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194   Human Inspired Dexterity in Robotic Manipulation


          10.3.3.4 Path Generation
          In this work, two components of the graph are connected by using either
          Type2, transit, or transfer paths. For all cases, a path between two configu-
          rations is computed by using a path planner such as [7].
             Let us assign a group ID for each node. When connecting two nodes, we
          set that the ID is the same for two nodes. After connecting two components
          included in the manipulation graph, we check the ID of initial and target
          nodes. If the IDs are the same for both nodes, we search for the path con-
          necting them. We use the depth-first search to obtain a solution path. If a
          Type1 path is included in the solution path, we consider replacing it by using
          a Type2 path.
             Completing a task by a dual-arm manipulator may require multiple
          manipulation styles. For example, pick-and-place in a simple environment
          may be realized only by using the right arm. The same task may be realized
          only by using the left arm. Or, sometimes the same task may be realized by
          once picking up the object with the right arm, and then placing it with the
          left arm. The manipulation style selected by using our proposed planner
          depends on the order of the component connection.
          10.3.4 Path Optimization

          The obtained manipulation path may include several regrasping and place-
          ment operations. To reduce the motion time and increase the reliability of
          manipulation, it is desirable that the number of regrasps is minimized. We
          iteratively use three operations for path optimization [1]: transfer-transfer
          path optimization, transit-transit path optimization, and Type2-Type2 path
          optimization.


          10.4 EXAMPLES

          First, we run the manipulation planner in the environment as shown in
          Fig. 10.5. We consider moving a rectangular object from a cage and place
          it on the middle of the table. A generated manipulation graph is shown in
          Fig. 10.5B. The solution path and its optimization are shown in Fig. 10.5C
          and D, respectively. As shown in this figure, the number of regrasps is much
          reduced. Fig. 10.6 shows the motion of the robot moving the object from
          the initial to the final placement. Fig. 10.7 shows the motion of the robot
          regrasping the object from the right hand to the left hand. The solution path
          in the manipulation graph (Fig. 10.4) is shown in Fig. 10.8A.
             In the second example, we also consider placing the object at the middle
          of the cage located at the left-hand side of the robot. Although it is possible
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