IEEE Robotics & Automation Magazine - December 2015 - 64

Table 2. The quality index for ten different starting positions. The three-fingered hand is tested on a cube,
and all of the resulting quality measures are reported.
Quality
Measure

Quality Index for Each Starting Position

MEV

5.5e03

5.2e03

4.6e03

4.2e03

4.1e03

3.4e03

2.4e03

2.3e03

1.7e03

0.1e03

GII

0.0329

0.0321

0.0319

0.0315

0.0311

0.0306

0.0305

0.0285

0.0258

MSVG

1.7316

1.7301

1.7278

1.7172

1.7127

1.7094

1.7000

1.6992

1.6733

1.6580

DTSC

0.3001

0.2785

0.2699

0.2503

0.2428

0.2288

0.2057

0.1923

0.1787

0.1579

UOT

5.6e09

220.95

218.95

201.93

180.40

178.94

175.03

170.70

154.20

141.90

sphere, a cylinder, and a cube. The objects are then created
using the specific functions SGsphere(), SGcylinder(),
and SGcube(). Finally, it is required to select the quality measure to be used for the grasp selection. The grasp planner is
now called and the best resulting grasp plotted.
The results for the SG3Fingered hand grasping a cube
with a 50-mm edge are shown in Table 2. Ten different starting positions are considered. The table shows the obtained
quality indexes using the
available quality meaA set of functions can be
sures: 1) manipulability
ellipsoid volume quality
used in scripting mode to
index (MEV), 2) grasp
isotropy index (GII), 3)
let the user have a simple
minimum singular value
of the matrix G (MSVG),
graphical representation
4) distance from the
singular configuration
of the manipulator and
(DSTC), and 5) uniformity measure (UOT).
the object.
Figure 2 shows the best
obtained grasp using the
SGdistSingularConfiguration()quality measure.

In Figure 10, three possible outputs of the grasp planning
algorithm are represented. We ran the grasp planner on the
three-fingered hand model to generate suitable grasps of the
three different objects available in SynGrasp. Ten possible
grasps were computed for each of the three objects, and the
best configurations were selected among them according to
the grasp isotropy index metric.
Applications
In this section, we report some practical applications of the
proposed toolbox. In particular, we describe how the
object-based mapping that is able to transfer human hand
synergies onto a robotic hand, described in the "Mapping
Human Hand Synergies onto Robotic Hands" section, has
been validated in an experimental setup. Starting from the
simulation obtained using SynGrasp, the capability of
reproducing object motions and exerted grasping forces has
been considered. All of the experiments have been performed on two robotic hands: 1) theDLR-HIT Hand II and
2) the modular hand.
64

IEEE ROBOTICS & AUTOMATION MAGAZINE

DECEMBER 2015

It is worth noting that the methods and results described
in the following section do not represent an experimental validation of the tools provided in SynGrasp. This section is
rather intended to show how the toolbox can be used to simulate grasping and manipulation tasks and to generate trajectories for robotic hands, exploiting MATLAB tools for
hardware/software integration.
Object Motion Evaluation
In this experiment, we compared the trajectory of the center
of a virtual grasped object moved by the paradigmatic hand
in SynGrasp and the trajectory of a real object grasped and
moved by the robotic hands. We tracked the grasped object
using a camera and the ARToolkit library [43], [44], which
consent to track the motion of a defined marker. Figure 11
shows the setup of the experiment.
We considered a cube as a grasped object. Only the first four
synergies were activated on the paradigmatic hand model.
Given this underactuation condition, for each configuration of
the hand, only one feasible rigid body motion of the cube exists,
corresponding to a particular combination of the four synergies
[9]. This particular combination was activated on the simulated
paradigmatic hand at each time step, resulting in an object
movement that is represented by the blue line in Figure 12. The
resulting motion of the paradigmatic hand was mapped on the
two considered robotic hands. The mapping algorithm presented in [38] was applied in the two cases using SynGrasp functions, as described in the "Mapping Human Hand Synergies
onto Robotic Hands" section. The joint angles obtained as the
output of the mapping procedure were directly sent to the
robotic hands using a serial connection (for the modular hand)
or via User Datagram Protocol (for the DLR-HIT hand II case).
The mapped movement produced an object displacement, and
the resulting trajectories are represented in Figure 12. We performed 20 trials for each robotic hand. The plotted trajectories
that we considered to analyze the performances have been computed as the average of the 20 obtained trajectories.
We can observe that the three paths have different lengths.
This is due to the scaling factor that we introduced in the mapping algorithm. Considering the module of the trajectory, the
paradigmatic hand performed a 5.9-mm movement. The
modular hand performed a 3.61-mm movement corresponding to the scaling factor k sc = 0.61 computed by the mapping
algorithm. The DLR-HIT Hand II, with a scaling factor of

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2015