# Design and Implementation of Composed Position/Force Controllers for Object Manipulation
## 2 Related Work  
Controller design for grasping objects in robotics has been an important research topic in the last few years. In this context, proportional-integral (PI) controllers and proportional-integral-derivative (PID) controllers have been designed and implemented to be used in the grippers of robotic arms. For instance, a two-finger gripper for the manipulation of deformable objects was implemented [24]. This gripper used a PI parallel force controller  
Figure 1: Actions prior to the object’s manipulation: (**a**) moving the robot so the object’s position is within the arm’s configuration space, (**b**) object detection and position estimation, and (**c**) planning and execution of trajectories to drive the arm close to the object. with prediction models in order to regulate the force exerted by the robot on the object; thus, the risk of damaging the objects during the grip was reduced. In order to manipulate objects, a force sensor and a flex sensor can be placed in a gripper [25]. This gripper should be controlled only by a motor that opens and closes the gripper. An algorithm and a control strategy are used to apply force to the object without damaging it. In [26], a gripper with two parallel fingers with two phalanges each and a fixed base was used to manipulate objects. The gripper was controlled only by a motor that provided different torques, and a touch sensor was placed on the fixed surface to measure the pressure applied to the object. In order to manipulate objects, a force sensor can be placed on each finger of a parallel gripper controlled by a single motor [27]. Other studies have tested the designs of controllers using either simulated grippers or simulated robotic hands. For instance, the authors of [28] simulated and manufactured a prototype of a robotic hand with five fingers. To control the kinematic and dynamic movements of each finger, a PID controller was used. They generated a path for each finger in the configuration space, achieving fast motion towards the target angle with a small error signal and little overshooting. However, as described by the authors, when they tested it in a real prototype, the overshooting signal was larger than in the simulation, and was mainly produced by disturbances in some inputs. Moreover, when the reference value was set to a long period of time, small oscillations occurred, again only in the real prototype. Furthermore, the authors of [29] made a mathematical analysis of the contact forces for a robotic finger of three degrees of freedom. The authors proposed two simulated PID controllers; one was used to achieve position and the other to regulate strength. Both controllers were tuned using fuzzy logic. Regarding using fuzzy logic in control design, the effects of membership functions (triangular, trapezoidal, and Gaussian) on a fuzzy control scheme for a three-finger system have been analyzed [30]. Moreover, another study [31] used a fuzzy control scheme in order to manipulate objects. This control scheme was composed of two fuzzy controllers. The first controller was employed to ensure a stable grip and the second to prevent slipping. In [32], a three-finger gripper to manipulate strawberries without damaging them was developed. A fuzzy controller was designed to compute the force to be exerted on the strawberry. The inputs for this controller were the readings of a capacitive sensor placed on each finger of the gripper. Due to a single motor on the mechanical gripper, the three fingers might be operated simultaneously. Likewise, Reference [33] proposed a fuzzy controller with a gripper using only a single servo motor in order to grasp unknown objects. The authors showed the effectiveness of the controller with three different types of object hardness: soft, moderate, and hard. Similarly to PI and PID controllers, simulations have been used to test fuzzy controllers. For example, in [34] simulated a fuzzy controller with tactile information to manipulate objects with a two-finger gripper.