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Temporal Planning and Resource Allocation

Temporal Planning and Resource Allocation. Stefanie Chiou, Rob Kochman, and Gary Look. Running Plans in the Real World. Need to account for time and resources when creating plans Papers featured:

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Temporal Planning and Resource Allocation

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  1. Temporal Planning and Resource Allocation Stefanie Chiou, Rob Kochman, and Gary Look

  2. Running Plans in the Real World • Need to account for time and resources when creating plans • Papers featured: • "Executing Reactive, Model-Based Programs through Graph-Based Temporal Planning" by Phil Kim, Brian C. Williams, and Mark Abramson (IJCAI ’01) • "Managing Multiple Tasks in Complex, Dynamic Environments" by Michael Freed (AAAI ’98).

  3. Paper • Executing Reactive, Model-based Programs through Graph-based Temporal Planning by Phil Kim, Brian Williams, and Mark Abramson

  4. Familiar Examples Mars Climate Orbiter: 12/11/98 Mars Polar Lander: 1/3/99

  5. Motivation • Embedded programming is hard • Easier to reason about state when programming

  6. Overview/Contributions • RMPL provides a new programming paradigm for programming robust systems of cooperative autonomous agents • TPN -> synthesis of temporal, causal link, and HTN planning • A “holy grail” for autonomous agents • Planner that implements these ideas

  7. RMPL Intro • RMPL supports four types of reasoning about system interactions • reasoning about contingencies • scheduling • inferring hidden state • controlling hidden state • This paper focuses on first two interaction types

  8. (Model-based) Embedded Programs Embedded Program Model-basedEmbedded Program Obs Cntrl S Plant S Plant • Embedded programs interact withplant sensors/actuators: • Read sensors • Set actuators • Model-based programs interact with plant state: • Read state • Write state setState getState Programmer must map between state and sensors/actuators. Model-based executive maps between sensors, actuators to states.

  9. Model-based Embedded Program Breakdown Model-basedEmbedded Program setState getState Model-based executive maps between sensors, actuators to states. Model-based Executive Sensor data Actuator commands S Plant

  10. Example: The model-based program sets engine = thrusting, and the deductive controller . . . Deduces that thrust is off, andthe engine is healthy Plans actions to open six valves Deduces that a valve failed - stuck closed Determines that valves on the backup enginewill achieve thrust, andplans needed actions. Oxidizer tank Fuel tank

  11. Time and Contingency Constructs in RMPL • if c thennext A • do A maintaining C • A,B (concurrency) • A;B (serialization) • A[l,u] (temporal bounds) • Choose{A,B} (choose)

  12. Path 2 A Path 1 B Choosing a route from A to B RMPL Code Example Group-Enroute()[l,u] = { choose { do { Group-Fly-Path(PATH1) [l*90%,u*90%]; } maintaining PATH1_OK, do { Group-Fly-Path(PATH2) [l*90%,u*90%]; } maintaining PATH2_OK }; { Group-Transmit(FAC,ARRIVED_TAI)[0,2], do { Group-Wait(TAI_HOLD1,TAI_HOLD2)[0,u*10%] } watching PROCEED_OK } }

  13. RMPL’s Representation of Time and Contingencies • Important to find a plan quickly • Idea: use a plan graph • Generalization of Simple Temporal Network (STN) • TPN defined (STN + conditionals + choices)

  14. STN example Start End

  15. Temporal Planning Networks (TPN) • A temporal planning network is just a generalization of a STN • Includes ability to represent conditionals and choices

  16. Ask(Proceed=Ok) TPN Example

  17. RMPL -> TPN conversion • A [l,u]: invoke activity A between l and u time units

  18. RMPL -> TPN conversion • c [l,u]: Assert that condition c is true now until [l ,u]

  19. RMPL -> TPN conversion • Ifc thennextA [l,u]: Execute A for [l ,u], if condition c is currently satisfied

  20. RMPL -> TPN conversion • doA [l,u] maintaining c : Execute A for [l ,u], and ensure that condition c holds throughout

  21. RMPL -> TPN conversion • A [l1,u1], B [l2,u2] : Concurrently execute A for [l1,u1], and B for [l2,u2]

  22. RMPL -> TPN conversion • A [l1,u1]; B [l2,u2] : Execute A for [l1,u1], and then B for [l2,u2]

  23. RMPL -> TPN conversion • choose {A [l1,u1]; B [l2,u2]} : Reduces to A [l1,u1] or B [l2,u2] non-deterministically

  24. Kirk • Compiles RMPL program into a TPN • Searches TPN for a temporally consistent plan • Temporally consistent plan is “embedded” into the TPN.

