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Topologically Sweeping Visibility Complexes via Pseudotriangulations
, 1996
"... This paper describes a new algorithm for constructing the set of free bitangents of a collection of n disjoint convex obstacles of constant complexity. The algorithm runs in time O(n log n + k), where k is the output size, and uses O(n) space. While earlier algorithms achieve the same optimal run ..."
Abstract

Cited by 86 (9 self)
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This paper describes a new algorithm for constructing the set of free bitangents of a collection of n disjoint convex obstacles of constant complexity. The algorithm runs in time O(n log n + k), where k is the output size, and uses O(n) space. While earlier algorithms achieve the same optimal running time, this is the first optimal algorithm that uses only linear space. The visibility graph or the visibility complex can be computed in the same time and space. The only complicated data structure used by the algorithm is a splittable queue, which can be implemented easily using redblack trees. The algorithm is conceptually very simple, and should therefore be easy to implement and quite fast in practice. The algorithm relies on greedy pseudotriangulations, which are subgraphs of the visibility graph with many nice combinatorial properties. These properties, and thus the correctness of the algorithm, are partially derived from properties of a certain partial order on the faces of th...
A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots
 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 2005
"... We present an algorithm for complete path planning for translating polyhedral robots in 3D. Instead of exactly computing an explicit representation of the free space, we compute a roadmap that captures its connectivity. This representation encodes the complete connectivity of free space and allows u ..."
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Cited by 7 (4 self)
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We present an algorithm for complete path planning for translating polyhedral robots in 3D. Instead of exactly computing an explicit representation of the free space, we compute a roadmap that captures its connectivity. This representation encodes the complete connectivity of free space and allows us to perform exact path planning. We construct the roadmap by computing deterministic samples in free space that lie on an adaptive volumetric grid. Our algorithm is simple to implement and uses two tests: a complex cell test and a starshaped test. These tests can be efficiently performed on polyhedral objects using maxnorm distance computation and linear programming. The complexity of our algorithm varies as a function of the size of narrow passages in the configuration space. We demonstrate the performance of our algorithm on environments with very small narrow passages or no collisionfree paths.