A popular technique for getting to a goal location in unknown terrain is planning with the freespace assumption. The robot assumes that the terrain is clear unless it knows otherwise. It always plans a shortest path to the goal location and re-plans whenever it detects an obstacle that blocks its path or, more generally, when it detects that its current path is no longer optimal. It has been unknown whether this sensor-based planning approach is worst-case optimal, given the lack of initial knowledge about the terrain. We demonstrate that planning with the freespace assumption can make good performance guarantees on some restricted graph topologies (such as grids) but is not worst-case optimal in general. For situations in which its performance guarantee is insufficient, we also describe an algorithm, called Basic-VECA, that exhibits good average-case performance and provides performance guarantees that are optimal up to a constant (user-defined) factor.
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