Most multifingered hands use a tendon mechanism to minimize the size and weight of the hand. Such tendon mechanisms suffer from the problems of striction and friction of the tendons resulting in a reduction of control accuracy. A design for a 3-D vision system integrated dexterous hand with motor control is described which overcomes these problems. The proposed hand is composed of three three-jointed grasping fingers with tactile sensors on their tips, a two-jointed eye finger with a cross-shaped laser beam emitting diode in its distal part. The two non-grasping fingers allow 3-D vision capability and can rotate around the hand to see and measure the sides of grasped objects and the task environment. An algorithm that determines the range and local orientation of the contact surface using a cross-shaped laser beam is introduced along with some potential applications. An efficient method for finger force calculation is presented which uses the measured contact surface normals of an object

Han, Youn-Sik

Luo, Ren C.

English

NASA Technical Reports Server

3-D Vision System Integrated Dexterous Hand
Ren C. Luo and Youn-Sik Han
Robotics and Intelligent Systems Laboratory
Department of Electrical and Computer Engineering
North Carolina State University
Raleigh, NC 27695-7911
1. Introduction
The limited capabilities of conventional two-jaw type grippers have prompted
research efforts concentrated on the development of a multifingered hand which can
grasp an object of arbitrary shape and manipulate it within its grasp.
Most multifingered hands use a tendon mechanism to minimize the size and
weight of the hand. Such tendon mechanisms suffer from the problems of stiction and
friction of the tendons. This results in a reduction of control accuracy. In order to
overcome these problems in control accuracy and to give the hand more flexibility and
intelligence, a design for a 3-D vision system integrated dexterous hand using motor
control is presented.
The proposed hand is composed of three three-jointed grasping fingers with
tactile sensors on their tips, a two-jointed 'eyed finger' with a microcamera in its distal
part, and another two-jointed 'laser-emitting finger' with a cross-shaped laser beam
emitting diode in its distal part. The two non-grasping fingers allow 3-D vision
capability and can rotate around the hand to see and measure the sides of grasped objects
and in its task environment.
Little research effort has been focused on the application of 3-D vision-in-hand
systems to perform the task of grasping and manipulating an object. In this paper, an
algorithm which determines the range and local orientation of the contact surface using a
cross-shaped laser light beam is introduced together with some potential applications.
Grasping and manipulating an object with a multifingered hand is a complicated
task and there still remain a number of unsolved problems. One inherent and important
problem is the determination of the proper internal grasping forces. Some work has been
concentrated on grasping or manipulation force analysis, however, finger force
determination has not been addressed. This problem can be solved efficiently using the
geometric information of the objects to be grasped acquired by the 3-D vision-in-hand
system. In this paper, an efficient method for the finger force calculation is presented
which uses the measured contact surface normals of an object.
Current industrial manipulators are usually equipped with two-jaw grippers.
These grippers not only have difficulty in handling objects with an arbitrarily complex
geometry, but also have difficulty in manipulating objects within their grippers.
An alternative solution to this problem is to design and build a flexible gripping
device which is capable of a large variety of tasks. Several investigators have developed
designs for such devices. A number of multi-fingered multi-jointed hands have been
developed, ranging from the nine degree of freedom (DOF) Stanford/JPL hand to the 16
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DOF Utah/MIT hand. Most of thesemulti-f'mgeredhandsaredriven througha cable
transmissionto minimize the sizeand weightof thehandandto give complianceto the
finger at the expenseof problemssuchas stictionand friction, control stability, time
response,and accuracy. To compensatefor theadverseeffectsof a cabletransmission
mechanism,it is necessaryto developrelativelycomplexlow-level control systemsthat
includecabletensioncontrol. Thesehandand finger configurations tend to mimic the
human hand, which is not necessarily the best configuration for a mechanical hand.
In this paper, we have developed a more compact design for a dexterous hand to
overcome the difficulties resulting from the use of a cable transmission. Furthermore, we
are currently developing a hand-based 3-D laser range finder which can rotate around the
hand so that it can perceive the object being grasped.
2. Hand Design
Recently, as a result of an increased research effort in the field of multifingered
hands, several hands have been developed. Almost all of the multifingered hands
developed are human-like, but this does not seem to be the optimal solution to the
problem of grasping objects of various shape and manipulating them for various tasks--
even though human-like hands have some advantages when imitating the function of
haman hand, especially in a teleoperation system.
Most of the multifingered hands that have been developed have a relatively small
hand workspace [Kerr et al 86] due to their human-like fingers and the finger joint
arrangement. The first and middle fingers are placed near to each other, limiting the
space to cooperate with each other. In addition, the first joint of each finger is a yawing
joint, not a twisting joint. If we allow some distance between fingers and make the first
