|In this paper we present a study on the visibility-based pursuit–
evasion problem in which bounds on the speeds of the pursuer and
evader are given. In this setting, the pursuer tries to find the evader
inside a simply connected polygonal environment, and the evader in
turn tries to avoid detection. The focus of the paper is to develop a
characterization of the set of possible evader positions as a function
of time (the reachable sets). This characterization is more complex
than the unbounded-speed case, because it no longer depends only
on the combinatorial changes in the visibility region of the pursuer.
The characterization presented can be used as a filter to keep track of
the possible evader’s position as a pursuer moves in the environment,
or it can be used to guide the construction of the pursuer search strategy.
This search algorithm is at least as powerful as a complete algorithm
for the unbounded-speed case, and with the knowledge of speed
bounds, generates solutions for environments that were unsolvable
previously. Given that numerical methods are needed to compute the
reachable sets, we also present a conservative approximation which
can be computed with a closed formula.