Post on 21-Jan-2016
description
Finding Optimal Solutions to Cooperative Pathfinding ProblemsTrevor Standley
Computer Science Department
University of California, Los Angeles
http://cs.ucla.edu/~tstand/
Introduction Pathfinding Problems
A single agent must find a path from a start state to a goal state
Cooperative Pathfinding Problems Multiple agents interact
Want to minimize the total cost
Motivation
Motivation
Motivation
My Formulation Gridworld pathfinding
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
The Standard Algorithm The standard algorithm is A*
Centralized algorithm
There is a standard heuristic
State representation – A position for each agent
State space – Exponential in the number of agents
An operator – Complete assignment of moves to agents- One of {N; NE; E; SE; S; SW; W; NW; and wait} for each agent
- Exponential in the number of agents
Obviously this algorithm is not taken seriously
My algorithm Optimal Complete Two main contributions
Operator decomposition
Independence detection
Operator Decomposition Intuition
Also a centralized algorithm
Still use A*
Change how operators are defined: only one agent moves at a time
Simple idea, tricky to get details right
Operator Decomposition Each operator assigns a move to a single agent Assignments are made in a fixed order Move assignments stored as part of the state
representation
Operator Decomposition Example
Operator Decomposition
The Savings of Operator Decomposition
Consequences of Operator Decomposition Branching factor becomes polynomial However, state space still exponential
Simple Independence Detection
Simple Independence Detection
1. Create a group for each agent
2. Plan paths for each group independently
3. Check for conflicts in new paths
4. Combine groups with conflicting paths
5. Repeat 2-4 until no conflicts
Simple Independence Detection
Simple Independence Detection Problem Are these agents independent?
Simple Independence Detection Problem Are these agents independent?
Better Independence Detection When a conflict is detected between two groups, try
to find an alternate path for one of the groups If that fails try to find an alternate path for the other
group Only combine groups if no alternate path could be
found
Independence Detection Which alternate paths are the best? Only search for optimal paths Paths can be found using operator decomposition Find paths that will lead to fewest number of future
conflicts Operator decomposition can be modified to find
optimal paths with few future conflicts
My Algorithm Uses decoupled planning where possible Only uses centralized planning for non-independent
subproblems Calls operator decomposition as a subroutine to do
the centralized planning
Results 10000 randomly generated problems with 2-60 agents
Conclusions Researchers have developed centralized and
decoupled approaches for solving cooperative pathfinding problems
Operator decomposition is an improved centralized approach
Independence detection is a hybrid approach Only uses centralized planning when necessary
Acknowledgments My advisor, Rich Korf. Dawn Chen for editing, advice, and artwork