Robot motion planning and the single cell problem in arrangements

@article{Halperin1994RobotMP,
  title={Robot motion planning and the single cell problem in arrangements},
  author={Dan Halperin},
  journal={Journal of Intelligent and Robotic Systems},
  year={1994},
  volume={11},
  pages={45-65}
}
  • D. Halperin
  • Published 1 March 1994
  • Mathematics
  • Journal of Intelligent and Robotic Systems
Robot motion planning has become a central topic in robotics and has been studied using a variety of techniques. One approach, followed mainly in computational geometry, aims to develop combinatorial, nonheuristic solutions to motion-planning problems. This direction is strongly related to the study of arrangements of algebraic curves and surfaces in low-dimensional Euclidean space. More specifically, the motion-planning problem can be reduced to the problem of efficiently constructing a single… 
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3 Citations
Background Citations
2
Methods Citations
1

3 Citations

A Review on Robot Motion Planning Approaches
TLDR
In this paper, about 100 research are reviewed and briefly described to identify and classify the amount of the existing work for each motion planning approach and the percentage of the application of each approach.
Robust Geometric Computing in Motion
TLDR
A discussion of the gap between the theory and practice of geometric algorithms, together with a brief review of existing solutions to some of the problems that this dichotomy brings about, and an overview of the CGAL project and library.
Efficient and small representation of line arrangements with applications
TLDR
This paper gives theoretical and empirical bounds to demonstrate the tradeoffs between the size of the new arrangement and the error from lossiness, and demonstrates that speedups by factors of several hundred are possible while introducing small errors.

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