IEEE Robotics & Automation Magazine - December 2015 - 77

respectively. Notice how the size of R increases almost linearly with the object resolution [see Figure 9(a)], as was
reasonably expected.
Conversely, the size of R C and of R G increases at a sublinear rate that depends on the object shape, as shown in Figure
9(b) and (c). However, this behavior is expected because the
sizes of R C and R G have to become constant when the resolution increases as the fingertip size is fixed.
Grasp Synthesis
Figure 10 shows the best-ranked grasp configurations for the
objects in Figure 8 for the cases of n = 2, f, 5 fingers. It is
worth noticing that depending on the dimension and shape
of the object, the best-grasp candidates for each object by
changing the number of employed fingers are similar when
the number of employed fingers is changed. This result confirms the numerical stability of the proposed algorithm. For
very irregular objects, e.g., the monster toy in the right-most
column of Figure 10, the best grasp configurations change
more with n due to the feasibility constraint, which depends
on the possibility of touching the object with more fingers
respecting the kinematic constraints.

Figure 11. The best-ranked grasp configurations for the half-filled
shaped bottle, i.e., when an offset is applied to the CoG.

The minimization of the gravitational effects has been
tested by considering the case of a half-filled bottle, i.e., by
changing the position of the CoG of the bottle with respect to
the case shown previously. Figure 11 shows the corresponding
best-ranked grasp candidates for n = 2, f, 5 fingers. In all
cases, the off-centering of the line of action of the applied fingertips forces is negligible, and, hence, the compensation of
gravitational effects is maximized.
Computational Complexity
The computational complexity of the proposed method has
been evaluated by measuring the computational time needed
for the grasp synthesis of the best-grasp candidate for the

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Figure 12. The computation times needed for the selection of the MIRs (blue), UCRs (green), and GRs (red) from the CAD models of
the (a) water glass, (b) wine glass, (c) mug, (d) shaped bottle, and (e) monster toy for a number of triangle-mesh resolutions.

DECEMBER 2015

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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