# Manipulation Planning for Large Objects through Pivoting, Tumbling, and Regrasping
## 5 Hierarchical Manipulation Planning
### Motion Level Planning
#### 5.2.2 Tumbling and Regrasping  
Changing the base surface of the object improves the obstacle avoidance performance. The object's base surface is the support surface between the object and the table. The proposed method has better collision-avoidance capability since pivoting gait is performed with the combination of tumbling and regrasping. By tumbling, we can control the area of support polygon and it contributes to the case when a manipulated object passes through a narrow passage. In addition, by regrasping, we may avoid the collision between the robotic arms and the environment. An example of the object motion is shown in Figure 13, where the gaits 1 cannot avoid the collision with the red obstacle since the object is not tumbled. If the object is tumbled to the right as shown in the right of Figure 13, the supporting polygon can be changed. Such a change allows the object to be moved without colliding the obstacle by performing the gaits 2. Tumbling motion contributes to change the type of gaits adaptively according to the environment.  
For changing the object's base surface, we design tumbling motion, which is a special case of pivoting when the rotation passes through the object's edge. Rotating an object up to SP is simple, where one EEF rotates the object around one edge (the line connecting the two supporting vertices) of the object until it moves to SP. The kinematics and dynamics of tumbling motion can be derived through minor modifications in (5)-(11). However, rotating an object up to USP is more complex. This is because to maintain an object in USP, the EEF must contact and hold the object, which leads to difficulty in changing the grasp poses. To solve this problem, we incorporate multiple arms to achieve regrasping by sequentially using different arms to contact the object. Figure 14 depicts a tumbling motion where the object is rotated to USP in the boundary of the table. If the right EEF does not contact the object, it will fall from the table. The tumbling motion is designed as follows: First, the left EEF contacts and rotates the piano (see motion I1). Meanwhile, the right EEF moves to the desired position, which is also the right EEF's grasp pose for contacting the object in USP (see motion r1). The left EEF rotates the object until it contacts the right EEF. Next, the right EEF alone holds the object. The stability is evaluated by calculating the contact wrench of the contact between the right EEF and the object, as well as that between the object and table, as mentioned in Section 4.3. The left EEF then leaves the object and moves to the desired grasp configuration (see motion I2). Compared to regrasping with a gripper, which can only regrasp an object in SP, a multi-arm robot can regrasp an object in both SP and USP.  
Figure 13: A change of the object’s supporting base improves the ability of collision avoidance. The object motion following the gaits 1 cannot avoid a collision with the red obstacle. If the object is tumbled, the supporting base will be changed. Such a change allows the object to be moved without colliding the obstacle by performing the gaits 2. To pass a narrow passage, gaits 2 is more area-efficient than gaits 1.  
In addition to regrasping an object in USP, regrasping motion in SP is also designed. When an object is in SP, we can easily plan the motions for regrasping without affecting the object pose. The regrasp motions are denoted by the yellow edges in Figures 10b and 11a.