Space-Aware Reconfiguration

We consider the problem of reconfiguring a set physical objects into desired target configuration, typical (sub)task in robotics and automation, arising product assembly, packaging, stocking store shelves, more. In this paper we address variant, which call space-aware reconfiguration, where goal is to minimize space needed for while obeying constraints on allowable collision-free motions objects. Since given start configurations, reconfiguration may be impossible, translate entire configuration rigidly location that admits valid sequence moves, each object moves turn just once, along straight line, from its starting location, so overall required by start, all intermediate, configurations minimized. investigate two variants often examined setting $n$ unit discs plane, depending whether are distinguishable (labeled) or indistinguishable (unlabeled). For labeled case, propose representation size $O(n^4)$ feasible initial rigid translations, use it find, $O(n^6)$ time, shortest translation, one minimizes enclosing disc axis-aligned rectangle both configurations. significantly harder unlabeled show almost every direction, there exists translation direction makes feasible. devise heuristic solutions, optimize under stricter notions feasibility. present an implementation such heuristic, solves instances with hundreds seconds.