joint of each finger a twisting joint, then the hand workspace will be enlarged and have
more dexterity.
Furthermore, most of these multifingered hands have adopted a cable
transmission system and their actuators are located remotely. This makes the design of
the control system very difficult because of the deflection, friction, and stiction of the
cables. Thus it is hard to control the fingertip position and force precisely during
manipulation. Therefore, it is better to design the transmission system so that it is rigid
and has a shorter transmission length by placing the motors near to the fingers.
For the reasons given above, we have developed a new design for a five-fingered
hand where one of the fingers is eyed and one emits a laser beam. The remaining three
fingers are used for grasping. The nongrasping fingers can rotate around the hand as
shown in the illustrative scheme (see Fig. 1).
It is necessary for a hand to have a minimum of three fingers in order to grasp an
object of arbitrary shape. Thus, the proposed hand has three grasping fingers. In order
to position the fingertip everywhere within the workspace, it is necessary for each finger
to have minimum of three degrees of freedom. Thus, each finger has been designed for
having three joints. The kinematic arrangement of finger joints are unlike the human
hand. Three fingers are equally spaced. The first joint of all three grasping fingers is a
revoluting joint which can provide a larger hand workspace and more dexterity.
Each of the nongrasping fingers is composed of two joints so that it can possibly
reorient itself in the direction of the object to be grasped in the adjacent task
environment. A micro-camera is located in the distal part of eyed finger and a laser
diode is implanted in the laser beam emitting finger.
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Figure1. Proposed illustrative scheme for a 3-D vision integrated dexterous hand
Each joint is driven by a micro dc servomotor with a reduction gearhead through
the gear and/or chain transmission. This provides for more rigidity in the control system
as compared to the remote cable transmission.
3. Grasping Algorithm using 3-D Visual Data
Manipulating an object with a multifingered hand is a non-trivial task. Not only
are the kinematic relationships between the finger joint motions and the object motion
complicated, but during the execution of the task the hand must also fh-mly grasp the
object and exert some force and moments to the task environment.
Salisbury has investigated grasping or manipulation force stability [Salisbury 82].
Since the object is overconstrained by the multifinger contacts, the system is statically
indeterminate. Several other researchers have determined the optimal internal forces.
Kerr has determined that the optimal internal forces are those with minimum norm under
an approximated frictional constraints [Kerr 86]. Hollerbach has developed a fast
189
algorithm to calculate the fingertip forces without using the Jacobian for the given
external and internal forces [Hollerbach et al 86]. Yoshikawa defined the concept of
internal forces as grasping forces [Yoshikawa et al 87]. Here we develop an approach
to determine the internal grasping forces and finger forces based on the contact surface
information that can be measured by the proposed 3-D laser range finding devices.
3.1 Determination of the Internal Grasping Force
Each fingertip force, fi, can be decomposed into two components: the internal
grasping force, fgi, and the manipulating forces, fmi, where subscript i denotes the finger
(i = 1,2,3). Th6 internal grasping force components are defined as these forces that
contribute to the grasping of a massless rigid object, and the manipulating force
components are defined as those forces that contribute to generate the resultant net forces
used to move an object. The main feature of the internal grasping forces is that the
forces are equilibrating by themselves and thus do not have any effect on the resultant
forces and moments. If we can determine these internal grasping forces, then the
manipulating forces and each fingertip force can easily be determined.
fl fl
r12 _23
Figure 2. Illustration of three points contact with friction on an object
There are an infinite number of solutions for the internal grasping forces because
the system is statically indeterminate. This arbitrariness has three degrees of freedom
when we use a hard finger (friction point contact) model in three finger grasping. Howev
er, by considering the friction coefficient between the contact points and the contact
surface, we can reduce the arbitrariness of the solutions to the degree of one. Also,
considering each total fingertip force as being limited by the maximum exertable finger
joint driving torque, we can finally determine the internal grasping forces. Since the
internal grasping force components of the fingertip forces (the fgi'S) are equilibrating by
themselves and do not contribute to the resultant force, we can formulate the equations as
follows.
where
l+f_ 4"fg3=0
1.rl -t g2.r2 + fg3.r3 = 0 (1)
ri • position vector of the ith contact point
190
This means that the L-'s form a closed triangle on the grasping plane, where the
_i • •, ° .
contact points (the Ci's) lie on the plane and the lines through the CI s arc intersecting at
one point, G (see Figure 3). Let G be called the grasp center point.
C
C1
C2
r12
fg3
Figure 3. Internal grasping forces and grasp centerpoint
The grasp center point should be inside the common intersection volume of the three
friction cones whose center axes are contacting the surface normal vectors, ai. Also, G
should lie on the grasp plane (see Figure 4).
Figure 4. Friction cones and contact normal vectors
Therefore, if we can properly choose -the grasp center point, G, for given contact
