Multi-Agent SystemsLecture 7Lecture 7

University “Politehnica” of Bucarest2004 - 2005

Adina Magda Floreaadina@cs.pub.ro

http://turing.cs.pub.ro/blia_2005

Distributed problem solving Distributed problem solving and planningand planningLecture outlineLecture outline

1 Distributed problem solving1 Distributed problem solving

2 Distributed planning2 Distributed planning

2.1 Centralized planning for distributed plans2.1 Centralized planning for distributed plans

2.2 Distributed planning for centralized plans2.2 Distributed planning for centralized plans

2.3 Distributed planning for distributed plans2.3 Distributed planning for distributed plans

2.4 Distributed planning and execution2.4 Distributed planning and execution

3 An example: Partial global planning3 An example: Partial global planning

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1. Distributed problem 1. Distributed problem solvingsolving

Group coherenceGroup coherence - agents want to work together - cooperative agents

CompetenceCompetence - agents must find ways to work together - coordinate to cooperate

Task and result sharing - an agent has many tasks to do and asks other agents to do some of its tasks; then it should integrate the results

Distributed planning - the problem to be solved is to design and execute a plan in a distributed manner, by many agents

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2 Distributed planning2 Distributed planning What can be distributed:

The process of coming out with a plan is distributed among agents

Execution is distributed among agents

PlanningPlanning State representation and plan representation Search vs planning

• representation of changes to the world state• representation of and reasoning about the plan

(steps/actions)

Linear planning Partial order planning Hierarchical planning Conditional planning

Planning Planning Search Search

2.1 Centralized planning for distributed plans2.1 Centralized planning for distributed plans Operators move(b,x,y) movetotable(b,x)

Precond: on(b,x) clear(b) clear(y) Precond: on(b,x) clear(b)Postcond: on(b,y) clear(x) Postcond: on(b,T) clear(x) on(b,x)on(b,x) clear(y)

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A

B D

C E

F

Si

C

A

E

B F

DSf

I'm BillAgent1

I'm TomAgent2

on(A,B) on(C,D) on(E,F)on(B,T) on(D,T) on(F,T)

on(B,A) on(F,D)on(A,E) on(D,C)on(E,T) on(C,T)

on(B,A)

S1: move(B,T,A)

on(B,T) clear(B) clear(A)

movetotable(A,B) move(A,B,y)

S2: move(A,B,E)

clear(A) clear(E) on(A,B)…………..………….

on(E,T)

S3: movetotable(E,F)

1. Given a goal description,a set of operators,and an initial state descriptiongenerate a partial order plan

S1: move(B,T,A) To satisfy the preconditions, we have:

S2: move(A,B,E) S2 < S1, S3 < S4

S3:movetotable(E,F) S6 < S4, S6 < S5

S4: move(F,T,D) Also

S5: move(D,T,C) S2 threat to S3 S3 < S2

S6: movetotable(C,D) S4 threat to S5 S5 < S4

Then the partial ordering is: S3 < S2 < S1

S6 < S5 < S4

S3 < S4

S3: movetotable(E,F) S2: move(A,B,E) S1: move(B,T,A)

S6: movetotable(C,D) S5: move(D,T,C) S4: move(F,T,D)

Any total ordering that satisfies this partial ordering is a good plan for Agent1

What if we have 2 agents?

DECOMP1

Subplan1 S3 < S2 < S1

Subplan2 S6 < S5 < S4

and S3 < S4

Agent1 S3 < send(clear(F)) < S2 < S1

Agent2 S6 < S5 < wait(clear(F)) < S46

< <

2. Decompose the plan intosubproblems so as to minimizeorder relations across plans

3. Insert synchronization

4. Allocate subplans to agents

S3: movetotable(E,F) S2: move(A,B,E) S1: move(B,T,A)

S6: movetotable(C,D) S5: move(D,T,C) S4: move(F,T,D)

DECOMP2

Subplan1 S3 < S5 < S4

Subplan2 S6 < S2 < S1

and S3 < S2 and S6 < S5

Agent1 S3 < send(don't_care(E)) < wait(clear(D)) < S5 < S4

Agent2 S6 < wait(don't_care(E)) < wait(clear(D)) < S2 < S1

Obviously, DECOMP2 has more order relations among subplans than DECOMP1

Therefore, we choose DECOMP1

S3 < send(clear(F)) < S2 < S1

S6 < S5 < wait(clear(F)) < S4

But

then back to DECOMP27

< <

4. If failure to allocate subplans

then redo decomposition (2)

If failure to allocate subplans with

any decomposition

then redo generate plan (1)

5. Execute and monitor subplans

I know howto move only

D, E, F

I know howto move only

A, B, C

2.2 Distributed planning for centralized plans2.2 Distributed planning for centralized plans Each of the planning agents generate a partial plan in parallel

then merge these plans into a global plan parallel to result sharing may involve negotiation

Agent 1 - is specialized in doing movetotable(b,x)

Agent 2 - is specialized in doing move(b,x,y)

