  We determine explicit formulas for geodesics (in the Euclidean metric) in the
configuration space of ordered pairs (x,x') of points in R^n which satisfy
d(x,x')>=epsilon. We interpret this as two or three (depending on the parity of
n) geodesic motion-planning rules for this configuration space. In the
associated unordered configuration space, we need not prescribe that the points
stay apart by epsilon. For this space, with a Euclidean metric, we show that
geodesic motion-planning rules correspond to ordinary motion-planning rules on
RP^{n-1}.
