## Abstract

We present an algorithm for constructing an inner approximation of the free space for a polyhedral robot with four degrees of freedom. The robot rotates about a fixed axis and translates in three dimensions with respect to a fixed polyhedral obstacle. We approximate the free space by subdividing the rotation dimension into short angle ranges, generating a three dimensional free space for each angle range, and constructing a graph for navigation in the four dimensional space. We also present an algorithm for path planning that is complete in the approximated space. The path planning algorithm produces paths that are guaranteed to be collision free and approximately maximizes obstacle clearance, ensuring safe and practical paths.

Original language | English (US) |
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Pages | 223-229 |

Number of pages | 7 |

State | Published - 2018 |

Event | 30th Canadian Conference on Computational Geometry, CCCG 2018 - Winnipeg, Canada Duration: Aug 8 2018 → Aug 10 2018 |

### Conference

Conference | 30th Canadian Conference on Computational Geometry, CCCG 2018 |
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Country/Territory | Canada |

City | Winnipeg |

Period | 8/8/18 → 8/10/18 |

## ASJC Scopus subject areas

- Geometry and Topology
- Computational Mathematics