## 1 Introduction
It was based on an algorithm to track the contact regions during the squeezing process and determine the stick/slip mode in the contact area. Fingers' displacements were considered rather than forces, and object stability was not guaranteed. Similarly, [PERSON] et al. [44] developed a manipulation pipeline that is able to estimate and control the shape of a deformable object with tactile information but the stability of the grasp is not considered. Authors in [45] proposed a new approach to lift a deformable 3D object, causing small deformations of the object by employing two rigid fingers with contact friction. This approach considered small deformations within the scope of the linear elasticity during the grasp operation and did not deal with the nonlinear relationships between deformations and forces of 3D soft objects. [PERSON] et al. [46] presented a simulation framework for using machine learning techniques to grasp deformable objects. In this framework, robot motions were parameterized in terms of grasp points, robot trajectory, and robot speed. [PERSON] et al. [47] presented a general approach to automatically handle soft objects using a dual-arm robot. An online Gaussian process regression model was used to estimate the deformation function of the manipulated objects and low-dimension features described the object's configuration. Finally, new works (such as [48; 49]) integrate deep-learning techniques, 3D vision, and tactile information in order to fold/unfold and pick-and-place clothes. Although all these works consider the deformation of the object while manipulating it, an initial stable grasp is supposed to be known and nonlinear force-deformation relations are not computed during the handling process. None of these works combine all the previously explained elements that are required for the implementation of a general and complete grasp planning pipeline for 3D deformable objects: a pregrasp strategy for reaching the object that takes into account grasp quality metrics for 3D deformable objects, and a grasp strategy for closing the fingers that guarantees a stable configuration of the object by considering its deformation and the applied contact forces. This paper involves an extension of our previous grasping strategy in [33] in order to implement this complete grasp planning pipeline. Firstly, we adapt the stability criteria developed for robotic grasp synthesis of rigid objects to 3D deformable objects (see Section 2 for a general description of the strategy and Section 3 for the new geometric criterion of the initial grasp). We also defined a new pregrasp strategy (Sections 4 and 5) in order to approach the deformable objects in an optimal way before manipulating them by using the previous grasping metrics. This grasping strategy is based on an interaction model developed by the authors in a previous work [40]. Section 6 indicates how this finger-object contact model is used in order to compute the contact forces to be applied by the fingers for a stable grasp of the deformable object and what their precise values are in the proposed experiments. We consider the problem of grasping and manipulation of a 3D isotropic deformable objects with a 3-fingered Barrett hand. This hand is installed as the end-effector of a 6-DOF Adept Viper robotic arm S1700D. Finally, a complete grasping planning strategy combining the pregrasp and grasp synthesis strategies of the hand + arm system is developed and tested with real objects (Section 7).