# Manipulation Planning for Large Objects through Pivoting, Tumbling, and Regrasping
## 1 Introduction  
Humans often manipulate large and heavy objects utilizing the contact of the object with environment. Although robotic manipulation of general-shaped large and heavy objects is challenging, we aim to realize a robot manipulating such objects by effectively utilizing the contact of the object with a table (Figure 1). Among the manipulation styles using contact with a table, pivoting refers to the style of inclining and rotating an object on its vertex. Pivoting enables a robot to manipulate a bulky object with a relatively small manipulating force because the robot does not need to lift the object [1]. Moreover, the pivoting gait, which is a manipulation style, enables a robot to move an object by pivoting it multiple times by changing its rotational vertex. In addition, to start the pivoting gait from the designated initial pose of the object, a robot may once tumble the object by rotating it on its edge. Pivoting gait has been explored for moving a simple box-shaped object [2; 3]; however, this study aims to realize the robotic manipulation of a general-shaped object by combining pivoting, tumbling, and regrasping (Figure 2). Let us consider the example shown in Figure 3, where a robot moves a blue-colored object to the designated location on a table, with avoiding an obstacle (red colored). In this case, the robot first tumbles the object to an upright posture and then passes through the narrow passage using the pivoting gait. For realizing such combined manipulation, we need to determine the object face required to contact with table and the grasping pose of the object. In addition, a robot may change the grasping pose multiple times, and such changes of the grasping pose are referred as regrasping. Our proposed planner comprises offline and online phases. In the offline phase, we first preprocess the mesh model of a general-shaped object clustered into superimposed segments [4] in order to determine the object's contact surface with table and the contact surfaces with the end-effectors (EEFs). In the online phase, we propose a hierarchical motion planning method to determine the motion of both the object and the robot. Hierarchical planning includes task level planning and motion level planning. In the task level, we sample the object configurations on the table considering the kinematic constraints of pivoting and tumbling. At this level, the planner constructs a graph, where each node in the graph represents an object pose and a grasp configuration, and each edge in the  
Figure 1: A dual-arm robot manipulates a piano by pivoting on the object’s vertex (marked by a yellow dot). Figure 3: Motion sequence for moving a piano forward and avoiding collision with an obstacle (red colored). Both the initial and goal object poses are in SP, whereas the intermediate object pose is in USP. The yellow trajectory indicates the motion of the object’s CoM. Figure 2: Manipulation of a piano by (**a**) pivoting, (**b**) tumbling, and (**c**) regrasping. graph indicates a primitive motion to transform the object poses or grasp configurations. The purpose of primitive motion is to realize either pivoting, tumbling, or regrasping. On the other hand, in the motion level, the robotic manipulation motions are generated. Here, the pivoting and tumbling motions are generated by predicting the object's future dynamics using model predictive control (MPC), considering the kinematic constraints for maintaining contact with the environment. Furthermore, this study expands the feasible object poses used in motion planning to both stable placements (SP) and unstable placements (USP). Here, SP indicates that the vertical projection of the object's center of mass (CoM) is included in the object's supporting area. The robot can easily regrasp the object in SP. On the other hand, in USP, a robot can manipulate an object within a limited support area, which offers more choice for avoiding collision in a narrow space.