  25. Kirk Phase1 • Select plan from TPN • Essentially a graph traversal • Check plan for temporal consistency Start

  26. Selecting the Plan Start Start

  27. Checking for Temporal Consistency • Convert TPN to a distance graph • Run Bellman-Ford to check for negative cycles (if any found, inconsistent)

  28. [30,40] 40 2 1 2 1 [10,20] 20 -30 [10,20] 0 -10 20 0 -10 [40,50] 3 4 50 3 4 70 -40 [60,70] -60 Converting TPNs to Distance Graphs • The interval [aij,bij] represents the statement: aij ≤Tj-Ti ≤bij • This is equivalent to: Tj-Ti ≤bij and Ti-Tj ≤-aij

  29. Checking for Temporal Consistency • Convert TPN to a distance graph • Run Bellman-Ford algorithm to check for negative cycles:

  30. Bellman-Ford Algorithm initializeCosts(G, s) for i=1 to |V(G)|-1 for each edge (u,v) in E(G) updateCost(u, v, w) for each edge (u, v) in E(G) if cost(v) > cost(u) + w(u. v) return false return true

  31. 40   20 -30 -10 20 0 -10 50   70 -40 -60 Bellman-Ford Example Source

  32. 40  20 20 -30 -10 20 0 -10 50   70 -40 -60 Bellman-Ford Example Source

  33. 40 60 20 20 -30 -10 20 0 -10 50   70 -40 -60 Bellman-Ford Example Source

  34. 40 60 20 20 -30 -10 20 0 -10 50 50  70 -40 -60 Bellman-Ford Example Source

  35. 40 60 20 20 -30 -10 20 0 -10 50 50 100 70 -40 -60 Bellman-Ford Example Source

  36. 40 60 20 20 -30 -10 20 0 -10 50 50 70 70 -40 -60 Bellman-Ford Example Source

  37. 40 60 20 20 -30 -10 20 0 -10 50 30 70 70 -40 -60 Bellman-Ford Example Source

  38. 40 50 20 20 -30 -10 20 0 -10 50 30 70 70 -40 -60 Bellman-Ford Example Source

  39. Kirk Phase 2 • Resolve threats and open conditions • Analogous to threats and open conditions in causal link planning • Identify intervals of inconsistent constraints using Floyd-Warshall • Order intervals to resolve threats • Close open conditions by making sure open conditions satisfied by some action in the plan

  40. Why This Paper? • It’s useful for our term project

  41. Vision • "Managing Multiple Tasks in Complex, Dynamic Environments" by Michael Freed (AAAI ’98). • Achieve goals in “task environments” • Complex • Time-pressured • Uncertain • Co-existing/Interacting

  42. APEX Goal: ATC • Goal: simulate human air traffic controllers • Largely routine activity • Complexity due to many simple tasks • Interruptions necessary

  43. APEX Goal: ATC

  44. APEX Goal: ATC

  45. APEX Goal: ATC

  46. Resource Conflicts • Separate tasks make incompatible demands • What to do? • Determine relative priority of tasks • Assign control to winner • Deal with the loser

  47. Conflict Resolution Strategies • Shed • Eliminate low importance tasks • When (Demand > Availability) • Delay/Interrupt • Introduces complications • Circumvent • Select methods that use different resources

  48. APEX Architecture: Two Parts • Resource Architecture • Set of resources • Cognitive • Perceptual • Motor • Action Selection Component Action Selection Component commands events Resource Architecture perception actuators World

  49. Procedure Definition Language (PDL) Example: Turning on headlights

  50. Procedure Definition Language (PDL) (procedure (index (turn-on-headlights) (step s1 (clear-hand left-hand)) (step s2 (determine-loc headlight-ctl => ?loc)) (step s3 (grasp knob left-hand ?loc) (waitfor ?s1 ?s2)) (step s4 (pull knob left-hand 0.4) (waitfor ?s3)) (step s5 (ungrasp left-hand) (waitfor ?s4)) (step s6 (terminate) (waitfor ?s5))) Example: Turning on headlights

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