In this work, we demonstrate how autonomous pizza tossing and catching can be achieved. Under the assumption that the pizza dough is grasped by a number of fingers with soft contact, we formulate the grasp constraints and use them to derive the individual and combined Euler-Lagrange dynamic equations of motion of the robotic manipulator and the dough. In particular, the dynamics of the dough is a modified version of the rigid-body dynamics, taking into account the change of inertia due to its deformation. Armed with these mathematical models, we tackle the two control problems of tossing and catching. For the tossing phase, we derive an exponentially convergent controller that stabilizes a desired velocity of the dough as it is let go. On the other hand, so as to catch the dough, we generate an optimal trajectory for the end-effector of the robotic manipulator. Finally, we derive control laws to make the optimal trajectory exponentially attractive. We demonstrate the developed theory with an elaborate simulation of the tossing and catching phases.

A coordinate-free framework for robotic pizza tossing and catching / Satici, Aykut C.; Ruggiero, Fabio; Lippiello, Vincenzo; Siciliano, Bruno. - (2016), pp. 3932-3939. (Intervento presentato al convegno 2016 IEEE International Conference on Robotics and Automation, ICRA 2016 tenutosi a Stockholm Waterfront Congress Center, swe nel 2016) [10.1109/ICRA.2016.7487582].

### A coordinate-free framework for robotic pizza tossing and catching

#### Abstract

In this work, we demonstrate how autonomous pizza tossing and catching can be achieved. Under the assumption that the pizza dough is grasped by a number of fingers with soft contact, we formulate the grasp constraints and use them to derive the individual and combined Euler-Lagrange dynamic equations of motion of the robotic manipulator and the dough. In particular, the dynamics of the dough is a modified version of the rigid-body dynamics, taking into account the change of inertia due to its deformation. Armed with these mathematical models, we tackle the two control problems of tossing and catching. For the tossing phase, we derive an exponentially convergent controller that stabilizes a desired velocity of the dough as it is let go. On the other hand, so as to catch the dough, we generate an optimal trajectory for the end-effector of the robotic manipulator. Finally, we derive control laws to make the optimal trajectory exponentially attractive. We demonstrate the developed theory with an elaborate simulation of the tossing and catching phases.
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2016
9781467380263
9781467380263
A coordinate-free framework for robotic pizza tossing and catching / Satici, Aykut C.; Ruggiero, Fabio; Lippiello, Vincenzo; Siciliano, Bruno. - (2016), pp. 3932-3939. (Intervento presentato al convegno 2016 IEEE International Conference on Robotics and Automation, ICRA 2016 tenutosi a Stockholm Waterfront Congress Center, swe nel 2016) [10.1109/ICRA.2016.7487582].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11588/639463`
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