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## Evaluation of the usefulness of exact methods to motion planning in configuration space

### Przemysław Dobrowolski

#### Abstract

This thesis considers the problem of planning a 3-dimensional rigid body motion with rotations. The task is associated with many practical usages: motion planning on assembly lines, device assembly checks and design of virtual prototypes. There exist two main classes of motion planning algorithms: exact and approximate. Both classes of algorithms can be characterized by different performance, quality of result and resource utilization. A survey of these algorithms leads to the conclusion that if an algorithm involves 3-dimensional rotations, there is always some kind of simplification in order to avoid motion planning in the space of rotations. The most common simplification is a discretization (splitting into small parts) of the space of rotations and considering only a translational motion in each fragment of space of rotations. To date, there is only a small number of research concerning motion in the 3-dimensional space of rotations. In this work, the author presents a study leading to the complete description of the configuration space of rotational movement in three dimensions and proposes three different algorithms for motion planning. The author presents his results and compares them with existing similar solutions. A few practical usages are also described. Among others, there is a possibility to use presented algorithms as procedures in a more general motion planning algorithm.
Record ID
WUT3b6ca7941f3749a39211250659060bb4
Diploma type
Doctor of Philosophy
Author
Przemysław Dobrowolski Przemysław Dobrowolski,, Faculty of Mathematics and Information Science (FMIS)
Title in Polish
Ocena przydatności metod dokładnych do szukania drogi w przestrzeni konfiguracji
Title in English
Evaluation of the usefulness of exact methods to motion planning in configuration space
Language
(en) English
Certifying Unit
Faculty of Electronics and Information Technology (FEIT)
Discipline
information science / (technology domain) / (technological sciences)
Status
Finished
Start date
26-03-2013
Defense Date
21-01-2014
Title date
28-01-2014
Supervisor
Krzysztof Marciniak Krzysztof Marciniak,, Department of Applied Computer Science and Computation Methods (FMIS/DACSCM)Faculty of Mathematics and Information Science (FMIS)
Internal reviewers
External reviewers
Ignacy Dulęba Ignacy Dulęba,, External affiliation of publication: Wroclaw University of Science and Technology
Pages
179
Keywords in English
motion planning, 3-dimensional rotations, configuration space, exact algorithm
Abstract in English
This thesis considers the problem of planning a 3-dimensional rigid body motion with rotations. The task is associated with many practical usages: motion planning on assembly lines, device assembly checks and design of virtual prototypes. There exist two main classes of motion planning algorithms: exact and approximate. Both classes of algorithms can be characterized by different performance, quality of result and resource utilization. A survey of these algorithms leads to the conclusion that if an algorithm involves 3-dimensional rotations, there is always some kind of simplification in order to avoid motion planning in the space of rotations. The most common simplification is a discretization (splitting into small parts) of the space of rotations and considering only a translational motion in each fragment of space of rotations. To date, there is only a small number of research concerning motion in the 3-dimensional space of rotations. In this work, the author presents a study leading to the complete description of the configuration space of rotational movement in three dimensions and proposes three different algorithms for motion planning. The author presents his results and compares them with existing similar solutions. A few practical usages are also described. Among others, there is a possibility to use presented algorithms as procedures in a more general motion planning algorithm.
Thesis file
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Uniform Resource Identifier
https://repo.pw.edu.pl/info/phd/WUT3b6ca7941f3749a39211250659060bb4/
URN
urn:pw-repo:WUT3b6ca7941f3749a39211250659060bb4

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