surface normal vectors ai, we can reduce the three degrees of arbitrariness to one by
using the equilibrium equations of the internal grasping forces (see Figure 5).
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C3
CI fI2__
C2
- fI2el2
Fig 5. Decomposition of internal grasping force components
Let ai* be the projection of the contact surface normal vector ai onto the grasp
plane. Then, in general, the prolonged lines of the ai* form a triangle on the grasp plane.
We can determine the grasp center point G to be the center point of the inward tangent
circle of this triangle so that the sum of deviations from each line will be minimized (see
Figure 6).
Then, the internal grasping forces fgi act along the unit vector
eiG = ( rG - ri ) / II rG - ri II (2)
where rG is the position vector of the grasp center point G.
Since the internal grasping forces are located inside of the friction cones, the
constraints of equation (3)
I ai. eiG I< cos( tan-I ui ) (3)
should be satistfied. (Here ui is the friction coefficient of each finger.)
object cannot be grasped with these contacts.
'_a2
Figure 6. Determination of the grasp center point G
Otherwise, the
192
Oncewe havedeterminedthegraspcenterpoint G, we caneasily determinethe
internalgraspingforcecomponentsfrom theequilibriumequations.
The internalgraspingforce fg! can be decomposed into two components which
are parallel to the edges of the grasp mangle. Let
Then,
eij = rij / II rij II
rij = rj - ri
f 1 = (fzl.e31) e31 + (f,,1-el2) el2
_gg_3 (_2.e12) el2 + (_2_e23) e23(fg3.e23) e23 + (fg3 e31) e31
(4)
3.2 Determination of Fingertip Force fi
As mentioned in previous section, we can determine the internal grasping force fgi
and its component magnitude fij. The relationship between the fingertip forces, fi, and
the internal grasping force components can be expressed as
fij= (fi.eij-fj.eij)= (fi-fj)-eij
This means that the internal grasping force component magnitude _i is the
difference in the projections of the fingertip forces fi and fj to the intercontact-line rij.
The above relationship can be rewritten as
(fi- fj)" rij = fij .11rij II
Then, by applying Hollerbach's method [Hollerbach et al 86], we can determine
the fingertip forces (the fis). These fingertip forces also should lie inside of the friction
cone
fi / II fi II. ai < cos (tan-1 ui)
where ui is the friction coefficient between the fingertip and the contact surface. If the
fingertip force does not meet this criterion, it can not be applied by the hard finger
contact, and thus we should find another place to locate the fingertip.
3.3 Determination of Finger Joint Torques
Taking advantage of the kinematic features of the fingers of the proposed hand, each
joint torque tik can easily be expressed as a function of the grasp intensity g from the
fingertip force fi, where subscript k denotes each finger joint number. Since tik should
not exceed the limit of maximum torque tikmax, we can determine the value of grasp
intensity g.
Since the internal grasping force does not contribute to the resultant force and
moment, adjusting the value of grasp intensity (or grasp security) g can result in more
flexibility in the control of the fingertip forces.
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4. 3-D Vision Integrated with the Hand for Grasp planningand Manipulation
As previously mentioned in the determination of finger force, the role of 3-D
vision in giving information about contact locations (contact point vectors ri and contact
surface normal vectors ai) is very important in the grasping planning stage. Also, 3-D
vision can play a major role during the reorientation of a grasped object during task
execution.
The proposed 3-D vision system is composed of one small camera and one cross-
shaped laser beam emitter, each of which is mounted on the distal part of two seperate
fingers. One finger is called the eyed finger and the other is called the laser beam
emitting finger. Each of these two fingers has one bending joint and is mounted on
rotating gears around the hand. Thus the camera will be able to see any side of the
grasped object, and can measure the distance to any point on surface of the object to be
grasped and the surface orientation of the object.
After grasping an object, the status of the grasped object may not be the same as
expected because of measurement and control error. Since the main control scheme of
the multifingered hand is force control, object motion is subject to the interaction
between the fingertip forces. Furthermore, there are many uncertainties in the contact
mechanics and the grasped object may not be the expected state. With the proposed 3-
D vision system, we can measure the status of the grasped object, namely, its orientation
and the position of a particular part of the object with respect to the hand frame. Figure 7
illustrates this basic concept.
We have simulated the operation of this sensor based dexterous hand using an
Appolo graphics workstation. Figure 8 shows an example of the simulation.
OC
Figure 7. Object posture measurements
194
Figure 8. Two views of simulated design of sensor based dexterous hand
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IEEE International Conference on Robotics and Automation, pp. 61-66.
Hollerbach, J.M., Narashman, S., Wood, J.E. (1986). Finger Force Computation without Grip Jacobian,
1986 IEEE International Conference on Robotics and Automation, pp. 871-875.
Jacobsen, S.C., Iversen, E.K., Biggers, K.B., Knutti, D.F., Johnson, R.T. (1986). Design of the Utah/MIT
Dexterous Hand. 1986 IEEE International Conference on Robotics and Automation, pp. 1520-1532.
Jameson, J.W., Leifer, L.J. (1986). Quasi-static Analysis : A Method for Predicting Grasp Stability. 1986
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