222,874 research outputs found
Sampling-based Algorithms for Optimal Motion Planning
During the last decade, sampling-based path planning algorithms, such as
Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have
been shown to work well in practice and possess theoretical guarantees such as
probabilistic completeness. However, little effort has been devoted to the
formal analysis of the quality of the solution returned by such algorithms,
e.g., as a function of the number of samples. The purpose of this paper is to
fill this gap, by rigorously analyzing the asymptotic behavior of the cost of
the solution returned by stochastic sampling-based algorithms as the number of
samples increases. A number of negative results are provided, characterizing
existing algorithms, e.g., showing that, under mild technical conditions, the
cost of the solution returned by broadly used sampling-based algorithms
converges almost surely to a non-optimal value. The main contribution of the
paper is the introduction of new algorithms, namely, PRM* and RRT*, which are
provably asymptotically optimal, i.e., such that the cost of the returned
solution converges almost surely to the optimum. Moreover, it is shown that the
computational complexity of the new algorithms is within a constant factor of
that of their probabilistically complete (but not asymptotically optimal)
counterparts. The analysis in this paper hinges on novel connections between
stochastic sampling-based path planning algorithms and the theory of random
geometric graphs.Comment: 76 pages, 26 figures, to appear in International Journal of Robotics
Researc
Incremental Sampling-based Algorithms for Optimal Motion Planning
During the last decade, incremental sampling-based motion planning
algorithms, such as the Rapidly-exploring Random Trees (RRTs) have been shown
to work well in practice and to possess theoretical guarantees such as
probabilistic completeness. However, no theoretical bounds on the quality of
the solution obtained by these algorithms have been established so far. The
first contribution of this paper is a negative result: it is proven that, under
mild technical conditions, the cost of the best path in the RRT converges
almost surely to a non-optimal value. Second, a new algorithm is considered,
called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost
of the best path in the RRG converges to the optimum almost surely. Third, a
tree version of RRG is introduced, called the RRT algorithm, which
preserves the asymptotic optimality of RRG while maintaining a tree structure
like RRT. The analysis of the new algorithms hinges on novel connections
between sampling-based motion planning algorithms and the theory of random
geometric graphs. In terms of computational complexity, it is shown that the
number of simple operations required by both the RRG and RRT algorithms is
asymptotically within a constant factor of that required by RRT.Comment: 20 pages, 10 figures, this manuscript is submitted to the
International Journal of Robotics Research, a short version is to appear at
the 2010 Robotics: Science and Systems Conference
Technical Report: A Receding Horizon Algorithm for Informative Path Planning with Temporal Logic Constraints
This technical report is an extended version of the paper 'A Receding Horizon
Algorithm for Informative Path Planning with Temporal Logic Constraints'
accepted to the 2013 IEEE International Conference on Robotics and Automation
(ICRA). This paper considers the problem of finding the most informative path
for a sensing robot under temporal logic constraints, a richer set of
constraints than have previously been considered in information gathering. An
algorithm for informative path planning is presented that leverages tools from
information theory and formal control synthesis, and is proven to give a path
that satisfies the given temporal logic constraints. The algorithm uses a
receding horizon approach in order to provide a reactive, on-line solution
while mitigating computational complexity. Statistics compiled from multiple
simulation studies indicate that this algorithm performs better than a baseline
exhaustive search approach.Comment: Extended version of paper accepted to 2013 IEEE International
Conference on Robotics and Automation (ICRA
The Provable Virtue of Laziness in Motion Planning
The Lazy Shortest Path (LazySP) class consists of motion-planning algorithms
that only evaluate edges along shortest paths between the source and target.
These algorithms were designed to minimize the number of edge evaluations in
settings where edge evaluation dominates the running time of the algorithm; but
how close to optimal are LazySP algorithms in terms of this objective? Our main
result is an analytical upper bound, in a probabilistic model, on the number of
edge evaluations required by LazySP algorithms; a matching lower bound shows
that these algorithms are asymptotically optimal in the worst case
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