Covering hostile terrains with partial and complete visibilities: On minimum distance paths

We present a method for finding paths for multiple Unmanned Air Vehicles (UAVs) such that the sum over their lengths is minimum as they cover a 3D terrain (represented as height fields). The paths are constrained to lie beneath an exposure surface to ensure stealth from enemy outposts. The exposure surface is also computed as a height field. The algorithm greedily clusters the terrain such that gain in visibility per distance would be higher for intra-cluster points than points across clusters. Paths generated on clusters formed by such a per distance visibility metric are reduced by more than 25% over other related decoupled methods. The method is extended to cover terrains with partial visibilities. The advantage of the coupled metric extends under constrained visibility also. We again show performance gain by comparing with an existing decoupled algorithm that solves a similar problem of minimum distance terrain coverage with constrained visibility. The paper reveals that decomposing the terrain based on visibility first and then distance is always better than the other way round to cover the terrain in shorter distances.