  The importance of area coverage with unmanned vehicles, in other words,
traveling an area with an unmanned vehicle such as a robot or a UAV completely
or partially with minimum cost, is increasing with the increase in usage of
such vehicles today. Area coverage with unmanned vehicles is used today in the
exploration of an area with UAVs, sweeping mines with robots, cleaning ground
with robots in large shopping malls, mowing lawn in a large area etc. The
problem has versions such as area coverage with a single unmanned vehicle, area
coverage with multiple unmanned vehicles, on-line area coverage (The map of the
area that will be covered is not known before starting the coverage) with
unmanned vehicles etc. In addition, the area may have obstacles that the
vehicles cannot move over. Naturally, many researches are working on the
problem and a lot of researches have been done on the problem until today.
Spanning tree coverage is one of the major approaches to the problem. In this
approach, at the basic level, the planar area is divided into identical squares
according to the range of sight of the vehicle, and centers of these squares
are assumed to be vertexes of a graph. The vertexes of this graph are connected
with the edges with unit costs and after finding the minimum spanning tree of
the graph, the vehicle strolls around the spanning tree. The method we propose
suggests a way to cover a non-planar area with unmanned vehicles. The method we
propose also takes advantage of the spanning-tree coverage approach, but
instead of assigning unit costs to the edges, we assigned a weight to each edge
using slopes between vertexes those the edges connect. We have gotten
noticeably better results than the results we got when we did not consider the
slope between two squares and used the classical spanning tree approach.
