Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collision Probabilities for Continuous-Time Systems Without Sampling
  [with Appendices]   Demand for high-performance, robust, and safe autonomous systems has grown
substantially in recent years. Fulfillment of these objectives requires
accurate and efficient risk estimation that can be embedded in core
decision-making tasks such as motion planning. On one hand, Monte-Carlo (MC)
and other sampling-based techniques can provide accurate solutions for a wide
variety of motion models but are cumbersome to apply in the context of
continuous optimization. On the other hand, "direct" approximations aim to
compute (or upper-bound) the failure probability as a smooth function of the
decision variables, and thus are widely applicable. However, existing
approaches fundamentally assume discrete-time dynamics and can perform
unpredictably when applied to continuous-time systems operating in the real
world, often manifesting as severe conservatism. State-of-the-art attempts to
address this within a conventional discrete-time framework require additional
Gaussianity approximations that ultimately produce inconsistency of their own.
In this paper we take a fundamentally different approach, deriving a risk
approximation framework directly in continuous time and producing a lightweight
estimate that actually improves as the discretization is refined. Our
approximation is shown to significantly outperform state-of-the-art techniques
in replicating the MC estimate while maintaining the functional and
computational benefits of a direct method. This enables robust, risk-aware,
continuous motion-planning for a broad class of nonlinear, partially-observable
systems.

26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga