Shadows in the singular metric
Four examples of shadows (dashed region) of a segment obstacle (green): the
shadows are defined as the sets of positions (x,y) in the plane
reachable from the configuration (0,0,0) of the car by a shortest path
colliding the segment.
(The white curves define the partition of the plane according to the shape of
the shortest paths reaching a position (x,y); see P. Souères, J.Y
Fourquet and J.P. Laumond, "Set of reachable positions for
a car", IEEE Trans. on Automatic Control, 39 (8), 1994.)
See :
M. Vendittelli and J.P. Laumond, "Visible positions for a car-like robot
amidst obstacles", 2nd Workshop on Algorithmic Foundations of Robotics,
WAFR'96, Toulouse, July 1996.
...and what happens if the car should move only
forward ?...
