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M*: A Complete Multirobot Path Planning Algorithm with Performance
"... Abstract — Multirobot path planning is difficult because the full configuration space of the system grows exponentially with the number of robots. Planning in the joint configuration space of a set of robots is only necessary if they are strongly coupled, which is often not true if the robots are we ..."
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Abstract — Multirobot path planning is difficult because the full configuration space of the system grows exponentially with the number of robots. Planning in the joint configuration space of a set of robots is only necessary if they are strongly coupled, which is often not true if the robots are well separated in the workspace. Therefore, we initially plan for each robot separately, and only couple sets of robots after they have been found to interact, thus minimizing the dimensionality of the search space. We present a general strategy called subdimensional expansion, which dynamically generates low dimensional search spaces embedded in the full configuration space. We also present an implementation of subdimensional expansion for robot configuration spaces that can be represented as a graph, called M*, and show that M * is complete and finds minimal cost paths. I.
Efficient and Complete Centralized MultiRobot Path Planning
"... Abstract — Multirobot path planning is abstracted as the problem of computing a set of noncolliding paths on a graph for multiple robots. A naive search of the composite search space, although complete, has exponential complexity and becomes computationally prohibitive for problems with just a few ..."
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Cited by 12 (2 self)
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Abstract — Multirobot path planning is abstracted as the problem of computing a set of noncolliding paths on a graph for multiple robots. A naive search of the composite search space, although complete, has exponential complexity and becomes computationally prohibitive for problems with just a few robots. This paper proposes an efficient and complete algorithm for solving a general class of multirobot path planning problems, specifically those where there are at most n2 robots in a connected graph of n vertices. This paper provides a full proof of completeness. The algorithm employs two primitives: “push”, where a robot moves toward its goal until no progress can be made, and “swap”, that allows two robots to swap positions without altering the position of any other robot. Additionally, this paper provides a smoothing procedure for improving solution quality. Simulated experiments compare the proposed approach with several other centralized and decoupled planners, and show that the proposed technique improves computation time and solution quality, while scaling to problems with 100s of robots, solving them in under 5 seconds. I.
kcolor multirobot motion planning
 in The Tenth International Workshop on Algorithmic Foundations of Robotics (WAFR
, 2012
"... Abstract: We present a simple and natural extension of the multirobot motion planning problem where the robots are partitioned into groups (colors), such that in each group the robots are interchangeable. Every robot is no longer required to move to a specific target, but rather to some target plac ..."
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Cited by 9 (4 self)
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Abstract: We present a simple and natural extension of the multirobot motion planning problem where the robots are partitioned into groups (colors), such that in each group the robots are interchangeable. Every robot is no longer required to move to a specific target, but rather to some target placement that is assigned to its group. We call this problem kcolor multirobot motion planning and provide a samplingbased algorithm specifically designed for solving it. At the heart of the algorithm is a novel technique where the kcolor problem is reduced to several discrete multirobot motion planning problems. These reductions amplify basic samples into massive collections of free placements and paths for the robots. We demonstrate the performance of the algorithm by an implementation for the case of disc robots in the plane and show that it successfully and efficiently copes with a variety of challenging scenarios, involving many robots, while a simplified version of this algorithm, that can be viewed as an extension of a prevalent samplingbased algorithm for the kcolor case, fails even on simple scenarios. Interestingly, our algorithm outperforms a stateoftheart implementation for the standard multirobot problem, in which each robot has a distinct color. 1
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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Decentralized prioritized planning in large multirobot teams
"... Abstract — In this paper, we address the problem of distributed motion planning for large teams of hundreds of robots in constrained environments. We introduce two distributed prioritized planning algorithms: an efficient, complete method which is shown to converge to the centralized prioritized pla ..."
