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An object is manipulated in a nonprehensile way when it is not caged between the fingertips or the hand's palm. Moreover, the so-called "force closure" constraint does not hold at each time of the manipulation task. This means that the motion can also be performed thanks to unilateral constraints: the part can thus roll, slide and break the contact with the robot manipulating it. Examples of everyday nonprehensile manipulation tasks are pushing objects, folding clothes, carrying a glass on a tray, cooking in a pan and so on. Nonprehensile manipulation can also be referred to as dynamic when the dynamics of both the object and the robot are essential to accomplishing the desired task. A standard approach within the robotics community is to split a compound nonprehensile manipulation task into several subtasks, which are more easy to deal with individually. Therefore, it is possible to define the so-called ``motion primitives'' like rolling (both holonomic and nonholonomic), throwing, bouncing, catching, sliding and so on. The main goal regarding Fabio Ruggiero's research is to design a common practical/theoretical framework where each motion primitive can be equipped with a proper motion planner and controller. A survey about nonprehensile manipulation is written by Fabio Ruggiero here, while the results of the here project are resumed here.

A holonomic rolling motion between two convex surfaces at contact is considered here and here. There are no constraints between the two surfaces but only the rolling one. In particular, the stabilization in full gravity of the precarious position of a disk free to roll on an actuated disk is addressed. The same set-up is considered here where passivity theory has been employed, and here and here in presence of the so-called ``matched disturbances'' within the control action. The found solution exploits the port-Hamiltonian approach. By generalizing the method, here, under certain assumptions about the shapes of the rolling surfaces, a proper change of coordinates allows to study the general case of nonprehensile planar rolling through classic nonlinear control techniques, where the design of the controller is much simplified. A nonprehensile manipulation task in case of nonholonomic rolling can be considered the motion control of the `ballbot'', that is a spherical robot with a cylindrical top. A geometric control approach without coordinates is proposed here.

Another task in which nonholonomic rolling is involved is the hula-hoop system. This system consists of a pole in contact with a hoop: the pole is intended to be moved for inducing, through contact, a spinning movement of the hoop. A high-gain observer and a controller are designed in here to avoid both velocity measurements and the complete dependence on the mathematical model. A formal mathematical analysis, which guarantees ultimate boundedness of all coordinates, is presented here.

The bouncing motion primitive is examined here and here, where the table tennis case study is considered. A motion planner for the paddle, also considering its orientation, is introduced in the cited manuscript. The whole aerodynamics of the flying ball is taken into account without neglecting the real-time execution of the implemented algorithm. The assumption of having a constant predefined impact time is relaxed here, while different metrics are compared to define the optimal impact time. Numerical tests are implemented to evaluate the algorithm. The throw of a deformable object is instead addressed here. The example of a pizza-maker who acrobatically throws the pizza in the air to stretch the dough is considered. The model and the control are designed by using a geometric approach without making use of coordinates.