Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents from their starting locations to given goal destinations. It has applications in automated warehouse systems, autonomous aircraft towing vehicles, office robots, and video game characters. The problem is formulated by representing the area as a grid of cells, with obstacles blocking certain cells. The objective is to find paths for N agents that minimize the sum of costs or makespan. Key assumptions include discrete time steps and agents occupying the same cell at the same time resulting in collisions. Different algorithms that have been developed to solve MAPF include search-based approaches like A* and rule-based approaches like push-and-swap.

1. Multi-Agent Path Finding
(MAPF)
Md.Ahasanul Alam(10)
Mustafizur Rahman(22)
Supervised by:
Dr. Ismat Rahman

2. What is MAPF
● Find collision-free paths for a team of agents from their current
locations to given destinations.
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3. Applications
● Automated warehouse systems
● Autonomous aircraft towing vehicles
● Office robots
● Game characters in video games.
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4. Formulation and Objective:
● Whole area is considered as block of cells
● Cells with obstacles are blocked
● N Agents are currently in N cells(x,y)
● Find N collision free paths
● Objective Function:
○ Sum of Cost
○ Makespan
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5. Assumptions
● No kinematic constraints
● Time is assumed discretized(t)
● Five different actions(Left,Right,Up,Down,No move)
● Having same (x,y,t) for two agents means collision.
● Vertex collision not allowed
● Edge collision not allowed
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6. Different Algorithms
● Searched based
○ CA*,Cost Tree Search,Conflict based search etc
● Rule based
○ Push and swap,push and rotate etc
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7. Cooperative Pathfinding (David et al. 2005)
● Cooperative A*(CA*) : considering other agent’s actions
● Hierarchical CA*(HCA*) : without considering other agent’s
actions
● Windowed HCA* (WHCA*) : cooperative search for fixed depth
limit
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8. Limitations
● Does not guarantee completeness
● Head to head collision
● Ordering is important
● What to do after reaching goal state?
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9. Increasing Cost Tree Search (Sharon et
al. 2013)
● Two level search
● High level:
○ Searching for minimal cost solution
● Low level:
○ Searching for a valid solution under the costs constraints
● Performance is number of agents and environment dependent
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10. Increasing Cost Tree Search (Sharon et al.
2013)
zd
Fig-1: Mapf example with two agents Fig-2: High level search Fig-3: Low level search, multi value
decision diagram
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11. Conflict Based Search (Sharon et al.2015)
● Two level search
● High level:
○ Search the Constraint Tree (CT)
○ Constraint denoted as (a,v,t)
○ Resolve conflict adding more constraints
● Low level:
○ Search for optimal path to goal state
○ Path is consistent with the constraints.
○ Doesn’t consider other agent during the search 11

12. Resolving Conflicts
● A conflict is denoted as Cn = (ai , aj , v, t)
● Split the node into two child nodes
● Add constraint (ai , v, t) and (aj , v, t) to two
Child nodes
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13. Improved CBS(Boyarski et al.2015)
● Poor choice of conflicts to split may
increase tree size
● Solution: Prioritize conflicts
○ Cardinal
○ Semi-Cardinal
○ Non-Cardinal
● Choose cardinal conflicts to split
● Semi-cardinal / non-cardinal conflicts may bypassed. 13

14. Adding Heuristics to CBS (Felner et al.2018)
● Makes the high level search more informed
● g-value : cost of node
● h-value : number of disjoint cardinal conflict.
● To determine h-value:
○ Build a cardinal conflict graph GCG = (VCG,ECG)
○ Take an edge (u,v) ε VCG arbitrarily and remove all the
edges connected to u or v
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15. Rule Based Search
● Push and swap :
○ Two primitives.
○ Push:Each agent moving along its shortest path to its goal
○ Swap: Once agent cannot make progress by pushing,swap
positions with the agent next to it along the shortest path.
○ At most n-2 agents for n vertices
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16. Rule Based Search
Swap operation not always possible.
(Polygon instance/bridge)
Fig:1
Fig:2 16

17. Potential Improvements
● What are the effects of different parameters that influence the
difficulty of the problem?
● Optimization on existing algorithms
● Algorithms that perform well for both objective functions
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18. References
● A. Felner et al,” Search-Based Optimal Solvers for the Multi-Agent Pathfinding Problem:
Summary and Challenges”. In Proceedings of the Symposium on Combinatorial Search
(SoCS), 28-37, 2017.
● Silver, David. "Cooperative Pathfinding." AIIDE 1 (2005): 117-122.
● Sharon, Guni, et al. "The increasing cost tree search for optimal multi-agent pathfinding."
Artificial Intelligence 195 (2013): 470-495
● Sharon, Guni, et al. "Conflict-based search for optimal multi-agent pathfinding." Artificial
Intelligence 219 (2015): 40-66.
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19. References
● Boyarski, Eli, et al. "ICBS: improved conflict-based search algorithm for multi-agent
pathfinding." Twenty-Fourth International Joint Conference on Artificial Intelligence
(IJACAI) . 2015.
● Felner, Ariel, et al. "Adding heuristics to conflict-based search for multi-agent path finding.
" Twenty-Eighth International Conference on Automated Planning and Scheduling.
(SoCS).2018.
● Luna, Ryan J., and Kostas E. Bekris. "Push and swap: Fast cooperative path-finding with
completeness guarantees." Twenty-Second International Joint Conference on Artificial
Intelligence. 2011.
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20. Thank You
&
Any questions?
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