Title: MultiAgent Systems Lecture 7 University Politehnica of Bucarest 2004 2005 Adina Magda Florea adinacs
1Multi-Agent SystemsLecture 7 University
Politehnica of Bucarest2004 - 2005Adina
Magda Floreaadina_at_cs.pub.rohttp//turing.cs.pub
.ro/blia_2005
2Distributed problem solving and planningLecture
outline
- 1 Distributed problem solving
- 2 Distributed planning
- 2.1 Centralized planning for distributed plans
- 2.2 Distributed planning for centralized plans
- 2.3 Distributed planning for distributed plans
- 2.4 Distributed planning and execution
- 3 An example Partial global planning
31. Distributed problem solving
- Group coherence - agents want to work together -
cooperative agents - Competence - 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
3
42 Distributed planning
- What can be distributed
- The process of coming out with a plan is
distributed among agents - Execution is distributed among agents
- Planning
- 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 ? Search
4
5- 2.1 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)
I'm Bill Agent1
I'm Tom Agent2
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)
1. Given a goal description, a set of
operators, and an initial state
description generate a partial order plan
5
6- S1 move(B,T,A) To satisfy the preconditions,
we have - S2 move(A,B,E) S2 lt S1, S3 lt S4
- S3movetotable(E,F) S6 lt S4, S6 lt S5
- S4 move(F,T,D) Also
- S5 move(D,T,C) S2 threat to S3 ? S3 lt S2
- S6 movetotable(C,D) S4 threat to S5 ? S5 lt S4
- Then the partial ordering is S3 lt S2
lt S1 - S6 lt S5 lt S4
- S3 lt 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 lt S2 lt S1
- Subplan2 S6 lt S5 lt S4
- and S3 lt S4
- Agent1 S3 lt send(clear(F)) lt S2 lt S1
- Agent2 S6 lt S5 lt wait(clear(F)) lt S4
lt
lt
2. Decompose the plan into subproblems so as to
minimize order relations across plans 3. Insert
synchronization 4. Allocate subplans to agents
6
7- 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 lt S5 lt S4
- Subplan2 S6 lt S2 lt S1
- and S3 lt S2 and S6 lt S5
- Agent1 S3 lt send(don't_care(E)) lt wait(clear(D))
lt S5 lt S4 - Agent2 S6 lt wait(don't_care(E)) lt wait(clear(D))
lt S2 lt S1 - Obviously, DECOMP2 has more order relations among
subplans than DECOMP1 - Therefore, we choose DECOMP1
- S3 lt send(clear(F)) lt S2 lt S1
- S6 lt S5 lt wait(clear(F)) lt S4
- But
- then back to DECOMP2
lt
lt
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 how to move only D, E, F
I know how to move only A, B, C
7
8- 2.2 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 lt S1 and S5 lt S4
- Merge PAgent1 with PAgent2 by checking
preconditons and threats - Establish thus order S3 lt S2, S6 lt S5, S3 lt S4
order of PAgent2 - Then give any instance of this partial plan to an
execution agent to carry it out
8
9- 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
9
10- 2.3 Distributed planning for distributed plans
- a) 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
10
11- 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 S1move(B,T,A) lt S2 pick_lifter lt S3
movehigh(E,T,B) - Agent2 R1move(C,T,D) lt R2 pick_lifter lt R3
movehigh(F,T,C)
Negative interactions what type?
R1
S1
need_l
S2
S3
Sf1
free_l
R2
R3
11
12Positive interactions
- Give examples of positive interactions
- redundant
- favor
- Problems with the approach?
- b) 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
12
13- c) 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
Edit content
Read references
Organize ideas
Edit text
..
Find editor
Check for errors
Edit figures
13
14Hierarchical behavior-space search
algorithm 1. 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, j1,N, j?i 2.2 Agenti gets
Gj, Pj from Agentj, j1,N, j?i 2.3 if Pi is
compatible with Pj, j1,N, j?i 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 i1,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 Agenti1, , AgentN (c) go
to step 2 6.4 send Pi to each Agentj, ji1,
N 6.5 for ji1, N do - Agentj checks
compatibility of Pj with Pi and replan, if nec.
- A kind of CSP
-
- Ordering
- - what heuristic?
Add exit condition for no solution
14
15- 2.4 Distributed planning and execution
- Real world incomplete and incorrect information
- a) 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
Start
on(A,B)?clear(C)?clear(A)
Checkarm(Ag1)
Ask Ag2 to move(A,B,C)
?armbroken(Ag1)
armbroken(Ag1)
move(A,B,C)
Context ?armbroken(Ag1)
Negotiate with Ag2 for it to achieve move
Plan to achieve on(B,A)
Finish
on(B,A)?on(A,C)
15
16- b) 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 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
16
173 Partial Global Planning
- Initially applied in the Distributed 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)
17
18- 3.1 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
Data input
Final solution
18
19- 3.2 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
20- 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
A Process 1/3 data
B Process 1/3 data
Who? Process 1/3 data
20
21- 3.3 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 - action
- Prec preconditions for the action
- Post results of the action
- D - the set of data to be processed by the
action - P - 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 action
- abres - an estimate of the characteristics of
and confidence in the abstract partial result
that will be developed as conclusion of action
21
22- 3.4 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
22
23- (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 agents
23
24- References
- 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.
24