# Design and Implementation of Composed Position/Force Controllers for Object Manipulation
## 6 Results and Discussion  
The robotic manipulator performs a set of actions in order to grasp an object firmly. The configuration of sensors placed at the fingertips, i.e., a sensor surrounded by a foamy surface, permits the grasping of different objects with diverse shapes. For instance, Figure 11 shows the process of grasping a solid plastic box. The set of actions can be divided into three stages:  
* **Stage 1**. The main goal of this stage is to center the object with respect to the center of the gripper. Assuming that the position of the object is known, the gripper starts approaching the object. Once the gripper has touched the object, it proceeds to position the object according to its center (the center of the gripper). This stage is known as \"positioning\" (Figure 11a-e). * **Stage 2**. Once the object has been centered according to the gripper, the fingers apply specific forces grasp firmly the object; consequently, the object is less vulnerable to falling. As soon as the object has been grabbed, the base of the robot begins rotating for 4.6 s, which is sufficient time for the base to rotate approximately 180 degrees. At this stage, the force PID, type-I, and type-II have to regulate the force to be applied. This stage is known as \"force\" (Figure 11f-j). * **Stage 3**. Finally, once the base of the robot has stopped, the arm moves down so that the gripper can release and position the object on the table (Figure 11k,I). Figure 12 presents the results from grasping a solid plastic box with a width of 6 cm. This action involved the three stages explained earlier. It is important to recall that the hybrid PID is composed of a position PID and a force PID; consequently, these two PIDs were switched on and off according to the action being performed. These changes are indicated at the bottom of Figure 12. Data were continuously collected for 18 s at a sampling rate of 100 Hz. It can be seen that the controllers coped with two key control tasks to grasp an object firmly: positioning and force. Regarding the positioning, the three controllers computed position references for each finger of the gripper at stage 1. It can be noticed from Figure 12 that to locate the object at the middle of the gripper, type-I and type-II fuzzy controllers decreased their initial position reference values for the left finger and increased their initial position reference values for the right finger. The three controllers obtained 1.8 rads as the reference position for the left finger, whereas the three controllers obtained a position reference of 3.4 rads for the right finger. In terms of force, the force regulation reference was 60 mV for both fingers. This reference value avoided damage to the object and excessive forces being exerted by the gripper motors. It can be seen that the type-I controller achieved the reference value for the left finger faster than type-II and PID controllers. Moreover, type-II and PID controllers did not achieve the force reference for the right finger. It is important to remark that from 3.62 s to 6.073 s, the hybrid PID switched from a positioning control task to a force control task, whereas the fuzzy controllers performed both control tasks (positioning and force regulation) simultaneously. Figure 11: Sequence of actions to grasp an object during the experiments: (**a–e**) approaching and centering the object; (**f–j**) grasping and moving the object; (**k**,J) object’s release. Focusing on stage 2, it can be seen that the three controllers achieved the reference values in terms of position for both fingers. However, regarding force, the three controllers achieved values for the left finger close to the reference, but only the type-I fuzzy controller obtained values for the right finger close to the reference. Additionally, the hybrid PID controller generated various oscillations during this stage. This fact might be related to the switching between the PIDs. Particularly, as is shown in Figure 12, there are some spikes in the PID controller's force graph.