# Design and Implementation of Composed Position/Force Controllers for Object Manipulation
## 1 Introduction  
Due to uncertainty on localization, mobile robot manipulation faces two key problems when trying to manipulate objects: firstly, computing the correct position at which the mobile robot needs to be for grasping an object, and secondly, calculating the specific position at which the object to be grasped is. Specifically, object manipulation through a robotic arm involves three actions: (i) moving the robot and positioning it at a place where its arm's configuration space intercepts the object's position (Figure 0(a)); (ii) planning and execution of the arm's trajectories--that is, to move the robotic arm towards a position where the object is inside the gripper's configuration space, i.e., where the gripper (end effector) may grasp the object [1,2] (Figure 0(b)); and (iii) tuning the gripping action--i.e., closing the gripper in order to take and manipulate the object properly [3, 4, 5] (Figure 0(c)). The first two actions are called the _pre-grasping_ stage, and the last action is named the _grasping_ stage. The gripper and their controller are key components at the grasping stage in order to manipulate objects accurately. Parallel motion grippers and angular motion grippers are the most commonly used in robotics for object manipulation [6]. Parallel grippers usually have only one motor; therefore, their fingers move simultaneously in order to handle objects. Recently, the use of grippers with angular motions has increased. Thanks to their configuration, these grippers extend the gripping range of objects, and differentconfigurations may be calculated to handle an object; therefore, these grippers might provide dexterous object manipulation similarly to human fingers. Detailed reviews regarding several types of grippers can be found in [7; 8; 9]. Focusing on controllers, the PID controller has been widely used in control systems [10; 11; 12; 13] due to its simplicity and robustness. In the last few years, there has been increasing interest in using fuzzy logic in different control systems [14; 15; 16; 17; 18; 19; 20]. Moreover, fuzzy logic has been used for implementing several applications. For instance: in a multicriteria decision-making process [21], energy consumption for bipedal walking robots [22], and search engine systems [23]. Fuzzy logic uses fuzzy values and rules to cope with uncertainty, just as humans do. These fuzzy values and rules may be implemented based on the user's experience instead of using complex mathematical models. In the present work, an angular gripper with two independent fingers was used. Prior to the manipulation stage, the actions described in Figure 1 were done. The object's position, initially unknown, was obtained by a perception system and was used to bring the arm close to the object. However, at this stage of the work, no visual surveying has been used. Instead, a tactile feedback control is performed. The object's dimensions were used to estimate the gripper's initial opening. Once the object was between gripper fingers, angular position and (when object do contact) pressure forces were used to control the motion of each finger independently. The pressure forces were obtained by piezoelectric sensors on the fingertips. The contributions of this work can be summarized as follows: The implementation of three switching force and position controllers (a PID, a fuzzy type-I and a fuzzy type-II) for grasping tasks with a two-fingered gripper (independent fingers). The evaluation and comparison of those controllers, via simulation and a real arm manipulator. A communication protocol to control and switch between controllers over an ROS. Finally, a control process over a two-fingered angular finger gripper that centers the object in order to apply equivalent forces with both fingers. This paper begins by analyzing some relevant related work (Section 2). Next it presents the details of the system (Section 3). The communication of the gripper with an ROS is described in Section 4. The grasping stage and the design of the proposed controllers are described in Section 5.