Simplicial Dijkstra and A∗ Algorithms: From Graphs to Continuous Spaces

@article{Yershov2012SimplicialDA,
  title={Simplicial Dijkstra and A∗ Algorithms: From Graphs to Continuous Spaces},
  author={Dmitry S. Yershov and S. LaValle},
  journal={Advanced Robotics},
  year={2012},
  volume={26},
  pages={2065 - 2085}
}
  • Dmitry S. Yershov, S. LaValle
  • Published 2012
  • Mathematics, Computer Science
  • Advanced Robotics
  • Abstract This paper considers the optimal feedback planning problem of a point robot among polygonal obstacles in . In this problem, the Euclidean distance traveled by the robot is minimized. The approximate optimal feedback plan is computed using a piecewise linear approximation of the cost-to-go function. The approximate cost-to-go function, in turn, satisfies the discrete version of dynamic programming principle defined using a simplicial decomposition of the environment. Adaptations of… CONTINUE READING
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    References

    SHOWING 1-10 OF 30 REFERENCES
    Field D*: An Interpolation-Based Path Planner and Replanner
    • 212
    • PDF
    Efficient computation of Euclidean shortest paths in the plane
    • J. Hershberger, S. Suri
    • Mathematics, Computer Science
    • Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science
    • 1993
    • 73
    • PDF
    Exact robot navigation using artificial potential functions
    • 1,762
    • PDF
    Efficient algorithms for globally optimal trajectories
    • J. Tsitsiklis
    • Mathematics
    • Proceedings of 1994 33rd IEEE Conference on Decision and Control
    • 1994
    • 698
    • PDF
    New lower bound techniques for robot motion planning problems
    • J. Canny, J. Reif
    • Computer Science
    • 28th Annual Symposium on Foundations of Computer Science (sfcs 1987)
    • 1987
    • 571
    The Discrete Geodesic Problem
    • 643
    • PDF
    Improved fast replanning for robot navigation in unknown terrain
    • Sven Koenig, M. Likhachev
    • Engineering, Computer Science
    • Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292)
    • 2002
    • 311
    • PDF
    Theta*: Any-Angle Path Planning on Grids
    • 439
    • PDF
    Shortest paths among obstacles in the plane
    • 152
    Computing geodesic paths on manifolds.
    • R. Kimmel, J. Sethian
    • Computer Science, Medicine
    • Proceedings of the National Academy of Sciences of the United States of America
    • 1998
    • 1,004
    • PDF