The Lusternik-Schnirelmann category cat and topological complexity TC are
related homotopy invariants. The topological complexity TC has applications to
the robot motion planning problem. We calculate the Lusternik-Schnirelmann
category and topological complexity of the ordered configuration space of two
distinct points in the product GΓRn and apply the results to
the planar and spatial motion of two rigid bodies in R2 and
R3 respectively.Comment: 10 pages, 1 figure. Final version. To appear in Bulletin of the
Australian Mathematical Societ