# Dynamic Nonprehensile Manipulation of a Moving Object Using a Batting Primitive
## 1 Introduction  
To date, a variety of robots have been used in automated production lines for object manipulation tasks in factories, and these robotic technologies have contributed significantly to the development of modern industry. Recently, with the fourth industrial revolution, robots have been introduced to provide various services not only in factories but also in human living environments. Robots used in factories perform simple repetitive operations such as pick-and-place using specially designed grippers; however, in an environment such as cafes and restaurants, human-level object manipulation ability is required. Therefore, to provide a wider range of services in a human living environment, robots must have a higher level of object manipulation similar to that of humans. In addition to manipulating objects using grasping, humans can manipulate objects freely by appropriately utilizing nonprehensile manipulations [1] without grasping, such as throwing, batting, rolling, pushing, and sliding. Most robots are still limited to prehensile manipulation using grasping. A robot that performs nonprehensile manipulation is rare owing to the difficulty of control using nonprehensile manipulations. When nonprehensile manipulation is performed, the object moves during manipulation. Since the moving object is not fixed to the robot, it is necessary to plan and control the future behaviorof the moving object based on the state of the robot and the moving object. Despite these difficulties, nonprehensile manipulation has advantages such as increased object manipulation methods, expansion of the robot workspace, and increased manipulation dexterity [2]. To improve the ability of robots to manipulate objects, the robots must have nonprehensile manipulation capabilities with these advantages. [PERSON] et al. conducted a survey on nonprehensile manipulation of robots to address the trends and open issues of nonprehensile manipulation studies [3]. According to [3], the nonprehensile manipulation task is complex and difficult. Because of the complexity and difficulty of the task, most studies divide the nonprehensile manipulation task into simpler subtasks called nonprehensile manipulation primitives. The representative nonprehensile manipulation primitives include throwing [4], catching [5], batting [6], pushing [7], sliding [8], and rolling [9]. Each of these nonprehensile manipulation primitives is selectively operated by a high-level supervisor depending on the task [10]. Among the nonprehensile manipulation primitives, batting is challenging because it requires precise and fast manipulation of the moving objects, and studies on this topic are lacking. In sporting events such as table tennis, tennis, and baseball, players have a batting ability to send the moving objects (balls) to the desired position with sophisticated and quick manipulation, while the batting performance of robots is insufficient. Therefore, this study aims to contribute to the improvement of the dexterity of robots by conducting research on batting, which requires more precise and quicker nonprehensile manipulation of moving objects than do the above-mentioned primitives. For a robot to perform a batting task, at least four methods are required. First, image processing is required to recognize a moving ball. Second, estimation of the future trajectory of the ball is required. Third, the motion of the robot arm must be controlled to affect the ball direction. Lastly, calibration is required to convert the coordinates between the robot arm's coordinate system and the vision sensor's coordinate system. This implies that the performance of each method affects the performance of the batting primitive; studies that can improve the performance of each method are discussed. [PERSON] et al. [11] developed a vision module for humanoid robotic table tennis. The vision module contains two stereo vision sensors with a 200 fps and an algorithm for predicting the rebound trajectory of a table tennis ball. [PERSON] et al.