Toward efficient trajectory planning: the path-velocity decomposition
International Journal of Robotics Research
Robot Motion Planning
Coordinating Pebble Motion On Graphs, The Diameter Of Permutation Groups, And Applications
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
A new approach to cooperative pathfinding
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 3
Graph abstraction in real-time heuristic search
Journal of Artificial Intelligence Research
Exploiting subgraph structure in multi-robot path planning
Journal of Artificial Intelligence Research
Tractable multi-agent path planning on grid maps
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
An Application of Pebble Motion on Graphs to Abstract Multi-robot Path Planning
ICTAI '09 Proceedings of the 2009 21st IEEE International Conference on Tools with Artificial Intelligence
A novel approach to path planning for multiple robots in bi-connected graphs
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Scalable Multi-Agent Pathfinding on Grid Maps with Tractability and Completeness Guarantees
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Towards optimal cooperative path planning in hard setups through satisfiability solving
PRICAI'12 Proceedings of the 12th Pacific Rim international conference on Trends in Artificial Intelligence
Push and rotate: cooperative multi-agent path planning
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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Multi-agent path planning is a challenging problem with numerous real-life applications. Running a centralized search such as A* in the combined state space of all units is complete and cost-optimal, 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 multi-agent path planning on undirected graphs. We present a basic version and several extensions. They have low-polynomial worst-case 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 re-used across instances on the same map. Speed-wise, MAPP is competitive or significantly faster than WHCA*, depending on whether MAPP performs all computations from scratch. When data that MAPP can re-use 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.