## 1 Introduction  
Nowadays, manipulation has become an increasingly important standing research topic in robotics. Most of the related works in this field consider the grasping of rigid bodies as an extensively studied area, which is rich with theoretical analysis and implementations using different robotic hands ([1; 2; 3; 4; 5; 6; 7; 8]). Robotic grasping of deformable objects has also acquired importance recently due to several potential applications in various areas, including biomedical processing, the food processing industry, service robotics, robotized surgery, etc. ([9; 10; 11; 12; 13; 14]). Recent surveys covering the literature related to the robotic grasping and manipulation of deformable objects can be found in [12; 15]. Nevertheless, efficient and precise (i.e., deformation/force control) robotic grasping of 3D deformable objects remains an underdeveloped area within the robotics community due to the technical and methodological difficulties of the problem. In fact, this problem involves implementing two main steps with their own subproblems: determining the initial location of the grasp points and moving the hand + arm system towards them (i.e., pregrasping strategy), and closing the fingers of the robotic hand until a robust grasp is reached while taking into account the deformation of the object (i.e., grasping strategy). In the case of the pregrasp strategies, two main problems arise: firstly, implementing a grasp quality measure to choose the most stable grasp configuration; secondly, applying the kinematic constraints of the hand + arm system so that the chosen grasp is reachable. Several previous surveys to quantify grasp quality were developed in [1; 16; 17; 18; 19]. All of these approaches have studied stable grasps and developed various stability criteria to find optimal grasps for rigid objects. Nevertheless, the development of algorithms that can efficiently synthesize grasps in 3D deformable objects is still a challenging research problem. [PERSON] et al. [20] analyzed the stable grasping of deformable objects based on extending the concept of force closure of rigid objects to deformable planar objects with bounded applied forces. [PERSON] et al. [21] presented a grasp planner that can reproduce the actions of a human hand to determine the contact points. Their algorithm combines the position information of the hand with visual and tactile data in order to achieve a hand-object configuration. This method is applied to planar objects without considering applied forces by fingers and object deformation. [PERSON] et al. [22] proposed a grasp quality metric for hollow plastic objects based on minimal work in order to combine wrench resistance and object deformation. [PERSON] et al. [23] presented a generic solution for doing pick and place operations of meat pieces with a vacuum gripper. This solution used a grasp quality metric that combines wrench resistance and object deformation. It was based on the computation of the required work to resist an external wrench and it can only be applied to planar objects, without a direct relation between applied forces and deformation. In fact, none of these works can be applied to general 3D deformable objects and they are solutions for specific types of objects. For the second step of the grasping problem (i.e., closing of the fingers), previous grasping synthesis methods are mainly based on the generation of force closure (FC) grasps ([24; 25; 26]). This means that the robotic hand is able to maintain the manipulated object inside the palm despite any external disturbance and evaluate the contact forces including those due to friction. FC is generally used to implement the grasping of rigid objects with a low number of frictional contacts by taking into account geometric criteria of their contact surfaces.