IEEE Robotics & Automation Magazine - June 2012 - 49

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pobj
qstart

Bimanual Grasp-RRT Planner

1 GraspRRTl

l
GraspRRTInstanceðqstart
; po Þ
r
GraspRRTInstanceðqstart
; po Þ

2 GraspRRTr

Bigrasp Scoring
Self-Collision Checking
Grasps
Trajectories
GraspRRT
GraspRRT
Left
Right
ht

l
r
Algorithm 4. BimanualGraspRRT (qstart
, qstart
,po )

3 GraspRRTl :startðÞ

Bimanual
Grasping
Trajectory

4 GraspRRTr :startðÞ
5 while ð!TimeOutðÞÞ do
6

/* process new results of GraspRRTl */
sl

8

if ðsl Þ then
Resultsl :addðsl Þ

9

foreach ðsr 2 Resultsr Þ do

10

Figure 7. An overview of the Bimanual Grasp-RRT planner.

GWS analysis is performed as described in "Quality of
a Grasp."
Planning Bimanual Grasping Motions
When large objects, like the wok in Figure 6, should be
grasped by a humanoid robot, both hands are needed for
applying a stable grasp. On the basis of the Grasp-RRT
planner, introduced in the last section, we propose the
Bimanual Grasp-RRT planner, which combines the
search for a bimanual feasible grasp along with the
search for a collision-free grasping motion for both
arms. Since the bimanual planner decouples the search
for left and right arm, the approach cannot be used for
planning common parts of the robot, as torso or platform. In case such joints should be considered for planning a bimanual motion, a different approach that does
not rely on decoupling must be chosen.
Bimanual Grasp-RRT
Figure 7 depicts an overview of the Bimanual Grasp-RRT
planner. This planner instantiates two Grasp-RRT planners, one for each end effector. These instances are started
in parallel so that the search for feasible grasps is done
simultaneously for the left and right hand. Furthermore,
they are configured to search and store grasps until the
main planner terminates.
The Bimanual Grasp-RRT planner collects the grasps
and the corresponding grasping trajectories for the left and
right end effector and tries to find a feasible bimanual solution by performing quality evaluations of bimanual grasping combinations. Every time a planner for one end
effector reports that a new grasping trajectory was found,
all possible bimanual combinations of this grasp together
with the already stored grasps of the other hand are built
and evaluated as described in the "Evaluation of Bimanual
Grasps" section. If the resulting bimanual score is above
the threshold .min , the self-collision status of the two
pruned grasping trajectories is checked. If no collision was
determined, the combined solution for both arms together
with the resulting grasping information is returned (see
Algorithm 4).

GraspRRTl :GetNewSolutionðÞ

7

if ðBiGraspEvaluationðsl ; sr Þ > .min &&
!SelfCollisionðsl ; sr ÞÞ then

11
12

GraspRRTl :stopðÞ

13

GraspRRTr :stopðÞ
return BuildSolutionðsl ; sr Þ

14
15

end

16

end

17

end

18

/* process new results of GraspRRTr */

19

...

20 end

Evaluation of Bimanual Grasps
The GWS analysis can be easily applied on bimanual
grasping. Considering a robot with two hands, one obtains
the two contact point sets Cgl and Cgr , for the left and right
hand. By analyzing GWS of the united set Cg0 ¼ Cgl [ Cgr , a
quality score of a bimanual grasp can be computed analogously to the single-handed case.
As shown in the "Experiments" section, the performance of a bimanual planner can be increased when the
force-closure test is only performed for the resulting bimanual grasp and not for the single-handed grasps since force
closure is only needed for the resulting grasp. This leads to
a significant improvement in performance, but the appearance of some of the resulting grasping configurations was
not appealing. Because of the missing force closure condition for one hand, sometimes degenerated grasps (e.g., just
two fingers in contact with the object) were generated,
when the corresponding grasp of the other hand was
already force closure. These bimanual grasps are evaluated
as satisfactory by the GWS algorithm, but the result does
not look natural. Hence, the GWS metric is not sufficient
for generating anthropomorphic-looking bimanual grasping configurations, and we extended the evaluation of
bimanual grasps. An enhancement can be achieved by
claiming force closure for both single-handed grasps.
Beside the aforementioned drawback of an increased planning time, the number of valid grasps that can be found
by such an approach is limited. Usually, there exists
bimanual force closure grasps that are composed of two
JUNE 2012

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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49



Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - June 2012

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