Bounded-curvature motion planning amid polygonal obstacles
We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths...
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ndltd-UBC-oai-circle.library.ubc.ca-2429-51532018-01-05T17:23:16Z Bounded-curvature motion planning amid polygonal obstacles Backer, Jonathan motion planning bounded-curvature curvature-constrained nonholonomic We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths that have explicit guarantees on when they will return a feasible path. We phrase our guarantees and run time analysis in terms of the complexity of the desired solution (see k and λ below). In a sense, our algorithms are output sensitive, which is particularly desirable because there are no known bounds on the solution complexity amid arbitrary polygonal environments. Our first major result is an algorithm that given Ε, αs, αt, and a positive integer k either (i) verifies that every feasible path has a descriptive complexity greater than k or (ii) outputs a feasible path. The run time of this algorithm is bounded by a polynomial in n (the total number of obstacle vertices in Ε), m (the bit precision of the input), and k. This result complements earlier work by Fortune and Wilfong: their algorithm considers paths of arbitrary descriptive complexity (it has no dependence on k), but it never outputs a path, just whether or not a feasible path exists. Our second major result is an algorithm that given E, αs, αt, a length λ, and an approximation factor Ε, either (i) verifies that every feasible path has length greater than λ or (ii) constructs a feasible path that is at most (1+ Ε) times longer than the shortest feasible path. The run time of this algorithm is bounded by a polynomial in n, m, Ε-1, and λ. This algorithm is the result of applying the techniques developed earlier in our thesis to the previous approximation approaches. A shortcoming of these prior approximation algorithms is that they only search a special class of feasible paths. This restriction implies that the path that they return may be arbitrarily longer than the shortest path. Our algorithm returns a true approximation because we search for arbitrary shortest paths. Science, Faculty of Computer Science, Department of Graduate 2009-02-26T21:46:12Z 2009-02-26T21:46:12Z 2009 2009-05 Text Thesis/Dissertation http://hdl.handle.net/2429/5153 eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ 1025471 bytes application/pdf University of British Columbia |
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motion planning bounded-curvature curvature-constrained nonholonomic |
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motion planning bounded-curvature curvature-constrained nonholonomic Backer, Jonathan Bounded-curvature motion planning amid polygonal obstacles |
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We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths that have explicit guarantees on when they will return a feasible path. We phrase our guarantees and run time analysis in terms of the complexity of the desired solution (see k and λ below). In a sense, our algorithms are output sensitive, which is particularly desirable because there are no known bounds on the solution complexity amid arbitrary polygonal environments.
Our first major result is an algorithm that given Ε, αs, αt, and a positive integer k either (i) verifies that every feasible path has a descriptive complexity greater than k or (ii) outputs a feasible path. The run time of this algorithm is bounded by a polynomial in n (the total number of obstacle vertices in Ε), m (the bit precision of the input), and k. This result complements earlier work by Fortune and Wilfong: their algorithm considers paths of arbitrary descriptive complexity (it has no dependence on k), but it never outputs a path, just whether or not a feasible path exists.
Our second major result is an algorithm that given E, αs, αt, a length λ, and an approximation factor Ε, either (i) verifies that every feasible path has length greater than λ or (ii) constructs a feasible path that is at most (1+ Ε) times longer than the shortest feasible path. The run time of this algorithm is bounded by a polynomial in n, m, Ε-1, and λ. This algorithm is the result of applying the techniques developed earlier in our thesis to the previous approximation approaches. A shortcoming of these prior approximation algorithms is that they only search a special class of feasible paths. This restriction implies that the path that they return may be arbitrarily longer than the shortest path. Our algorithm returns a true approximation because we search for arbitrary shortest paths. === Science, Faculty of === Computer Science, Department of === Graduate |
author |
Backer, Jonathan |
author_facet |
Backer, Jonathan |
author_sort |
Backer, Jonathan |
title |
Bounded-curvature motion planning amid polygonal obstacles |
title_short |
Bounded-curvature motion planning amid polygonal obstacles |
title_full |
Bounded-curvature motion planning amid polygonal obstacles |
title_fullStr |
Bounded-curvature motion planning amid polygonal obstacles |
title_full_unstemmed |
Bounded-curvature motion planning amid polygonal obstacles |
title_sort |
bounded-curvature motion planning amid polygonal obstacles |
publisher |
University of British Columbia |
publishDate |
2009 |
url |
http://hdl.handle.net/2429/5153 |
work_keys_str_mv |
AT backerjonathan boundedcurvaturemotionplanningamidpolygonalobstacles |
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