Agent 1 - based on Sf it comes out with the partial plan

PAgent1 = { S3: movetotable(E,F) satisfies on(E,T)

S6: movetotable(C,D) satisfies on(C,T)

no ordering }

Agent 2 - based on Sf it comes out with the partial plan

PAgent 2 = { S1: move(B,T,A), S2: move(A,B,E) satisfies on(B,A) on(A,E)

S4: move(F,T,D), S5: move(D,T,C) satisfies on(F,D) on(D,C)

ordering S2 < S1 and S5 < S4 }

Merge PAgent1 with PAgent2 by checking preconditons and threats

Establish thus order S3 < S2, S6 < S5, S3 < S4 + order of PAgent2

Then give any instance of this partial plan to an execution agent to carry it out8

The problem is decomposed and distributed among various planning specialists, each of which proceeds then to generate its portion of the plan

similar to task sharing may involve backtracking

Agent 1 - knows only how to deal with 2-block stacks

Agent 2 - knows only how to deal with 3-block stacks

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C

A

E

B F

DSf

C

A

E B F

D

A

B D

C E

F

Si

2.3 Distributed planning for distributed plans2.3 Distributed planning for distributed plansa) Plan merginga) Plan merging Agents formulate local plans to satisfy their goals Local plans are exchanged Local plans are combined analyzing for positive and negative interaction Add messages and/or timing commitments to resolve negative plan

interactions and to exploit positive plan interactions

Interacting situations Positive interactions between plans

– redundant actions • static detection: sequencing

– favour actions• dynamic detection: incorporation

Negative interactions between plans– harmful actions– exclusive actions– incompatible actions

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movehigh(b,x,y)

Precond: have_lifter clear(b) clear(y) on(y,z) z T

Postcond: on(b,y) clear(x) on(b,x) clear(y) free_lifter pick_lifter

Precond: free_lifter

Postcond: have_lifter free_lifter

Agent1: { S1:move(B,T,A) < S2: pick_lifter < S3: movehigh(E,T,B) }

Agent2: { R1:move(C,T,D) < R2: pick_lifter < R3: movehigh(F,T,C) }

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A B D CEF

Si

D

A

B

E F

CSf

S1

S2

S3

R1

R3

R2

need_l

free_l

B

A

B

CSf1

Negative interactionswhat type?

Give examples of positive interactions redundant favor

Problems with the approach?

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Positive interactions

b) Iterative plan formationb) Iterative plan formation build all feasible plans build partial order plans to facilitate plan

merging build abstract plans to be iteratively refined

- see next section and PGP section

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c) Hierarchical distributed planningc) Hierarchical distributed planning Design plans on several levels of abstraction Use abstract plans Abstract operator - a kind of macro-operator = sequence of

applicable operators

Write paper

Readreferences

Organizeideas

Editcontent

Findeditor

Edittext

Editfigures

Checkfor errors

…..

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Hierarchical behavior-space search algorithm1. Level 0, Agent_List = {Agent1, …, AgentN}

2. for every Agenti in Agent_List do

2.1 Agenti sends description of Gi and Pi to every Agentj, j=1,N, ji

2.2 Agenti gets Gj, Pj from Agentj, j=1,N, ji

2.3 if Pi is compatible with {Pj}, j=1,N, ji

then Agenti removes itself from Agent_List

3. if Agent_list = { } then exit

4. Be N the new number of agents in Agent_List

5. Sort agents in Agent_List

6. for i=1,N-1, cf. ordering do

6.1 make Agenti the current superior

6.2 Agenti determines conflicts between {Pi}

6.3 if conflicts to be resolved at a lower level

then (a) Level Level + 1

(b) Agent_List = {Agenti+1, …, AgentN}

(c) go to step 2

6.4 send Pi to each Agentj, j=i+1, N

6.5 for j=i+1, N do

- Agentj checks compatibility of Pj with Pi and replan, if nec.

A kind of CSP: Ordering: - what heuristic?

Add exit conditionfor no solution

2.4 Distributed planning and execution2.4 Distributed planning and executionReal world: incomplete and incorrect information

a) Contingency planninga) Contingency planning Conditional planning - deals with incomplete information by

constructing a conditional plan that accounts for each possible situation or contingency that could arrive

sensing actions a context of a plan step, i.e., a union of conditions on the environment that must

hold in order for a step to be executed introduces disjunctive steps + conditional links among plan steps

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move(A,B,C)

Start

Ask Ag2 to move(A,B,C)

Checkarm(Ag1)

Finish

Negotiate with Ag2for it to achieve move

Context:armbroken(Ag1)

armbroken(Ag1) armbroken(Ag1)

on(B,A)on(A,C)

on(A,B)clear(C)clear(A)A

B C

A

C

B

… Plan to achieve on(B,A)

b) Execution monitoringb) Execution monitoring The agent does not execute the plan with "its eyes closed" - It

monitors what is happening while it executes the plan and it can do replanning to achieve a goal in a new situation

