1. Planning and Scheduling

2. 2 USC INFORMATION SCIENCES INSTITUTE Some background Many planning problems have a time-dependent component –  actions happen over time intervals,  goals have time windows when they should be achieved  Need to synchronize with other agents Normal Situation calculus, STRIPS, etc. don’t support this very well Planners choose actions to achieve goals. Picking a time line is typically seen as scheduling

3. 3 USC INFORMATION SCIENCES INSTITUTE Handling time in planners How should we model temporal problems Do we need new planning algorithms or will modifications on others be enough? Can we plan first, then schedule? Should the two be merged?

4. 4 USC INFORMATION SCIENCES INSTITUTE Different time-related issues in planning If actions take different time intervals, partial-order planners must account for this Actions with continuous effects – e.g. drive truck from LA to San Francisco Concurrent/simultaneous actions – may have different effects or preconditions

5. 5 USC INFORMATION SCIENCES INSTITUTE Actions with continuous effects Drive from LA to SF takes 5 hours. Location changes continuously If the action gets interrupted – e.g. need to recall the truck 1 hour later. Where is it? Some approaches: situation calculus with differential equations for the state, event calculus.

6. 6 USC INFORMATION SCIENCES INSTITUTE Concurrent actions Synergy: to open the door, hold handle down and pull simultaneously – neither action achieves anything alone Interference: if two actions require the same resource (e.g. a spanner), cannot both take place simultaneously

7. 7 USC INFORMATION SCIENCES INSTITUTE Generalizing STRIPS STRIPS action: if preconds hold in current situation, can apply action ‘now’, and effects hold in ‘next’ situation. If action takes place over an interval – should preconds hold just when the action starts? Throughout the interval? When do the effects take place?

8. 8 USC INFORMATION SCIENCES INSTITUTE Temporal Graph Plan Consider the question: can we use Graphplan ideas for temporal planning? What are the problems, if actions have different durations?

9. 9 USC INFORMATION SCIENCES INSTITUTE TGP action model STRIPS actions, plus start time, end time, duration All preconds must hold at the start Preconds not affected by the action must hold throughout execution Effects are undefined during execution and only hold at the final time point

10. 10 USC INFORMATION SCIENCES INSTITUTE Temporal planning graph Propositions and actions monotonically increasing Mutexes monotonically decreasing Nogoods are monotonically decreasing So..

11. 11 USC INFORMATION SCIENCES INSTITUTE Cyclic planning graph Earliest start time

12. 12 USC INFORMATION SCIENCES INSTITUTE Distinguishing mutex conditions Some mutexes are always true – eternal Some can become false – conditional Action/Proposition mutex

13. 13 USC INFORMATION SCIENCES INSTITUTE

14. 14 USC INFORMATION SCIENCES INSTITUTE Propagating mutexes Can maintain which are conditional or eternal mutexes: Note: these are temporal conditions, essentially on when instances of A and P can coexist

15. 15 USC INFORMATION SCIENCES INSTITUTE Solution extraction

16. 16 USC INFORMATION SCIENCES INSTITUTE Dealing with uncountable choices.. The algorithm makes every action take place as late as possible by using persistence ONLY when nothing else would work.

17. 17 USC INFORMATION SCIENCES INSTITUTE Approximating mutex conditions Checking disjunctions can be expensive, so try to maintain a form like

18. 18 USC INFORMATION SCIENCES INSTITUTE Conclusions Can extend mutex reasoning to temporal case But it’s not easy!

19. 19 USC INFORMATION SCIENCES INSTITUTE ASPEN Combine planning and scheduling steps as alternative ‘conflict repair’ operations Activities have start time, end time, duration Maintain ‘most-commitment’ approach – easier to reason about temporal dependencies with full information  C.f. TLPlan

20. 20 USC INFORMATION SCIENCES INSTITUTE Temporal constraints

21. 21 USC INFORMATION SCIENCES INSTITUTE Activity decompositions

22. 22 USC INFORMATION SCIENCES INSTITUTE Conflict types

23. 23 USC INFORMATION SCIENCES INSTITUTE Contributors for a non-depletable resource violation

24. 24 USC INFORMATION SCIENCES INSTITUTE Contributors for a depletable resource violation

25. 25 USC INFORMATION SCIENCES INSTITUTE Domain-independent heuristics Prefer to solve conflicts that require new activities, then timeline conflicts To repair a conflict, prefer moving activities, then adding a new activity Try to solve conflicts while introducing as few others as possible

26. 26 USC INFORMATION SCIENCES INSTITUTE Conclusions Successfully integrates planning and scheduling Does it do so in the most profitable way? What can we say about guarantees for the algorithm?