UBC Theses and Dissertations
Characterizing minimum-length coordinated motions for two disks Liu, Paul
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 (but not necessarily unique) 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.
Item Citations and Data
Attribution 4.0 International