Conditional planning = thinks before to several alternatives Monitoring and replanning = defers the job; I shall see what to do if

new conditions occur

c) Social lawsc) Social laws What actions are legal to be executed in a certain context Find conflicting situations, analyze what concurrent actions lead to

these situations and prohibit such concurrent actions by social laws It is fit, in general, for loosely coupled subproblems / subplans

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3 Partial Global Planning3 Partial Global Planning Initially applied in the Distributed Monitoring VehicleDistributed Monitoring Vehicle (DVM)

Testbed, then extended to be domain independent

Integrates planning and execution

Coordination by means of partial plans exchange

Partial plans: abstract plans + partial ordering plan merging

The domain - unpredictable, unreliable information

The tasks are inherently distributed; each agent performs its own task

The agents are not aware of the global state of the system; however there is a common goal: converge on a consistent map of vehicle movements by integrating the partial tracks formed by different agents into a single complete map or into a consistent set of local maps distributed among agents

Cooperative agents (collectively motivated)

3.1 Aircraft monitoring scenario3.1 Aircraft monitoring scenario each type of aircraft produces a characteristic spectrum of acoustic frequencies

signals may be improperly sensed, there is ghosting and environmental noise

there are two agents A and B whose regions of interest overlap; each agent receives data only about its own region, from its acoustic sensor

the goal is to identify any aircraft that is moving through the region of interest, determine their types and track them through regions

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Final solutionData input

3.2 Agent functioning3.2 Agent functioning

1. Represent its own expected activity by a set of local (tentative) plans, at two levels: higher level (abstract plans) and detailed level; local plans may involve alternative actions depending on the result of previous actions and changes in the environment

conditional plans; hierarchical plans

2. Communicate abstract local plans to the other agents and get from them such plans another form of communication

3. Model collective activity of the agents by forming Partial Global Plans and finding out how they can be improved for better coordination– identify when the goals of one or more agents can be considered subgoals

of a single global goal partial global goal

– construct a PGP and identify opportunities for improved coordination

– search for an improved PGP

4. Based on 3, propose changes to one or more agents' plans

negotiation

5. Modify its local plan according to the proposal and plan what and when results will be communicated to the other agents 19

2 types of problem-solving activities: task-level activities - build a map of vehicle movements meta-level activities - decide how and with whom to coordinate

Result sharing - agents exchange appropriate results at the right time

Task sharing - allow agents to propose potential plans that involve the transfer of tasks among them

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A: Process 1/2 data Who?: Process 1/2 data

A: Process 1/3 data B: Process 1/3 data Who?: Process 1/3 data

3.3 Plan representation3.3 Plan representation

A plan represents future activity at two levels of detail: at the higher level it outlines the major steps it expects to take to

achieve its goal - abstract plan at a detailed level it specifies primitive actions to achieve the next

step in the abstract plan; as the plan is executed, new details are added incrementally

actionPrec – preconditions for the actionPost – results of the actionD - the set of data to be processed by the actionP - the set of procedures to be applied to the data

Tstart - the estimated start time of the action

Tend - the estimated end time of the actionabres - an estimate of the characteristics of and confidence in the abstract partial result that will be developed as conclusion of action

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3.4 PGP formation and coordination3.4 PGP formation and coordination(1) Task decomposition

(2) Local plan formation

(3) Local plan abstraction

(4) Communication about local abstract plans Meta-Level Organization: specifies roles and controls communication For each agent, the MLO specifies:

- the agents it has authority over

- the agents that have authority over it

- the agents that have equal authority

(5) Partial global goal identification Set of operators that generate global goals based on local goals

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(6) Partial global plan construction and modification partial global goal plan-activity-map = plan actions to be executed concurrently by itself

and the other agents, including costs and expected results of actions - PGP

Criteria for rating the actions: the action extends a partial result (vehicle tracking hypothesis) the action produces a partial result that might help some other

agents in forming partial results how long the action is expected to take

(7) Communication planning From the modified plan-activity-map, the agent builds a solution-

construction-graph = how the agents should interact, including specifications about what partial results to exchange and when to exchange them

(8) Translate to local level the activities in the revised plan

(9) If authority, send PGP to the other agents23

ReferencesReferences E.H. Durfee. Distributed problem solving and planning. In Multiagent

Systems - A Modern Approach to Distributed Artficial Intelligence, G. Weiss (Ed.), The MIT Press, 2001, p.121-164.

V.R. Lesser. A retrospective view of FA/C distributed problem solving. IEEE Trans. On Systems, Man, and Cybernetics, 21(6), Nov/Dec 1991, p.1347-1362.

E.D. Durfee, V.R. Lesser Partial global planning: A coordination framework for distributed hypothesis formation. IEEE Trans. On Systems, Man, and Cybernetics, 21(5), Sept. 1991, p.1167-1183.

K.S. Decker, V.R. Lesser. Generalizing the partial global planning algorithm. International Journal of Intelligent Cooperative Information Systems, 1(2), 1992, p. 319-346.

S. Russell, P. Norvig. Artificial Intelligence: A Modern Approach. Prentice hall, 1995, Ch. 11, 12, 13.

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