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Working together Lecture outline

Multi-Agent Systems Lecture 6 University “Politehnica” of Bucarest 2005 - 2006 Adina Magda Florea adina@cs.pub.ro http://turing.cs.pub.ro/blia_06. Working together Lecture outline. 1 Coordination strategies 1 Distributed problem solving 2 Distributed planning

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Working together Lecture outline

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  1. Multi-Agent SystemsLecture 6University “Politehnica” of Bucarest2005 - 2006Adina Magda Floreaadina@cs.pub.rohttp://turing.cs.pub.ro/blia_06

  2. Working togetherLecture outline 1 Coordination strategies 1 Distributed problem solving 2 Distributed planning 3 An example: Partial global planning

  3. 1 Coordination strategies • Coordination = the process by which an agent reasons about its local actions and the (anticipated) actions of others to try to ensure the community acts in a coherent manner Coordination Self-interested agents own goals Collectively motivated agents common goals Coordination for coherent behavior Cooperation to achieve common goal Competitive conflicting goals Neutral to one another disjunctive goals 3

  4. Model • Protocol • Communication • Perfect coordination ??? • Centralized coordination • Distributed coordination • Tightly coupled interactions- distributed search • Cognitive agents– DPS (distributed planning, task sharing, resource sharing) • Heterogeneous agents- interaction protocols: Contract Net, KQML conversations, FIPA protocols • Dynamic interactions– Shared mental states, commitments and conventions • Complex interactions- organizational structure to reduce complexity • Unpredictable interactions- social laws • Conflict of interests - interaction protocols: voting, auctions, bargaining, market mechanisms, extended Contract Net, coalition formation Cooperative Neutral or competitive 4

  5. 2. Distributed problem solving • Distributed planning - the problem to be solved is to design and execute a plan in a distributed manner, by many agents – discussed here • 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 – discussed at negotiation 5

  6. 3 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 6

  7. 3.1 Planificare monoagent • Operatori de plan – planificare liniara - Actiune. - Lista Preconditiilor - Lista Adaugarilor - Lista Eliminarilor • Operatori de plan – planificare neliniara - Actiune. - Lista Preconditiilor - Lista Postconditiilor 7

  8. STRIPS – planificare liniara • Operatori de plan STACK(x,y), UNSTACK(x,y), PICKUP(x), PUTDOWN(x) • Predicate: ON(x,y), ONTABLE(x), CLEAR(x), HOLD(x), ARMEMTY • Axiome: 8

  9. Reprezentarea STRIPS • Operatori de plan LP: LE: CLEAR(y)HOLD(x) LA: ON(x,y)ARMEMPTY LP: LE: LA: PICKUP(x) LP: LE: LA: PUTDOWN (x) LP: LE: LA: 9

  10. TWEAK – planificare neliniaraReprezentare Actiune Preconditii: Postconditii: Actiune: PICKUP(x) Preconditii: Postconditii: 10

  11. TWEAK – planificare neliniara Operatii de modificare a planului: (1) adaugarea de pasi este operatia prin care se creaza noi pasi care se adauga la plan; (2) promovarea este operatia de stabilire a unei ordonari (temporale) intre doi pasi de plan; (3) legarea simpla este operatia de atribuire de valori variabilelor pentru a valida preconditiile unui pas de plan; (4) separarea este operatia de impiedicare a atribuirii anumitor valori unei variabile; (5) eliminarea destructivitatii este operatia de introducere a unui pas S3 (un pas deja existent in plan sau un pas nou) intre pasii S1 si S2, in scopul de a adauga un fapt invalidat de pasul S1 si necesar in pasul S2. 11

  12. 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) C Si A D B Sf B F A E D C E F 3.1 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 Tom Agent2 I'm Bill Agent1 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 12

  13. 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 Subplan1S3 < S2 < S1 Subplan2 S6 < S5 < S4 and S3 < S4 Agent1 S3 < send(clear(F)) < S2 < S1 Agent2 S6 < S5 < wait(clear(F)) < S4 < < 2. Decompose the plan into subproblems so as to minimize order relations across plans 3. Insert synchronization 4. Allocate subplans to agents 13

  14. < < 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 Subplan1S3 < S5 < S4 Subplan2 S6 < S2 < S1 and S3 < S2 and S6 < S5 Agent1 S3 < send(on(E,T)) , wait(clear(D)) < S5 < S4 Agent2 S6 < send(clear(D)), wait(on(E,T)) < 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 DECOMP2 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 14

  15. 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 < S1 and S5 < S4 } • Merge PAgent1 with PAgent2 by checking preconditons and threats • Establish thus order S3 < S2, S6 < S5, S3 < S4 + orderof PAgent2 • Then give any instance of this partial plan to an execution agent to carry it out 15

  16. C Si A D B Sf B F A E D C E D A F E C F B • 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 16

  17. 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 17

  18. Si E Sf E C B D F A F A B C D C A B B Negative interactions what type? • 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) } R1 S1 need_l S2 S3 Sf1 free_l R2 R3 18

  19. 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 19

  20. 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 20

  21. Hierarchical 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, j=1,N, ji 2.2 Agenti gets Gj, Pj from Agentj, j=1,N, ji 2.3if Pi is compatible with {Pj}, j=1,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 i=1,N-1, cf. ordering do 6.1 make Agenti the current superior 6.2 Agenti determines conflicts between {Pi} 6.3if 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 6.5for 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 condition for no solution 21

  22. A A C C B B 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) armbroken(Ag1) Ask Ag2 to move(A,B,C) 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) 22

  23. 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 23

  24. 3 Partial Global Planning • Initially applied in the Distributed Monitoring Vehicle (DVM) Testbed • 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) 24

  25. 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 • 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 Final solution Data input 25

  26. 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 26

  27. A: Process 1/2 data Who?: Process 1/2 data 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 27

  28. 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 28

  29. 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 29

  30. (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 • PGP – hill-climbing algorithm • Criteria for rating the actions (eval function): • 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 30

  31. Algorithm for PGP plan step reordering • For the current ordering, rate individual actions and sum the rating • For each action, examine the later actions for the same agent and find the most highly rated one. If it is higher rated, then swap the actions • If the new ordering is more highly rated than the current one, then replace the current ordering with the new one and Go to step 2 • Return the current ordering 31

  32. (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 32

  33. 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. 33

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