38,987 research outputs found
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
RMPD - A Recursive Mid-Point Displacement Algorithm for Path Planning
Motivated by what is required for real-time path planning, the paper starts
out by presenting sRMPD, a new recursive "local" planner founded on the key
notion that, unless made necessary by an obstacle, there must be no deviation
from the shortest path between any two points, which would normally be a
straight line path in the configuration space. Subsequently, we increase the
power of sRMPD by using it as a "connect" subroutine call in a higher-level
sampling-based algorithm mRMPD that is inspired by multi-RRT. As a consequence,
mRMPD spawns a larger number of space exploring trees in regions of the
configuration space that are characterized by a higher density of obstacles.
The overall effect is a hybrid tree growing strategy with a trade-off between
random exploration as made possible by multi-RRT based logic and immediate
exploitation of opportunities to connect two states as made possible by sRMPD.
The mRMPD planner can be biased with regard to this trade-off for solving
different kinds of planning problems efficiently. Based on the test cases we
have run, our experiments show that mRMPD can reduce planning time by up to 80%
compared to basic RRT
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