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Cooperative Pathfinding

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Presentation on theme: "Cooperative Pathfinding"— Presentation transcript:

1 Cooperative Pathfinding
David Silver

2 Overview The problem Solution methods Live demo (!?) Results
Local repair A* Cooperative A* Hierarchical, Cooperative A* Windowed, Hierarchical, Cooperative A* Live demo (!?) Results

3 The Problem N agents N goals Find N paths
Such that no two paths overlap

4 The Problem with the Problem
Search space is enormous e.g. 100x100 gridworld ~(10,000)N states Branching factor of 5N {N, E, S, W, wait} for each agent Need to solve in real-time e.g. complete search within 1ms

5 Reformulating the Problem
Err… isn’t this course called Single Agent Search? So simplify the problem to a series of single agent searches. Two approaches considered: A* with local repair Cooperative A*

6 1. A* with Local Repair Search for route to goal Ignore other agents
If collision is imminent, route again Increase agitation level with each reroute Cross fingers and hope for the best

7 Problems with Local Repair
Failure to reach goal Long solution lengths Frequent recalculation Appearance of ‘stupidity’

8 2. Cooperative A* Consider each agent in turn, greedily
Search for a route to goal, avoiding reserved states Mark the agent’s route in a reservation table Basic heuristic uses Manhattan distance

9 Search Space The new search space has 3 dimensions
2 dimensional grid Time dimension Reservation table marks illegal states Mark each state on any agent’s path Sparse data structure Implemented using hash table

10 Problems with Cooperative A*
Poor heuristic, many nodes expanded Need to improve heuristic Problems with agents at destination Need to continue searching Sensitive to agent order Dynamically rotate through agent orders

11 How to improve the heuristic?
Pattern databases no good Search space too large Goal may be different each time Map may change dynamically So use hierarchical A* (Holte) Search for goal at abstract level Use abstract distance as heuristic 3 ideas for reusing abstract search

12 3. Hierarchical, Cooperative A*
Domain abstraction Ignore time dimension Ignore reservation table Basic gridworld search Cooperative A* as before But using abstract distance as heuristic Abstract distance computed on demand

13 Reverse, Resumable A* Search backwards from Goal Search towards Start
But only terminate when requested node is reached Keep Open, Closed lists Resume search whenever a new node is requested Consistent heuristic required

14 4. Windowed, Hierarchical, Cooperative A*
Break up search into manageable pieces Like an intermediate abstraction layer Full search up to N steps Ignore time/reservations after N steps After N steps this is the same as abstract layer So use abstract distance to complete search

15 Windowing S window N abstract edge d(N,G) = h(N,G) G

16 Continuing the search Continue search after reaching destination
May need to get out of the way Use edge costs: 0 if sitting on destination 1 for other edges Abstract distance to goal for final edge

17 Using Windows Compute window for all agents initially
Then recompute each agent when half way through window Stagger computation to spread out processing time Can keep abstract distances until destination changes

18 Demo I hope this works!

19 Results: nodes expanded

20 Results: path length

21 Further ideas Additional layers in the hierarchy Prioritising agents
e.g. ignore half the reservations Prioritising agents Overriding low priority agents Abstracting in space as well as time e.g. Using N-cliques

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