### Abstract

Let P = {p_{1}, …, p_{n}} and Q = {q_{1}, …, q_{m}} be two simple polygons in the plane with non-intersecting interiors, the vertices of which are specified by their cartesian coordinates in order. The translation separability query asks whether there exists a direction in which P can be translated by an arbitrary distance without colliding with Q. It is shown that all directions that admit such a motion can be computed in O(n log m) time, where n > m, thus improving the previous complexity of O(nm) established for this problem. In designing this algorithm a polygon partitioning technique is introduced that may find application in other geometric problems. The algorithm presented in this paper solves a simplified version of the grasping problem in robotics. Given a description of a robot hand and a set of objects to be manipulated, the robot must determine which objects can be grasped. The solution given here assumes a two-dimensional world, a hand without an arm, and grasping under translation only.

Original language | English (US) |
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Pages (from-to) | 55-63 |

Number of pages | 9 |

Journal | Robotica |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1987 |

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### ASJC Scopus subject areas

- Software
- Control and Systems Engineering
- Mathematics(all)
- Computer Science Applications

### Cite this

*Robotica*,

*5*(1), 55-63. https://doi.org/10.1017/S0263574700009644