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Planning Dexterous Dual-Arm Manipulation  193


                 Let us now consider CG r \CG l . For simplicity, we do not have to con-
              sider the foliation structure of this component. We consider generating a set
              of configurations in CG r \CG l by randomly sampling the object pose in 3D
              and the grasping pose of each hand.


              10.3.2.3 Target Object Placement
              Let us consider the object configuration at the target. For a set of target
              object placements p fj (j ¼ 1, …, J), we consider a set of grasps g ri and g li ,
              (i ¼ 1, …, I). Within CG r \CP, we consider solving the inverse kinematics
              of the right arm for the given (g ri , p fi ). If the inverse kinematics is solvable and
              the arm configuration is collision free, we consider applying this configura-
              tion as a node included in this component of the graph. The same discussion
              applies for CG l \CP and CG r \CG l \CP.

              10.3.3 Component Connection

              Now, we consider connecting the various components of the graph.


              10.3.3.1 Type2 Path
              Let us consider the case where two components are connected by using a
              Type2 path. We consider randomly selecting one node from both compo-
              nents and trying to connect them by using a Type2 path. We consider iter-
              ating this operation a predefined times.

              10.3.3.2 Transfer Path
              To connect two components by using a transfer path, we first randomly
              select a node from one of the components. Then, while keeping the same
              grasp, we consider changing the robot posture so that the configuration is
              included in the other component. If we can find such a collision-free path,
              we conclude that the connection between two components can be estab-
              lished by using a transfer path.


              10.3.3.3 Transit Path
              To connect two components by using a transit path, we first randomly select
              a node from one of the components. Then, while keeping the same object
              placement, we consider changing the grasp so that the configuration is
              included in the other component. If we can find such a collision-free path,
              we conclude that the connection between two components can be estab-
              lished by using a transit path.
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