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The Increasing Cost Tree Search for Optimal MultiAgent Pathfinding
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... We address the problem of optimal path finding for multiple agents where agents must not collide and their total travel cost should be minimized. Previous work used traditional singleagent search variants of the A* algorithm. We present a novel formalization for this problem which includes a search ..."
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Cited by 14 (6 self)
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We address the problem of optimal path finding for multiple agents where agents must not collide and their total travel cost should be minimized. Previous work used traditional singleagent search variants of the A* algorithm. We present a novel formalization for this problem which includes a search tree called the increasing cost tree (ICT) and a corresponding search algorithm that finds optimal solutions. We analyze this new formalization and compare it to the previous stateoftheart A*based approach. Experimental results on various domains show the benefits and drawbacks of this approach. A speedup of up to 3 orders of magnitude was obtained in a number of cases.
Tractable MultiAgent Path Planning on Grid Maps
"... Multiagent path planning on grid maps is a challenging problem and has numerous reallife applications. Running a centralized, systematic search such as A * is complete and costoptimal but scales up poorly in practice, since both the search space and the branching factor grow exponentially in the ..."
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Cited by 13 (3 self)
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Multiagent path planning on grid maps is a challenging problem and has numerous reallife applications. Running a centralized, systematic search such as A * is complete and costoptimal but scales up poorly in practice, since both the search space and the branching factor grow exponentially in the number of mobile units. Decentralized approaches, which decompose a problem into several subproblems, can be faster and can work for larger problems. However, existing decentralized methods offer no guarantees with respect to completeness, running time, and solution quality. To address such limitations, we introduce MAPP, a tractable algorithm for multiagent path planning on grid maps. We show that MAPP has lowpolynomial worstcase upper bounds for the running time, the memory requirements, and the length of solutions. As it runs in lowpolynomial time, MAPP is incomplete in the general case. We identify a class of problems for which our algorithm is complete. We believe that this is the first study that formalises restrictions to obtain a tractable class of multiagent path planning problems. 1
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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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.
MAPP: a Scalable MultiAgent Path Planning Algorithm with Tractability and Completeness Guarantees
"... Multiagent path planning is a challenging problem with numerous reallife applications. Running a centralized search such as A * in the combined state space of all units is complete and costoptimal, but scales poorly, as the state space size is exponential in the number of mobile units. Traditiona ..."
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Multiagent path planning is a challenging problem with numerous reallife applications. Running a centralized search such as A * in the combined state space of all units is complete and costoptimal, but scales poorly, as the state space size is exponential in the number of mobile units. Traditional decentralized approaches, such as FAR and WHCA*, are faster and more scalable, being based on problem decomposition. However, such methods are incomplete and provide no guarantees with respect to the running time or the solution quality. They are not necessarily able to tell in a reasonable time whether they would succeed in finding a solution to a given instance. We introduce MAPP, a tractable algorithm for multiagent path planning on undirected graphs. We present a basic version and several extensions. They have lowpolynomial worstcase upper bounds for the running time, the memory requirements, and the length of solutions. Even though all algorithmic versions are incomplete in the general case, each provides formal guarantees on problems it can solve. For each version, we discuss the algorithm’s completeness with respect to clearly defined subclasses of instances. Experiments were run on realistic game grid maps. MAPP solved 99.86 % of all mobile units, which is 18–22 % better than the percentage of FAR and WHCA*. MAPP marked 98.82 % of all units as provably solvable during the first stage of plan computation. Parts of MAPP’s computation can be reused across instances on the same map. Speedwise, MAPP is competitive or significantly faster than WHCA*, depending on whether MAPP performs all computations from scratch. When data that MAPP can reuse are preprocessed offline and readily available, MAPP is slower than the very fast FAR algorithm by a factor of 2.18 on average. MAPP’s solutions are on average 20% longer than FAR’s solutions and 7–31 % longer than WHCA*’s solutions. 1.
Bridging the Gap Between Centralised and Decentralised MultiAgent Pathfinding
 FOURTEENTH AAAI / SIGART DOCTORAL CONSORTIUM (2009)
, 2009
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Abstract Path Planning for Multiple Robots: A Theoretical Study
, 2010
"... An abstraction of the problem of multirobot path planning is introduced in this paper. The basic task is to determine spatialtemporal plan for each robot of a group of robots where each robot is given its initial position in the environment and it needs to go to the given goal position. Robots mu ..."
