On the Complexity of Motion Planning for Multiple Independent Objects; PSPACE- Hardness of the "Warehouseman's Problem"

Hopcroft, John E.; Schwartz, Jacob T.; Sharir, Micha

doi:10.1177/027836498400300405

Cited by 386 publications

(204 citation statements)

References 3 publications

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“…This approach usually comes with stronger theoretical guarantees such as completeness [29,39,40,41,44] or even optimality [51] of the returned solutions. However, due to the computational hardness of MRMP [21,22,26,42,45], coupled techniques do not scale well with the increase in the number of robots. We do mention that, when simplifying assumptions are made concerning the separation of initial and goal positions, MRMP can be solved in polynomial time, as function of the number of robots and the complexity of the workspace environment (see, [1,43,47]).…”

Section: A Multi-robot Motion-planningmentioning

confidence: 99%

Effective Metrics for Multi-Robot Motion-Planning

Atias

Solovey

Halperin

2017

Robotics: Science and Systems XIII

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Abstract-We study the effectiveness of metrics for MultiRobot Motion-Planning (MRMP) when using RRT-style sampling-based planners. These metrics play the crucial role of determining the nearest neighbors of configurations and in that they regulate the connectivity of the underlying roadmaps produced by the planners and other properties like the quality of solution paths. After screening over a dozen different metrics we focus on the five most promising ones-two more traditional metrics, and three novel ones which we propose here, adapted from the domain of shape-matching. In addition to the novel multi-robot metrics, a central contribution of this work are tools to analyze and predict the effectiveness of metrics in the MRMP context. We identify a suite of possible substructures in the configuration space, for which it is fairly easy (i) to define a so-called natural distance, which allows us to predict the performance of a metric. This is done by comparing the distribution of its values for sampled pairs of configurations to the distribution induced by the natural distance; (ii) to define equivalence classes of configurations and test how well a metric covers the different classes. We provide experiments that attest to the ability of our tools to predict the effectiveness of metrics: those metrics that qualify in the analysis yield higher success rate of the planner with fewer vertices in the roadmap. We also show how combining several metrics together leads to better results (success rate and size of roadmap) than using a single metric.

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Section: A Multi-robot Motion-planningmentioning

confidence: 99%

Effective Metrics for Multi-Robot Motion-Planning

Atias

Solovey

Halperin

2017

Robotics: Science and Systems XIII

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“…Sliding-block puzzles generalize the 15-puzzle by allowing unmovable blocks, and blocks that are larger than 1 × 1. Generally the goal of a sliding-block puzzle is to move a block to a single location (the "warehouseman's problem" [21]), to find out if a single block is movable [18,19], or somehow reorder all blocks [20]. In contrast, in the kissing problem, the objective is for all blocks to touch each other.…”

Section: Introductionmentioning

confidence: 99%

The Kissing Problem: How to End a Gathering When Everyone Kisses Everyone Else Goodbye

et al. 2013

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Abstract. This paper introduces the kissing problem: given a rectangular room with n people in it, what is the most efficient way for each pair of people to kiss each other goodbye? The room is viewed as a set of pixels that form a subset of the integer grid. At most one person can stand on a pixel at once, and people move horizontally or vertically. In order to move into a pixel in time step t, the pixel must be empty in time step t − 1. The paper gives one algorithm for kissing everyone goodbye.(1) This algorithm is a 4 + o(1)-approximation algorithm in a crowded room (e.g., only one unoccupied pixel).(2) It is a 10 + o(1)-approximation algorithm for kissing in a comfortable room (e.g., at most half the pixels are empty). (3) It is a 25+o(1)-approximation for kissing in a sparse room.

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“…It has been shown that in general, sliding-block puzzles are PSPACE-complete [25,26]. However, under certain simplifying assumptions and for cases of such puzzles like the one we consider here (Figure 2), a polynomial algorithm can be constructed to move a single block from any initial position to any final position [26].…”

Section: A Case Study: the Sliding Block Puzzlementioning

confidence: 99%

Composition of Motion Description Languages

Zhang

Tanner

Hybrid Systems: Computation and Control

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Abstract. We introduce a new formalism to define compositions of interacting heterogeneous systems, described by extended motion description languages (MDLes). The novelty of the formalism is in producing a composed system with a behavior that could be a superset of the union of the behaviors of its generators. We prove closedness of MDLes under this composition and we show that in the class of systems modeled using MDLes, language equivalence can be decidable. Our approach consists of representing MDLes as normed processes, recursively defined as a guarded system of recursion equations in restricted Greibach Normal Form over a basic process algebra. Basic processes have well defined semantics for composition, which we exploit to establish the properties of our composed MDLes.

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On the Complexity of Motion Planning for Multiple Independent Objects; PSPACE- Hardness of the "Warehouseman's Problem"

Cited by 386 publications

References 3 publications

Effective Metrics for Multi-Robot Motion-Planning

Effective Metrics for Multi-Robot Motion-Planning

The Kissing Problem: How to End a Gathering When Everyone Kisses Everyone Else Goodbye

Composition of Motion Description Languages

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