Analysis of probabilistic roadmaps for path planning
Kavraki, L.E.; Kolountzakis, M.N.; Latombe, J.-C.
Robotics and Automation, IEEE Transactions on
Volume 14, Issue 1, Feb 1998 Page(s):166 - 171
Digital Object Identifier 10.1109/70.660866
Summary:We provide an analysis of a path planning method which uses
probabilistic roadmaps. This method has proven very successful in
practice, but the theoretical understanding of its performance is still
limited. Assuming that a path γ exists between two configurations
a and b of the robot, we study the dependence of the failure probability
to connect a and b, on: 1) the length of γ; 2) the distance
function of γ from the obstacles; 3) the number of nodes N of the
probabilistic roadmap constructed. Importantly, our results do not
depend strongly on local irregularities of the configuration space, as
was the case with previous analysis. These results are illustrated with
a simple but illuminating example. In this example, we provide estimates
for N, the principal parameter of the method, in order to achieve
failure probability within prescribed bounds. We also compare, through
this example, the different approaches to the analysis of the planning
method
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