UBC Theses and Dissertations

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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.

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Attribution 4.0 International