This paper considers the problem of planning collision-free motion of three disks in the plane. One of the three disks, the robot, can autonomously translate in the plane, the other two move only when in contact with the robot. This represents the abstract formulation of a manipulation planning problem. Despite the simplicity of the formulation, the decidability of the problem had remained unproven so far. We prove that the problem is decidable, i.e., there exists an exact algorithm that decides wether a solution exists in nite time.
Decidability of robot manipulation planning: three disks in the plane / Vendittelli, Marilena; J. P., Laumond; B., Mishra. - STAMPA. - 107:(2015), pp. 641-657. (Intervento presentato al convegno Workshop on the Algorithmic Foundations of Robotics tenutosi a Boğaziçi University in Istanbul, Turkey nel August 3-5, 2014) [10.1007/978-3-319-16595-0].
Decidability of robot manipulation planning: three disks in the plane
VENDITTELLI, Marilena;
2015
Abstract
This paper considers the problem of planning collision-free motion of three disks in the plane. One of the three disks, the robot, can autonomously translate in the plane, the other two move only when in contact with the robot. This represents the abstract formulation of a manipulation planning problem. Despite the simplicity of the formulation, the decidability of the problem had remained unproven so far. We prove that the problem is decidable, i.e., there exists an exact algorithm that decides wether a solution exists in nite time.| File | Dimensione | Formato | |
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