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...mmunity in the context of finding an optimal assignment of workers to goals [7] . This has recently been applied to multi-robot task allocation [3] and trajectory planning [6, 10, 18, 9]. As shown in =-=[18, 24]-=-, coupling goal assignment with trajectory planning paradoxically reduces the complexity. This paper, following the authors’ previous work [19], considers the problem of simultaneously planning trajec...

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... variant 2 of the multi-robot motion planning problem. In this problem, pebbles need to be moved from one set of vertices of a graph to another, while following a certain set of rules—see for example =-=[5, 6, 13, 14, 16, 30]-=-. Our contribution. Surprisingly, the unlabeled version of the multi-robot motion-planning problem has hardly received any attention in the computational-geometry literature. Indeed, we don’t know of ...

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...hable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was shown that distance optimal paths can be computed to complete with a tight convergence time guarantee =-=[30]-=-, using a fully centralized algorithm. In this study, we establish the existence of a more fundamental ordering of the vertices on the underlying graph network, induced by a fixed goal formation. The ...

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... graph network with unit edge lengths, can be scheduled with time n+ℓ−1 (in which ℓ is the largest of the distances between all pairing of start/goal formation locations), which is a tight time bound =-=[28]-=-. Furthermore, it was shown that a minimum time constraint and a minimum distance constraint cannot be satisfied simultaneously in general [28]. Using a fully centralized approach, an O(n 3 + nE) algo...

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...usly solving the position assignment problem and controlling robots between two formations was presented in [16]. Position assignment to transition between two formations was also considered in [19], =-=[18]-=- for large teams of simple particle robots. Somewhat similar to our Virtual Rigid Body, the paper [11] defined a virtual structure representation, upon which the authors developed controllers for driv...

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... for example the paper by Bereg et al. [2] which provides upper and lower bounds for the unlabeled case, or the paper by Dumitrescu and Jiang [3] who show that deciding whether a collection of labeled or unlabeled discs amidst obstacles can be moved between two configurations within k steps is NP-hard. Finally, we mention the problem of pebble motions on graphs, which can be considered as a discrete variant of the multi-robot motion planning problem. In this problem, pebbles need to be moved from one set of vertices of a graph to another, while following a certain set of rules—see for example [4, 5, 11, 12, 14, 29]. 1 Our contribution. Surprisingly, the unlabeled version of the multi-robot motion-planning has hardly received any attention in the computational-geometry literature. Indeed, we don’t know of any papers that solve the problem in an exact and complete manner, except in the very restricted setting studied by Turpin et al. [23] that we mentioned above. We therefore study the following basic variant of the problem: given m unit discs in a simple polygon with n vertices, each at their own start position, and m target positions, find collision-free motions for the discs such that at the end of the...

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...proxy to quantities such as the total energy consumption of all robots. Note that a distance-optimal solution for the target assignment problem generally does not imply time optimality and vise versa =-=[31]-=-. As the name implies, an assignment (or matching) problem is embedded in the problem of target assignment in robotic networks. The assignment problem is extensively studied in the area of combinatori...