Geodesics in the configuration spaces of two points in R^{n}
D. M. Davis
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') ≥ ε. We interpret this as two or three (depending on the parity of n) geodesic motionplanning rules for this configuration space.
In the associated unordered configuration space, we need not prescribe that the points stay apart by ε. For this space, with a Euclideanrelated metric,
we show that geodesic motionplanning rules correspond to ordinary motionplanning rules on RP^{n1}.
Tbilisi Mathematical Journal, Vol. 14(1) (2021), pp. 149162
