An optimal solution to the linear search problem for a robot with dynamics

In this paper we derive the control policy that minimizes the total expected time for a point mass with bounded acceleration, starting from the origin at rest, to find and return to an unknown target that is distributed uniformly on the unit interval. We apply our result to proof-of-concept hardware experiments with a planar robot arm searching for a metal object using an inductive proximity sensor. In particular, we show that our approach easily extends to optimal search along arbitrary curves, such as raster-scan patterns that might be useful in other applications like robot search-and-rescue.