Page 192 - Human Inspired Dexterity in Robotic Manipulation

Planning Dexterous Dual-Arm Manipulation 191

• Type2b: A transit path from (g r1 , p 1 )to(g r2 , p 1 ) followed by a transfer path
from (g r2 , p 1 )to (g r2 , p 2 ).
Type1 paths are not physically realizable due to physical constraint. If two
nodes are connected by using a Type1 path, it is replaced by a sequence of
Type2a or Type2b paths in a postprocess of the manipulation plan. This is
the consequence of the so-called reduction property demonstrated in [2].
We also note that, although we just focus on CG r \CP, three kinds of paths
can also be defined in CG l \CP.
On the other hand, CG r \CG l also has foliation structure. Especially,
CG r \CG l \CP has a three-foliation structure. However, as shown in
the next section, we can plan the object manipulation without considering
the foliation structure in CG r \CG l .

10.3 MANIPULATION PLANNER
10.3.1 Graph Structure

Based on the manipulation space defined in the previous section (Fig. 10.1),
we now construct the manipulation graph. First, we consider categorizing
the object placement CP into three classes: initial, intermediate, and target
placements, respectively. Then, according to the grasping state CG r , CG l ,
and CG r \CG l , the manipulation space is divided into ten components
as shown in Fig. 10.4. Here, each component includes a set of configurations
denoted as nodes.
The component belonging to the initial object placement has a single
object pose with multiple grasping postures because the grasp planner gen-
erates multiple grasping configurations. On the other hand, in the interme-
diate object placement, multiple object configurations may be associated
with multiple grasping configurations.
Two components are connected by using one of the three kinds of paths:
transit, transfer, or Type2 path. Also, although all components of the manip-
ulation graph have a foliation structure, the search is performed only by con-
sidering the foliation structures of the intersection between the intermediate
object placement and the right-hand and left-hand hand configuration
spaces. The reason will be explained later in this section.

10.3.2 Graph Components
We now explain how to generate each component of the manipulation
graph.