controller also introduces errors when
implementing the joint angles generated by the algo-
rithm. Furthermore, robot kinematic parameter identifi-
cation and sensor calibration need to be performed accu-
rately. With external measurements of the human model
parameters and recent sensor calibration, the fingertip
position error is on the order of 1 cm. This is still con-
siderably better than the linear joint angle mapping and
pose mapping algorithms. The thumb tip position when
using these previous algorithms is often in error ofmore
than 3 cm.
8.3 Future Research
Further research is now directed toward reducing
the fingertip-mapping error. In particular, both open
and closed loop calibration is now
being investigated for
both kinematic parameter identification as well as sensor
calibration for both the human and robot hands. Closed
loop calibration would result in greater ease for model-
ing operator hands because no external measurement
tools are
required.
9 Conclusion
The OFM was successful in achieving dextrous
teleoperation of kinematically dissimilar hands by con-
tinuously generating the optimum fingertip mapping
throughout the fingertip workspace. It is feasible to
solve for the optimal fingertip mapping by a
geometric
analysis, and it results in an algorithm that is not unac-
ceptably computationally intensive.
For OFM implementation on different combinations
of hand master-robot hands, some of the equations de-
scribing the forward and inverse kinematics may have to
be rederived. The rederivation will follow the structure
of the OFM algorithm:
•
develop a human hand model,
• choose a common reference frame that maximizes
the human-robot workspace overlap,
•
write the human forward kinematics using the hand
master data,
• scale the human hand model, and
•
use a
goal priority-based method for inverse kine-
matics; fingertip position is first priority and orien-
tation second.
The algorithm is general enough that it can be applied
to many combinations of robot hands and hand masters,
but best teleoperation results are found with a combina-
tion of a hand master that accurately and fully measure
human hand movement and a
roughly anthropomorphic
robot hand.
Acknowledgments
Support for this research was provided by Office ofNaval Re-
search Grants N00014-88-K-0338 and N00014-90-J-1849,
and by the Natural Sciences and Engineering Research Council
(NSERC) Network Centers of Excellence Institute for Robot-
ics and Intelligent Systems (IRIS). Personal support for
J.M.H. was provided by the NSERC/Canadian Institute for
Advanced Research (CIAR) Industrial Chair in Robotics and
for R.N.R. by an NSERC Postgraduate Scholarship.
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