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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 complex nonprehensile manipulation task into several subtasks, that is more easy to deal with individually. Therefore, it is possible to define the so-called “manipulation primitives” like rolling (both holonomic and nonholonomic), throwing, bouncing, catching, sliding, and so on. The primary 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 RoDyMan project are resumed in here and 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. The found assumptions are overcome in here, where the interconnection and damping assignment passivity-based control, rooted within the port-Hamiltonian formalism, is found to be a valid method to generalize the nonprehensile planar rolling manipulation primitive, without explicitly solving the so-called matching equations. In truth, the approach here can be applied to systems that do not belong to the class of nonprehensile manipulation tasks, as here.

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.

A further task concerning nonholonomic rolling is the classical ball-and-plate benchmarking system. A method to reconfigure in a nonprehensile way the position and the orientation of a sphere rolling on a plate is proposed in here. The nonholonomic nature of the task is solved at a planning level. Then, an integral passivity-based control is designed to track the planned trajectory. The port-Hamiltonian formalism is employed to model the whole dynamics. A humanoid-like robot is used to bolster the proposed method experimentally.

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.

The friction-induced nonprehensile manipulation primitive is addressed here where, taking inspiration from the pizza-peel dexterous task, a plate which is intended to induce a rotating movement on a disk is studied. A dynamic model based on the Euler-Lagrange equations is first derived. Then, a controllability analysis of this model is carried out. Later, a closed-loop control strategy is proposed to induce the desired rotating speed in the disk, while maintaining the position of both the disk and the plate as close to zero as possible. A stability analysis is performed to show the boundedness of all the states, the oscillatory response of all of them, and the maximum amplitude of these oscillations.

Wheel slip may cause a significative worsening of control performance during the movement of a mobile robot, especially in those cases where the robot must push an object to the desired location. A method to avoid wheel slip is proposed here through a nonlinear model predictive control. The constraints included within the optimization problem limit the force exchanged between each wheel and the ground. The approach is validated in a dynamic simulation environment. The slippage may also occur between the robot and the object during pushing, preventing the correct achievement of the task. A linear time-varying model predictive control is designed here to include the unilateral constraint within the control action properly. The approach is verified in a dynamic simulation environment through a Pioneer 3-DX wheeled robot executing the pushing manipulation of a package.