Space-Aware Reconfiguration

Dan Halperin, Marc van Kreveld, Golan Miglioli-Levy*, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the problem of reconfiguring a set of physical objects into a desired target configuration, a typical (sub)task in robotics and automation, arising in product assembly, packaging, stocking store shelves, and more. In this paper we address a variant, which we call space-aware reconfiguration, where the goal is to minimize the physical space needed for the reconfiguration, while obeying constraints on the allowable collision-free motions of the objects. Since for given start and target configurations, reconfiguration may be impossible, we translate the entire target configuration rigidly into a location that admits a valid sequence of moves, where each object moves in turn just once, along a straight line, from its starting to its target location, so that the overall physical space required by the start, all intermediate, and target configurations for all the objects is minimized. We investigate two variants of space-aware reconfiguration for the often examined setting of nunit discs in the plane, depending on whether the discs are distinguishable (labeled) or indistinguishable (unlabeled). For the labeled case, we propose a representation of size O(n4) of the space of all feasible initial rigid translations, and use it to find, in O(n6) time, a shortest valid translation, or one that minimizes the enclosing disc or axis-aligned rectangle of both the start and target configurations. For the significantly harder unlabeled case, we show that for almost every direction, there exists a translation in this direction that makes the problem feasible. We use this to devise heuristic solutions, where we optimize the translation under stricter notions of feasibility. We present an implementation of such a heuristic, which solves unlabeled instances with hundreds of discs in seconds.

Original languageEnglish
Pages (from-to)1157-1194
Number of pages38
JournalDiscrete and Computational Geometry
Issue number4
StatePublished - Jun 2023


FundersFunder number
Blavatnik Computer Science Research Fund
Yandex Machine Learning Initiative for Machine Learning
National Science Foundation
German-Israeli Foundation for Scientific Research and Development
Nederlandse Organisatie voor Wetenschappelijk OnderzoekG-1367-407.6/2016, 612.001.651, 260/18
Israel Science Foundation825/15, 1736/19
Tel Aviv University
Ministry of Science and Technology, Israel103129


    • Disc reconfiguration
    • Motion planning
    • Smallest enclosing disc


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