A Coordinate-Free Framework for Robotic Pizza Tossing and Catching

This chapter presents a solution to the problem of autonomous pizza tossing and catching. Under the assumption that robotic fingers grasp the pizza dough with soft contact, the grasp constraints are formulated and used 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. Through these mathematical models, the two control problems of tossing and catching are formulated. For the tossing phase, an exponentially convergent controller that stabilizes a desired velocity of the dough as it leaves the fingers, is derived. On the other hand, to catch the dough, an optimal trajectory for the end-effector of the robotic manipulator is generated. Finally, the control laws to make the optimal trajectory exponentially attractive are derived. The developed theory is demonstrated with an elaborate simulation of the tossing and catching phases. This chapter is based on the works presented in [1].