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Cited by 7 (0 self)
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Abstract — In this paper, we address the problem of distributed motion planning for large teams of hundreds of robots in constrained environments. We introduce two distributed prioritized planning algorithms: an efficient, complete method which is shown to converge to the centralized prioritized planner solution, and a sparse method in which robots discover collisions probabilistically. Planning is divided into a number of iterations, during which every robot simultaneously and independently computes a planning solution based on other robots ’ path information from the previous iteration. Paths are exchanged in ways that exploit the cooperative nature of the team and a statistical phenomenon known as the “birthday paradox”. Performance is measured in simulated 2D environments with teams of up to 240 robots. We find that in moderately constrained environments, these methods generate solutions of similar quality to a centralized prioritized planner, but display interesting communication and planning time characteristics. I.
RealTime Path Planning for Coordinated Transport of Multiple Particles using Optical Tweezers
"... Abstract—Automated transport of multiple particles using optical tweezers requires realtime path planning to move them in coordination by avoiding collisions among themselves and with randomly moving obstacles. This paper develops a decoupled and prioritized path planning approach by sequentially a ..."
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Cited by 7 (6 self)
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Abstract—Automated transport of multiple particles using optical tweezers requires realtime path planning to move them in coordination by avoiding collisions among themselves and with randomly moving obstacles. This paper develops a decoupled and prioritized path planning approach by sequentially applying a partially observable Markov decision process algorithm on every particle that needs to be transported. We use an iterative version of a maximum bipartite graph matching algorithm to assign given goal locations to such particles. We then employ a threestep method consisting of clustering, classification, and branch and bound optimization to determine the final collisionfree paths. We demonstrate the effectiveness of the developed approach via experiments using silica beads in a holographic tweezers setup. We also discuss the applicability of our approach and challenges in manipulating biological cells indirectly by using
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.
Multiagent Path Planning and Network Flow
"... Abstract This paper connects multiagent path planning on graphs (roadmaps) to network flow problems, showing that the former can be reduced to the later, therefore enabling the application of combinatorial network flow algorithms, as well as general linear program techniques, to multiagent path pl ..."
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Cited by 5 (4 self)
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Abstract This paper connects multiagent path planning on graphs (roadmaps) to network flow problems, showing that the former can be reduced to the later, therefore enabling the application of combinatorial network flow algorithms, as well as general linear program techniques, to multiagent path planning problems on graphs. Exploiting this connection, we show that when the goals are permutation invariant, the problem always has a feasible solution path set with a longest finish time of no more than n+V −1 steps, in which n is the number of agents and V is the number of vertices of the underlying graph. We then give a complete algorithm that finds such a solution in O(nV E) time, with E being the number of edges of the graph. Taking a further step, we study time and distance optimality of the feasible solutions, show that they have a pairwise Pareto optimal structure, and again provide efficient algorithms for optimizing each of these practical objectives. 1
D.: Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multirobot motion planning
 CoRR
, 2013
"... Abstract—We present a framework for multirobot motion planning which incorporates an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs. Our pathfinding algorithm, which we call discreteRRT (dRRT), is an adaption of the celebrated RRT algori ..."
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Abstract—We present a framework for multirobot motion planning which incorporates an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs. Our pathfinding algorithm, which we call discreteRRT (dRRT), is an adaption of the celebrated RRT algorithm, for the discrete case of a graph. By rapidly exploring the highdimensional configuration space represented by the implicit roadmap, dRRT is able to reach subproblems where minimal coordination between the robots is required. Integrating the implicit representation of the roadmap, the dRRT algorithm, and techniques that are tailored for such subproblems on the implicit roadmap allows us to solve multirobot problems while exploring only a small portion of the configuration space. We believe that our approach, which is probabilistically complete, is the stateoftheart for scenarios that require tight coupling of multiple robots. We demonstrate this experimentally on various challenging scenarios where our algorithm is faster by a factor of at least fifteen when compared to existing algorithms that we are aware of. I.
K.: Efficient multirobot motion planning for unlabeled discs in simple polygons
 CoRR
, 2013
"... Abstract. We consider the following motionplanning problem: we are given m unit discs in a simple polygon with n vertices, each at their own start position, and we want to move the discs to a given set of m target positions. Contrary to the standard (labeled) version of the problem, each disc is ..."
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Abstract. We consider the following motionplanning problem: we are given m unit discs in a simple polygon with n vertices, each at their own start position, and we want to move the discs to a given set of m target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in