1. Identifying and Resolving Conflicts among Agents with Hierarchical Plans
Brad Clement and Ed Durfee
Artificial Intelligence Laboratory
University of Michigan
{bradc,
presentation available at

2. What does this have to do with negotiation?
Mechanisms for
recognizing the need to resolve conflicts
identifying what needs to be resolved (resource conflicts)
identifying who should be involved
finding candidate global solutions for different settlements
Not a technique specifying how conflicts are resolved

3. Why negotiate plans?
Coordinating plans with conflicts involves negotiation.
Plans relate goals to actions.
Conditions and effects of actions represent resources.
Values are often placed on actions.
Understanding changes in intended actions during negotiation is natural. DA A B DB

4. Plan Coordination Low-level plan coordination
(Georgeff ‘83, Ephrati & Rosenchein ‘94, etc.)
High-level plan effect localization (Lansky ‘90)
Combine approaches for multilevel coordination
coordinate hierarchical plans at multiple levels
need to reason about interactions at abstract level

5. Why Hierarchical Plans?
Negotiation is easier at higher levels
Better solutions may exist at lower levels
crisper
coordination
lower cost
negotiation
levels
more flexibility

6. Hierarchical Plans A DA B DB1 2 3 4
Conditions (pre, in, & post) often specified only for primitives
Need refinement info at abstract level
Robust plan execution systems (PRS, RAPS, JAM)
0,0->0,4
0,0->1,1
1,3->0,4
0,0->1,1HI
0,0->1,1LO
1,1->1,3
1,3->0,4HI
1,3->0,4LO
0,0->0,1
0,0->1,0
1,1->1,2
1,3->0,3
1,3->1,4
0,1->1,1
1,0->1,1
1,2->1,3
0,3->0,4
1,4->0,4

7. Summary Information must, may always, sometimes external preconditions
pre: at(A,1,3) in: at(A,1,3), at(B,1,3), at(B,0,3), at(A,0,3), at(B,0,4), at(A,1,3) post: at(A,1,3), at(B,1,3), at(B,0,3), at(A,0,4), at(A,0,3), at(B,0,3), at(B,0,4)
must, may
always, sometimes
external preconditions
external postconditions
1,3->0,4HI
1,3->0,3
0,3->0,4
pre: at(A,1,3) in: at(A,1,3), at(B,1,3), at(B,0,3) post: at(A,0,3), at(A,1,3), at(B,1,3), at(B,0,3)
pre: at(A,0,3) in: at(A,0,3), at(B,0,3), at(B,0,4) post: at(A,0,4), at(A,0,3), at(B,0,3), at(B,0,4) 1 2 3 4
pre: at(A,1,3) in: at(A,1,3), at(B,1,3), at(B,0,3), at(B,1,4), at(A,0,3), at(A,1,4), at(B,0,4), at(A,1,3) post: at(A,1,3), at(B,1,3), at(B,0,3), at(A,0,4), at(A,0,3), at(A,1,4), at(B,0,3), at(B,1,4), at(B,0,4)
1,3->0,4 DA A 1
1,3->0,4HI
1,3->0,4LO DB 2 B

8. Determining Temporal Relations
CanAnyWay(relation, psum, qsum) - relation can hold for any way p and q can be executed
MightSomeWay(relation, psum, qsum) - relation might hold for some way p and q can be executed A B DA DB
B - before
O - overlaps
CanAnyWay(before, psum, qsum)
ØCanAnyWay(overlaps, psum, qsum)
MightSomeWay(overlaps, psum, qsum)

9. Top-Down Search search state search operators set of expanded plans
set of temporal constraints
set of blocked subplans
search operators
expand, block, constrain
CAW used to identify solutions
MSW used to identify failure
CAW and MSW improve search
CAW and MSW
synchronize, look deeper, or backtrack
MSW identifies threats to resolve
blocked
temporal constraints
blocked

10. Top-Down Search A A B B 1 2 Simple Swap 4 3 5 Conditional Swap1 2 5 3 4
Simple Swap A B
Choose B(2,0)->(0,0)Rt Expand B(2,0)->(0,0)Rt Choose A(0,0)->(2,0)Rt Expand A(0,0)->(2,0)Rt Backtrack Block A(0,0)->(2,0)Rt Choose A(0,0)->(2,0)Lt Synchronization found Coordination Successful
Conditional Swap
Expand B(2,0)->(0,0) Expand A(0,0)->(2,0) No Synchronization Coordination failed

11. Coordinating at Abstract Levels Can Improve PerformanceDA DB
Total Cost
BFS algorithm
top-level best
mid-level best
coordination
primitive-level best
Coordination Cost Execution Cost

12. Negotiating a Global Plan
Recognize the need to negotiate by identifying resource conflicts (threats)
Identify who should be involved
Identify what needs to be negotiated (choices that can resolve conflicts)
Find global solutions for different concessions
negotiation during search
negotiation after decentralized search and solution sharing
Plug in any negotiation technique?
Should negotiation problems be recast as plans?

13. Contributions Procedure for deriving summary information
can be applied in hierarchical planning (HTNs)
Rules for determining temporal plan relations at abstract levels
General top-down search algorithm for coordination/negotiation
Formalization of concepts and algorithms
Theory for Coordinating Concurrent Hierarchical Planning Agents Using Summary Information, AAAI ‘99

14. Work in Progress & Future Work
Evaluating candidate settlements
Constructing a concurrent hierarchical planner
Coordinating/negotiating overlapping goals
Adopting other agents’ plans/goals
Dealing with global plan failure during execution
Summarizing plan information differently (probabilistic)
Handling more expressive plan representations
Scaling number of agents and difficulty of coordination
Interleaving planning, plan execution, and negotiation

15. Difficulty of CAW and MSW Rule Specification1 A
MSW(overlaps, psum, qsum)
false if postconditions conflict
unsound
false if conflicts with pin and qpre  qin or ppost and qin where
pin is set of must, always inconds of p not achieved by inconds of q
ppost is set of postconds of p
qpre is set of must preconds of q not achieved by in- or postconds of p
qin is set of must, always inconds of p not achieved by inconds of p
O - overlaps 1 B 2
pre: at(A,0,0) in: at(A,0,0), at(A,0,0), at(A,0,1), at(A,0,1), at(A,1,1), at(B,0,0), at(B,0,1), at(B,1,1), at(B,1,0) post: at(A,0,0), at(A,0,1), at(A,1,1), at(A,1,0), at(B,0,0), at(B,0,1), at(B,1,1), at(B,1,0)
pre: at(B,2,0) in: at(B,2,0), at(B,2,0), at(B,2,1), at(B,2,1), at(B,1,1), at(A,2,0), at(A,2,1), at(A,1,1), at(A,1,0) post: at(B,2,0), at(B,2,1), at(B,1,1), at(B,1,0), at(A,2,0), at(A,2,1), at(A,1,1), at(A,1,0)

16. Formalizing Concurrent Hierarchical Plans
General model of concurrent interaction of hierarchical plans
Formalization of planning concepts and tools
Provable properties of summary information
Sound and complete rules for determining temporal relations
Toolbox for building sound and complete planning and negotiation mechanisms