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An abstraction of the problem of multirobot path planning is introduced in this paper. The basic task is to determine spatialtemporal plan for each robot of a group of robots where each robot is given its initial position in the environment and it needs to go to the given goal position. Robots must avoid obstacles and must not collide with each other. The abstraction adopted in this work models the environment within that robots are moving as an undirected graph. Robots are placed in vertices of the graph; at most one robot is placed in each vertex and at most one vertex remains unoccupied.The move is allowed into the unoccupied vertex or into the vertex being vacated by an allowed move supposed that no other robot is entering the same target vertex. The relation of multirobot path planning to the problem of pebble motion on a graph (which the most widely known representative is 15puzzle) is discussed. The optimization variant of the abstract multirobot path planning is particularly studied. The task is to find a solution of the makespan as small as possible in the optimization variant. The main contribution of the paper is the proof of the NPcompleteness of the decision version of the optimization variant of multirobot path planning. The reduction of Boolean satisfiability to multirobot path planning is used in the proof.
Abstract Path Planning for Multiple Robots: An Empirical Study
, 2010
"... The problem of multirobot path planning is addressed in this work. The task is to construct a sequence of moves for each robot of the group of robots that are moving in certain environment. Initially each robot is placed in some location in the environment and it needs to go to the given goal pos ..."
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The problem of multirobot path planning is addressed in this work. The task is to construct a sequence of moves for each robot of the group of robots that are moving in certain environment. Initially each robot is placed in some location in the environment and it needs to go to the given goal position. Robots must avoid obstacles and must not collide with each other along the process of relocation according to the constructed sequences of moves. An abstraction where the environment is modeled as an undirected graph is adopted – vertices represent locations in the environment and edges represent unblocked way between two neighboring locations. Robots are represented as elements placed in vertices of the graph while at least one vertex is unoccupied to allow robots to move. The move is allowed into the unoccupied vertex or into the vertex being vacated by an allowed move supposed that no other robot is entering the same target vertex. Two polynomial time algorithms for solving the problem of multirobot path planning suboptimally with respect to the makespan and their variants are presented in this work. Both algorithms are targeted on the case with biconnected graphs with relatively small number of unoccupied vertices. The precise theoretical and experimental analysis of presented algorithms is provided. It has been shown theoretically and experimentally that presented algorithms outperform the only existent algorithm capable of solving the given class of the problem in terms of quality of generated solutions. In terms of speed, presented algorithms proved to be as fast as the existent one at least.
Maintaining Team Coherence under the Velocity Obstacle Framework
"... Many multiagent applications may involve a notion of spatial coherence. For instance, simulations of virtual agents often need to model a coherent group or crowd. Alternatively, robots may prefer to stay within a prespecified communication range. This paper proposes an extension of a decentralized ..."
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Many multiagent applications may involve a notion of spatial coherence. For instance, simulations of virtual agents often need to model a coherent group or crowd. Alternatively, robots may prefer to stay within a prespecified communication range. This paper proposes an extension of a decentralized, reactive collision avoidance framework, which defines obstacles in the velocity space, known as Velocity Obstacles (VOs), for coherent groups of agents. The extension, referred to in this work as a Loss of Communication Obstacle (LOCO), aims to maintain proximity among agents by imposing constraints in the velocity space and restricting the set of feasible controls. If the introduction of LOCOs results in a problem that is too restrictive, then the proximity constraints are relaxed in order to maintain collision avoidance.
Proceedings of the TwentySecond International Joint Conference on Artificial Intelligence Push and Swap: Fast Cooperative PathFinding with Completeness Guarantees
"... Cooperative pathfinding can be abstracted as computing noncolliding paths for multiple agents between their start and goal locations on a graph. This paper proposes a fast algorithm that can provide completeness guarantees for a general class of problems without any assumptions about the graph’s t ..."
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Cooperative pathfinding can be abstracted as computing noncolliding paths for multiple agents between their start and goal locations on a graph. This paper proposes a fast algorithm that can provide completeness guarantees for a general class of problems without any assumptions about the graph’s topology. Specifically, the approach can address any solvable instance where there are at most n2 agents in a graph of size n. The algorithm employs two primitives: a “push ” operation where agents move towards their goals up to the point that no progress can be made, and a “swap ” operation that allows two agents to swap positions without altering the configuration of other agents. Simulated experiments are provided on hard instances of cooperative pathfinding, including comparisons against alternative methods. The results are favorable for the proposed algorithm and show that the technique scales to problems that require high levels of coordination, involving hundreds of agents. 1