Visibility-Based Pursuit-Evasion

This section addresses another motion strategy problem that deals with uncertainty in sensing. The model is:

• The robot is a point (the ``pursuer'') that moves in a 2D world that is bounded by a simple polygon (it is simply-connected).
• The world contains a point ``evader'' that can move arbitrarily fast.
• The task is to move the pursuer along a path that guarantees that the evader will eventually be seen using line-of-sight visibility in the 2D world.

The problem can be formulated as a search in an information space, in which each information state is of the form (q,S). The information state represents the position of the pursuer, q, and the set, S, of places where the evader could be hiding.

The key idea in developing a complete algorithm that will construct a solution if one exists is to partition the world into cells, such that inside of each cell there are no critical changes in information.

A finite graph search can be performed over these cells, cells might generally be visited multiple times. As the pursuer moves from cell to cell, the information state is maintained by maintaining binary labels on the gaps in visibility.

As the pursuer moves, gaps can generally split, merge, appear, or disappear, but within a cell, none of these changes occur. When a transition occurs from one cell to another, a simple transition rule specifies the new information state.

Examples

Even though there are slight variations in the environment from example to example, all of these can be solved, except for the last one.

Each example below is labeled T_i, in which i is the number pursuers needed to solve the problem.

This example requires the peak to be visited k-1 times for k pairs of ``feet''.