Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper and Lower Bounds for End-to-End Risks in Stochastic Robot
  Navigation   We present novel upper and lower bounds to estimate the collision probability
of motion plans for autonomous agents with discrete-time linear Gaussian
dynamics. Motion plans generated by planning algorithms cannot be perfectly
executed by autonomous agents in reality due to the inherent uncertainties in
the real world. Estimating collision probability is crucial to characterize the
safety of trajectories and plan risk optimal trajectories. Our approach is an
application of standard results in probability theory including the
inequalities of Hunter, Kounias, Frechet, and Dawson. Using a ground robot
navigation example, we numerically demonstrate that our method is considerably
faster than the naive Monte Carlo sampling method and the proposed bounds are
significantly less conservative than Boole's bound commonly used in the
literature.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg