## 7 Experimental Validation of the Grasp Planning Pipeline for the Hand + Arm System  
The different steps of our complete grasp planning pipeline are validated with simulation and real experiments. First of all, the synthesis algorithm for the first initial grasp configuration proposed in Section 3 (i.e., Algorithm 1) is validated for three different shapes: a sphere, a cylinder, and a cube (Figure 10). This algorithm has been implemented in Matlab, by integrating a discrete 3D tetrahedral representation of the shape of these objects. The number of nodes of this 3D representation and the values of the two grasping quality metrics computed by the algorithm for the three objects are shown in Table 1. The initial grasping points obtained are shown in Figure 10 and they do not consider any deformation of the objects. These initial grasp configurations are used as input for the pregrasp and grasp execution steps of the grasp planning pipeline. For validating both steps, real experiments with the Adept arm and the [PERSON] hand grasping a foam cube (Figure 11) and a cylinder (Figure 12) are performed. Both objects represent typical shapes found in grasping applications of industrial products: a planar-faced surface (e.g., a cube) and a revolution surface (e.g., a cylinder). After the grasping, the object is lifted and carried to another position over the table in order to validate the stability of the grasp. The first step consists of generating and executing the path of the Adept arm for the pregrasp configuration in simulation, ensuring that the object is within the [PERSON] hand workspace (as explained for the cube in Figure 9a-c). The trajectory of the arm and the closing of the hand are then performed in the simulation (Figure 9d) until the fingers come into contact with the object. The second step is to model the interaction between the fingers and the object for closing the fingers against the object surface in order to get the required contact forces in simulation (as explained in Section 6). The real contact forces at each finger are obtained by strain gauges installed in the phalanxes of the [PERSON] hand. Thereby, the [PERSON] hand is iteratively closed until the contact forces obtained from the simulation of the contact model are attained (as shown in Figure 13). Thus, a stable final grasp of the deformable object is obtained and the object can be lifted without any danger of falling down. Figure 13 shows the variation in the norm of the three forces applied to the cube during the simulation of the contact model. At the initial step (\(t_{0}\)) of the simulation, the fingers move towards \begin{table}
\begin{tabular}{c c c c} \hline  & **Sphere** & **Cube** & **Cylinder** \\  & **(80 mm)** & **(80-80-80 mm)** & **(R35 mm\(\ast\)L140 mm)** \\ \hline Number of nodes & 182 & 162 & 226 \\ \hline Q1 & 0.0491 & 0.2302 & 0.1145 \\ \hline Q2 (mm) & 4.8659 & 13.334 & 11.6667 \\ \hline \end{tabular}
\end{table} 
Table 1: Evaluation of the initial grasping criteria for a sphere, a cube, and a cylinder. Figure 10: Configuration of the initial grasping points for a sphere, a cube, and a cylinder. the object in order to reach the initial contact points. When the fingers come into contact with the object (\(t_{1}\)), the contact model starts to evaluate the applied forces. This figure also shows that the contact forces are continuous and directly related to the amount of local deformation inside the contact area. The fingers continue to apply forces until equilibrium conditions are satisfied (i.e., reaching the three fingers' contact forces thresholds, identified by horizontal dashed lines in Figure 13). Once this state is reached and the three force thresholds are obtained, the fingers should keep these contact forces in order to ensure stable handling and then the simulation can stop. Figure 11: Pick-and-place of the cube by the Adept robot and the [PERSON] hand: (**a**) grasping, (**b**) lifting, and (**c**) leaving.