# Learning Form Closure Grasping with a Four-Pin Parallel Gripper
## 1 Introduction  
Robotic manipulation is still a challenging task for the robotics community [1; 2]. In recent years, progress in grasp detection has in some way improved the generalization of robotic grasping systems, enabling a wider application of such systems in pick-and-place tasks. For example, [PERSON] et al. reported on a picking system that is capable of grasping a diverse range of objects with a rate of more than 300 mean picks per hour [3]. [PERSON] et al. proposed a similar robotic pick-and-place system to grasp and recognize known and novel objects without the need to train for novel objects [4]. In addition to pick-and-place tasks, there is also a need for post-grasp manipulations [5; 6]. Compared with pick-and-place tasks, the latter requires the object to be grasped in a known pose so that further actions can be performed with the object. For example, [PERSON] et al. proposed a data-driven statistical framework for post-grasp manipulation that enables robots to place, drop and insert [7]. [PERSON] et al. implemented a reinforcement learning policy that can learn object reorientation on a physical shadow dexterous hand [8]. [PERSON] et al. reported an in-hand manipulation benchmark to evaluate the planning and control of such systems [9]. To achieve the aforementioned manipulation tasks, a robotic hand or gripper is a prerequisite, and its design issue should be focused on. The design of robotic hands or grippers has developed immensely over the last few decades [10], evolving in the following aspects: (1) the number of fingers has extended from 2 to 3 [11], 4 [12] or 5 [13], (2) the actuation type has changed from fully actuated [14] to underactuated [15], (3) the material has varied from rigid [16] to soft [17], and (4) the task type has transformed from repetitive tasks to flexible tasks. In general, the developments benefit from the advancements in high-performance MCU, MEMS and materials. However, in real applications, a trade-off should still be considered between stability and flexibility. Four-pin grippers are usually treated as a compromise since they can achieve stable grasping of objects and adapt to changes, which makes them perfect for flexible industrial applications. To guarantee stable post-grasp manipulation, several grasp quality evaluation concepts have been proposed [18]. Among them, form closure and force closure are commonly used when the object model is explicitly given. Considering the realization of these two concepts, force closure can be achieved by any two-pin gripper or two-fingered robotic hand, andform closure can be achieved by at least seven-pin grippers or seven-fingered robotic hands. Although relocalizing the object to a desired pose using the former concept could be damaged by external disturbance forces caused by the environment, the former still seems to be a sensible solution for robotic hardware, since it is neither easy to plan seven contact points on an object nor feasible to design a seven-pin gripper or a seven-fingered hand. However, the latter concept would be more competitive with regard to confining the form closure problem to a plane and considering force closure in the orthogonal direction, thus enabling 2.5D grasping using four pins or fingers [12]. In previous work, a series of four-pin parallel grippers was designed to achieve 2.5D form closure grasping [5; 12; 19]. Combined with the form closure grasping algorithm, the grasping points can be planned for regular 2.5D objects in a clean experiment set-up. However, in the real grasping process, modeling of the uncertainty between the object, the robot and the environment is manageable, leading to failure when the geometry of the object or the gripper pins is not identical to the CAD models that are used to construct the environmental constraints.