A Sample-based Convex Cover for Rapidly Finding an Object in a 3-D Environment

In this paper we address the problem of generating a motion strategy to find an object in a known 3-D environment as quickly as possible on average. We use a sampling scheme that generates an initial set of sensing locations for the robot and then we propose a convex cover algorithm based on this sampling. Our algorithm tries to reduce the cardinality of the resulting set and has the main advantage of scaling well with the dimensionality of the environment. We then use the resulting convex covering to generate a graph that captures the connectivity of the workspace. Finally, we search this graph to generate trajectories that try to minimize the expected value of the time to find the object.