Solving Pursuit-Evasion Problems on Height Maps

In this paper we present an approach for a pursuit-evasion problem that considers a 2.5d environment represented by a height map. Such a representation is particularly suitable for large-scale outdoor pursuit-evasion. By allowing height information we not only capture some aspects of 3d visibility but can also consider target heights. In our approach we construct a graph representation of the environment by sampling points and their detection sets which extend the usual notion of visibility. Once a graph is constructed we compute strategies on this graph using a modification of previous work on graphsearching. This strategy is converted into robot paths that are planned on the height map by classifying the terrain appropriately. In experiments we investigate the performance of our approach and provide examples including a map of a small village with surrounding hills and a sample map with multiple loops and elevation plateaus. Experiments are carried out with varying sensing ranges as well as target and sensor heights. To the best of our knowledge the presented approach is the first viable solution to 2.5d pursuit-evasion with height maps.