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Distance optimal formation control on graphs with a tight convergence time guarantee
 In IEEE International Conference on Decision and Control
, 2012
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Planning Optimal Paths for Multiple Robots on Graphs
"... Abstract — In this paper, we study the problem of optimal multirobot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions for our MPP formulation, respectively. The resultin ..."
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Cited by 5 (3 self)
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Abstract — In this paper, we study the problem of optimal multirobot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions for our MPP formulation, respectively. The resulting algorithms from these ILP models are complete and guaranteed to yield true optimal solutions. In addition, our flexible framework can easily accommodate other variants of the MPP problem. Focusing on the time optimal algorithm, we evaluate its performance, both as a stand alone algorithm and as a generic heuristic for quickly solving large problem instances. Computational results confirm the effectiveness of our method. I.
Structure and Intractability of Optimal MultiRobot Path Planning on Graphs∗
"... In this paper, we study the structure and computational complexity of optimal multirobot path planning problems on graphs. Our results encompass three formulations of the discrete multirobot path planning problem, including a variant that allows synchronous rotations of robots along fully occup ..."
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In this paper, we study the structure and computational complexity of optimal multirobot path planning problems on graphs. Our results encompass three formulations of the discrete multirobot path planning problem, including a variant that allows synchronous rotations of robots along fully occupied, disjoint cycles on the graph. Allowing rotation of robots provides a more natural model for multirobot path planning because robots can communicate. Our optimality objectives are to minimize the total arrival time, the makespan (last arrival time), and the total distance. On the structure side, we show that, in general, these objectives demonstrate a pairwise Pareto optimal structure and cannot be simultaneously optimized. On the computational complexity side, we extend previous work and show that, regardless of the underlying multirobot path planning problem, these objectives are all intractable to compute. In particular, our NPhardness proof for the time optimal versions, based on a minimal and direct reduction from the 3satisfiability problem, shows that these problems remain NPhard even when there are only two groups of robots (i.e. robots within each group are interchangeable).
DisCoF: Cooperative Pathfinding in Distributed Systems with Limited Sensing and Communication
"... Abstract Cooperative pathfinding is often addressed in one of two ways in the literature. In fully coupled approaches, robots are considered together and the plans for all robots are constructed simultaneously. In decoupled approaches, the plans are constructed only for a subset of robots at a time ..."
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Abstract Cooperative pathfinding is often addressed in one of two ways in the literature. In fully coupled approaches, robots are considered together and the plans for all robots are constructed simultaneously. In decoupled approaches, the plans are constructed only for a subset of robots at a time. While decoupled approaches can be much faster than fully coupled approaches, they are often suboptimal and incomplete. Although there exist a few decoupled approaches that achieve completeness, global information (which makes global coordination possible) is assumed. Global information may not be accessible in distributed robotic systems. In this paper, we provide a windowbased approach to cooperative pathfinding with limited sensing and communication range in distributed systems (called DisCoF). In DisCoF, robots are assumed to be fully decoupled initially, and may gradually increase the level of coupling in an online and distributed fashion. In some cases, e.g., when global information is needed to solve the problem instance, DisCoF would eventually couple all robots together. DisCoF represents an inherently online approach since robots may only be aware of a subset of robots in the environment at any given point of time. Hence, they do not have enough information to determine nonconflicting plans with all the other robots. Completeness analysis of DisCoF is provided. 1
1Motion Planning for Unlabeled Discs with Optimality Guarantees
"... Abstract—We study the problem of path planning for unlabeled (indistinguishable) unitdisc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guarantee ..."
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Abstract—We study the problem of path planning for unlabeled (indistinguishable) unitdisc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time Õ m4 +m2n2, where m is the number of robots and n is the total complexity of the workspace. Moreover, the total length of the returned solution is at most OPT+4m, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency. I.