• grasp analysis
• Humanoid Robots
• kineto-static
• loco-manipulation
• quasi-static
• Robotic Hands

In robotic grasping, it is usual the distinction between tip grasp and whole-hand grasp. In the first case, only fingertips interact with the grasped object, as it happens grasping e.g. a strawberry. In the second case, on the contrary, also internal phalanges are in contact with
the object, as it happens, for example, grabbing an hummer from the handle.
Similarly, it is usual for a humanoid robot to interact with the environment with the feet and the hands. But the interaction can also occur in the internal limbs, as the torso or the knees, as e.g. lifting up a large box. We refer to these cases as whole-body loco-manipulationtasks.
In both the cases, collectively referred to as whole-body robot interactions, multiple contacts, can greatly affects the robot capabilities. As a consequence, the presence of a high number of degrees of freedom is not sufficient to ensure the full controllability of the interaction forces and/or of the system displacements. This thesis presents novel thinking and approaches to the kineto-static analysis of whole-body robot interaction, general enough to treat compliant and/or underactuated robots.
In the first part, the developed approaches and tools are presented and explained analyzing the problem of grasping with synergistically underactuated robotic hands. The quasi-static model of the whole system is obtained considering the congruence and the equilibrium equations, both for the grasped object and the robotic hand. The constitutive equations of the contact are introduced via a penalty formulation, making the problem of the contact force computation statically determined.
Grouping together all the previous equations, the Fundamental Grasp Equation (FGE) is obtained. The FGE is investigated acting both on (i) its coefficient matrix, the Fundamental Grasp Matrix (FGM) and on (ii) the solution space of the system, i.e. the nullspace of the FGM. From the elaboration of the FGM, the canonical form of the Fundamental Grasp Equation (cFGE) is obtained, both in numeric and symbolic form. The cFGE provides some relevant information on the system as the subspace of the controllable internal forces, the subspace of the controllable object displacements, and the grasp compliance matrix. Moreover, some relevant manipulation tasks are defined in terms of nullity or non-nullity of the system variables (joint angles, joint torques, object displacements, etc...), as e.g. the pure squeeze of the object, in which the contact forces change without affecting the object configuration, and the kinematic grasp displacements in which the object is moved without influencing the contact forces. In order to discover the feasibility of such predefined tasks, a method for investigating the solution space of the FGE is presented, based on the computation of the reduced row echelon form (RREF) of suitable matrices.
Some of the previous methods have been used to support the design of two prototypes: the Velvet Finger and the Pisa/IIT SoftHand. The Velvet Finger is a smart gripper, equipped with conveyor belts on the surfaces of its phalanges. In this case, the decomposition of the solution space of the FGE was used to extract the necessary information for evaluating the manipulability capabilities of the prototype, showing the convenience of the actuation design with respect to other more conventional solutions. The Pisa/IIT SoftHand is a humanoid robotic hand in which the human inspired principle of the synergistic underactuation is implemented via the adaptive synergy mechanism. The construction of the cFGE for both the cases brings to find the conditions for which the two underactuation methods are equivalent
in terms of controllable forces and displacements. The first part of the thesis is completed by the definition of the reduced form of the Fundamental Grasp Equation (rFGE), obtained substituting all the congruence equations into the others. As a consequence, the rFGE can be seen as the first order approximation of a suitable system of nonlinear equations, called the Equilibrium Manifold (EM) of the system. The EM formulation was exploited to approach the problem of regulating the grasp compliance in the non trivial case of a robotic hand equipped with variable stiffness actuators (VSA) and synergistic underactuation. In the second part of the thesis, the previous concepts are usedto study compliant humanoid robots in whole-body loco-manipulation tasks. The introduction of the quasi-static form of the congruence, the equilibrium and the constitutive equations of the system allows to define the Fundamental Loco-Manipulation Equation (FLME). After the canonical form of the Fundamental Loco-Manipulation Equation (cFLME) is found, some relevant information can be extracted as
the subspace of the controllable contact forces and the controllable displacements of the center of mass of the robot. Relevant locomanipulation tasks are later defined in terms of (non-)nullity of the system variables. Moreover, the basis of the controllable contact forces
is used to show that the contact force distribution problem can be formulated in convex fashion.
Finally, a discussion of similarities and differences between grasping and loco-manipulation problems is performed, after which a unified formulation is given by the Fundamental Whole-Body Interaction Equations (FWE). The FWE shows that grasping and locomanipulation problems can share not just analysis methods, but also part of the analysis results, e.g. the symbolic expressions of the blocks composing the respective canonical forms of the Fundamental Equations, for equivalent actuation conditions.