## 8 Conclusions  
This work has been devoted to the complete process of deformable object grasp planning with an industrial manipulator (robotic hand + robotic arm). First of all, this requires the definition of the grasp points over the surface of the object and thus, the determination of an initial grasp configuration. Later, we presented our approach for determining the pregrasp strategy for reaching this initial grasp by taking into account the kinematic constraints of the arm and the hand. Thereby, the grasp planning has been divided into two phases: firstly, determining the configuration of the robot arm to bring the hand close to the object; secondly, determining the appropriate configuration of the fingers of the hand to grasp the object. The determination of the joint parameters of the arm and the hand is ensured by the resolution of their inverse kinematics. In the case of the hand, the implemented strategy consists first of putting the TCP (line perpendicular to the palm of the hand) at an intersection with the center of the grasp triangle (obtained in the initial grasp synthesis) and aligning it with the normal vector of this grasp triangle. The second step is to iteratively search for a solution to the articular parameters of the three fingers of the [PERSON] hand in order to bring them into correspondence with the grasping points previously defined by force-closure-type stability conditions. Thereby, this final grasp solution combines the initial grasp based on a general geometric criteria for force closure (i.e., it only considers the shape of the object) with the kinematic constraints of the robotic hand by applying the proposed pregrasp strategy. Nevertheless, this grasp configuration does guarantee the robustness of the grasp only for rigid objects but not for deformable objects. Thus, a force-deformation serving scheme is  
Figure 13: Grasping forces applied by the three fingers of the [PERSON] hand (F1, F2 and F3) in simulation. activated when the fingers come into contact with the deformable object to be grasped. This scheme is based on a simulation of the object-fingers interaction (previously developed by the authors in [33]), which obtains the contact force thresholds that should be applied by the fingers in order to guarantee a stable grasp while deforming the surface of the object. Finally, an iterative closing of the real fingers is performed in order to attain these contact forces with the real object. Objects with simple geometrical shapes (sphere, cube, and cylinder) were chosen for the experiments to more efficiently simulate the interaction model described in Section 6. The proposed pregrasp/grasp pipeline is not restricted to simple shapes and can be applied to any shape of object. In fact, the mesh construction process required by the interaction model has been applied by the authors to very irregular shapes of meat pieces in a previous work [10]. This grasp planning pipeline is designed for nonlinear deformable objects to be manipulated by three-fingered robotic hands, but its architecture could be redesigned as a group of interchangeable modules in future works. These modules could include the following: other types of objects (e.g., changing the contact interaction model for rigid objects, granular media [53]), new sensing data (i.e., combining tactile and vision information for estimating the 3D shape of the object and the real contact forces in real-time [54]), multiple robotic fingers (e.g., dexterous robotic hands [55]), or even more complex manipulation tasks (e.g., in-hand manipulation [56]). Conceptualization, Methodology: all authors; Software: L.Z., J.A.C.R., L.S. and B.C.B. ; Validation: L.Z. and L.S. ; Writing--original draft: [PERSON]; Writing--review & editing: [PERSON] and J.A.C.R. All authors have read and agreed to the published version of the manuscript. This work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement no 869855 (Project 'SoftManBot'). L.Z.