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

Robotic manipulation and sensing of deformable objects in domestic and industrial applications: a survey

“…For instance, a robot able to manipulate soft tissue in real time could assist a surgeon in a medical procedure, or help out in a domestic setting by handling food items to prepare a meal. As an example, one recent attempt of dynamic food manipulation was described by Satici et al (2016), who proposed a theoretical framework to dynamically manipulate a pizza dough, specifically to toss and catch the dough with a humanoid robot. However, their results are yet to be validated on a real platform.…”

Nonprehensile Manipulation of Deformable Objects: Achievements and Perspectives from the Robotic Dynamic Manipulation Project

“…On the other hand, the robotics literature is not fully developed for nonprehensile manipulation tasks. The classic way to cope with them is to split a task in simpler subtasks, referred to as nonprehensile manipulation primitives [3], such as throwing [4], dynamic catching [5], batting [6], juggling [7], dribbling [8], pushing [9], sliding [10], rolling [11] and so on. Each primitive, equipped with its own motion planner and controller, is then turned on and off during a complex manipulation task by a high-level supervisor [12].…”

“…In the following, the results achieved so far within the RODYMAN project for the above three outlined research challenges are described. Videos of the related experiments can be found in the related YouTube channel 4 .…”

“…The combined model of the dough grasped with robotic fingers through unilateral constraints, and the kinematics and dynamics of the robot manipulator has been derived in [4]. Upon that, a control law achieving the desired tossing motion can be designed.…”

“…Only the case where the final position is left free and is part of the minimization problem is considered. More details can be found in [4].…”