Models and motion planning.

We study the consequences of two of the realistic input models proposed in the literature, namely unclutteredness and small simple-cover complexity, for the motion planning problem. We show that the complexity of the free space of a bounded-reach robot with f degrees of freedom is O(nf/2) in the plane, and O(n2f/3) in three dimensions, for both uncluttered environments and environments of small simple-cover complexity. We also give an example showing that these bounds are tight in the worst case. Our bounds fit nicely between the θ(nf) bound for the maximum free-space complexity in the general case, and the θ(n) bound for low-density environments. [ABSTRACT FROM AUTHOR]