63,943 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
Probabilistic Plan Synthesis for Coupled Multi-Agent Systems
This paper presents a fully automated procedure for controller synthesis for
multi-agent systems under the presence of uncertainties. We model the motion of
each of the agents in the environment as a Markov Decision Process (MDP)
and we assign to each agent one individual high-level formula given in
Probabilistic Computational Tree Logic (PCTL). Each agent may need to
collaborate with other agents in order to achieve a task. The collaboration is
imposed by sharing actions between the agents. We aim to design local control
policies such that each agent satisfies its individual PCTL formula. The
proposed algorithm builds on clustering the agents, MDP products construction
and controller policies design. We show that our approach has better
computational complexity than the centralized case, which traditionally suffers
from very high computational demands.Comment: IFAC WC 2017, Toulouse, Franc
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