1 research outputs found
Characterizing minimum-length coordinated motions for two discs
We study the problem of determining optimal coordinated motions for two disc
robots in an otherwise obstacle-free plane. Using the total path length traced
by the two disc centres as a measure of distance, we give an exact
characterization of a shortest collision-avoiding motion for all initial and
final configurations of the robots. The individual paths are composed of at
most six (straight or circular-arc) segments, and their total length can be
expressed as a simple integral with a closed form solution depending only on
the initial and final configuration of the robots. Furthermore, the paths can
be parametrized in such a way that (i) only one robot is moving at any given
time (decoupled motion), or (ii) the angle between the two robots' centres
changes monotonically.Comment: long-form of conference submission, 26 pages, 18 figure