## 1 Introduction
Nevertheless, traditional FC-based approaches cannot be applied to deformable objects due the complexity of their interaction with the robotic hand's fingers: the object deforms (i.e., its size and shape are changed) and the contact surfaces evolve dynamically while contact forces are applied by the fingers. New reactive methods based on the detection and avoidance of slippage have been developed in order to solve this limitation in the grasping of deformable objects. For instance, [PERSON] et al. [27] computed the tangential forces required for slippage avoidance and adjusted the fingers' relative positions and grasping forces accordingly, taking into account an estimation of the weight of the grasped object. The main drawback of this approach is that the relationship between applied forces and object deformation is not considered. [PERSON] et al. [28] proposed a new slip detection sensor based on video processing in order to perceive multidimensional information, including absolute slip displacement, the deformation at the object surface, and force information. This method is only applied for 2D objects with transparent and reflective surface, such as pure glass. However, these types of materials are not common in deformable objects. In addition, the stress state of the gripper-object interface is not precisely analyzed when taking into account the properties of the object's material. In order to solve all these limitations of reactive strategies, it is crucial to use a suitable contact model ([29; 30; 31; 32]) that explains the coupling between the contact forces and the object deformations. A precise contact model can be exploited to provide a set of grasping forces and torques that can be applied to maintain equilibrium before and after the deformation [33]. Thereby, the grasp stability can be computed in real-time while the contact surfaces evolve during deformation. This evolution of the object surface is obtained by sampling mechanical deformation models [34], mainly mass-spring systems ([35; 36]), finite element methods (FEM) ([37; 38]), and impulse-based methods ([39]). The mass-spring system is a fast and interactive physical model with a solid mathematical foundation and well-understood dynamics. This model provides a more realistic force/deformation behavior in the case of large deformations, while maintaining the capability of real-time response. FEM provides higher accuracy, but it requires higher numerical computation, which is more appropriate for offline simulations. Therefore, this paper uses a deformation model based on nonlinear mass-spring elements distributed across a tetrahedral mesh: lumped masses are attached to the nodes and nonlinear springs represent the edges. The tracking of the mesh nodes positions is assured by solving a dynamic equation based on [PERSON]'s second law. The main interests of this deformation model are the dynamic predictions of the object's deformations and its realistic behavior, which results from the nonlinearity of the object. More details about this object deformation model can be found in previous works [40] and it will be used by the new proposed grasp synthesis algorithm. Several previous works have taken into account the deformation of soft objects while grasping them without integrating precise contact interaction models. [PERSON] et al. [41] presented a vision-based deformation controller for elastic planar objects without considering the grasp properties. This method takes into account just one contact point which cannot be used with a multifingered hand for grasping deformable objects. Similarly, [PERSON] et al. presented a model-free algorithm in [42] based on visual information for automatically selecting the contact points between the fingers and the object's contour in order to control its shape. However, contact forces and object stability were not considered. Grasping deformable planar objects using contact analysis was proposed in [43].