Title: Motion Planning for a Convex Polygon in a Polygonal Environment.

Abstract:
Let $O = \{O_1, ..., O_m\}$ be a set of pairwise disjoint convex polygons 
with a total of $n$ vertices. Let B be a robot with $k$ sides. In this talk
will present a randomized algorithm by Agarwal et. al [1] that computes the
boundary of the free space in expected time  $O(k^2n^2 \lambda_6(kn) \log(kn) \log (n)).

[1] P. K. Agarwal, B. Aronov, and M. Sharir. Motion planning for a convex polygon in a polygonal environment. Discrete Comput. Geom., 22:201--221, 1999.