IEEE Robotics & Automation Magazine - June 2021 - 29

the revolute joints at the base of the fingers to rotate akin to
a Stewart-Gough platform. As a result, all grasping and
manipulation experiments were carried out using a purely
open-loop control scheme that commanded linear actuators
to positions determined by the inverse kinematics of
the hand. The actual position and orientation of the object
were recorded using the marker and the fixed camera but
not used for any kind of feedback control. More sophisticated
control will be carried out in the future using actual
object pose and potentiometer values from the fingers.
In addition to tracking the actual position and orientation
of the object for workspace characterization, a slip metric was
calculated to quantify the amount of slippage occurring at the
contact fingertips along the object's surface. The three potentiometers,
which were mounted on the axes of the revolute
joints at the base of the fingers, were used to read the angle
between the palm and each of the fingers. By knowing this
angle and the current stroke length of each linear actuator, the
actual position of the three fingertips in space could be calculated.
The deformation of the triangle formed by the three fingertips
during a manipulation sequence could be quantified
by the slip metric at each step. The metric is computed as the
maximum difference between the corresponding side lengths
of the contact triangle at the current pose ()s
at the initial grasp ()sk, initial
k, current
from that
slip = max '
k 123= ,,
normalized by the initial lengths:
.
ss
-
kk
,,
sk, initial
currentinitial
1
(5)
The metric could also be utilized for thresholding and stopping
a manipulation sequence before an object was expected
to be dropped, providing a reliable alternative to vision-based
drop detection.
Single-DoF Axes Characterization
and Range of Motion
The following experiments were carried out to quantitatively
evaluate the performance of the Stewart Hand for manipulation
along a single axis of motion. The first set of tests characterized
the accuracy of these motions for each of the six axes,
while the second set of experiments with YCB and foam
objects served to assess whether this range of motion extended
across objects of different shapes and sizes.
Axes Characterization
As noted previously, a 60-mm-diameter sphere object is used to
characterize the performance of the hand in the translation (x,
y, and z) and rotation (roll, pitch, and yaw) directions. The circular
profile of the object ensures that consecutive grasps are
equivalent and that the hand can repeatedly grip a repositioned
object at the same starting position. Once the object is grasped
from the reset mechanism, the hand is commanded to the
kinematic end of the range of motion along a particular axis,
and the object's actual position and orientation are recorded as
the hand carries out the manipulation sequence. The results of
three trials on each of the six axes are shown in Figure 7.
The hand performs reorientations of the object with relatively
high accuracy and is also able to execute z translations
with minimal error. The ranges of motion for rotations and
z-axis translation are limited only by the stroke of the linear
actuators. Thus, a larger stroke would result in even larger ranges
of motion along these axes. The xy translation performance
of the hand is quite linear but deviates substantially from the
theoretical case. This is attributed primarily to the competing
grasping force from the tendon differential and the manipulation
force from the linear actuators. To translate the object in
the xy-plane, the linear actuators for at least one of the fingers
extend, and the rest of the fingers are required to rotate away
from the palm. While the return spring on each finger can aid
the latter motion, the grasping motor still continues to apply the
same force across all the fingers as a result of the differential.
For instance, the positive y-axis range is truncated, as it
points directly in the direction of one of the fingers, requiring
it to rotate opposite the grasping torque. Friction in the tendon
differential opposes this finger motion, and, subsequently, the
motion of the object is hindered. However, the open-loop control
continues to extend the linear actuators, and, as a result,
the fingertips start to slip on the object. The drop in the actual
negative x-axis range was observed to stem from these fingers
substantially slipping around the object toward the end of the
range and ineffectively applying contact forces in the desired
direction of motion. The effect of the grasping torque on the
poor xy translation range is evaluated in the " Effect of Grasping
Motor Torque on Planar Workspace " section and discussed
in more detail in the " Discussion " section.
As mentioned, a slip metric was devised using data from
the potentiometers at the base of the fingers and the linear
actuator positions to determine the contact triangle at the fingertips.
The contact triangle at the initial grasp could then be
compared to that during a manipulation sequence. Figure 8
shows a top-down view of how this triangle deforms around
the surface of the spherical object as it is translated through
the x and y ranges of motion (since these axes experienced the
most significant slippage). The contacts can also move in the
z-axis along the surface of the sphere, and some of the contact
locations appear to cross the dotted circle denoting the object
boundary at the grasp (this would not have been possible
with a cylindrical object). The plots in Figure 8 describe the
trend of the slip metric evaluated at each step of the motion.
As is evident from the figure, the amount of slippage at the
fingertips (and the corresponding slip metric value) increases
away from the center through x and y translation sequences.
Range of Motion With YCB and Foam Objects
We validated the real-world performance of the optimized
hand by commanding the hand to grasp 10 objects-eight
from the YCB Object and Model Set and two identically
sized foam cylinders (one rigid and one soft)-and manipulating
them to the end of the axes' ranges of motion [Figure
9(a)] [23]. The objects were selected for their wide
variety of shapes and sizes, and they tested the differential's
ability to achieve and maintain adaptive finger contacts.
JUNE 2021 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
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IEEE Robotics & Automation Magazine - June 2021

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