1. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 1 Chapter 6 Planning-Graph Techniques Dana S. Nau CMSC 722, AI Planning University of Maryland, Fall 2004 Lecture slides for Automated Planning: Theory and Practice

2. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 2 Motivation l A big source of inefficiency in search algorithms is the branching factor u the number of children of each node l e.g., a backward search may try lots of actions that can’t be reached from the initial state l One way to reduce branching factor: l First create a relaxed problem u Remove some restrictions of the original problem »Want the relaxed problem to be easy to solve (polynomial time) u The solutions to the relaxed problem will include all solutions to the original problem l Then do a modified version of the original search u Restrict its search space to include only those actions that occur in solutions to the relaxed problem g0g0 g1g1 g2g2 g3g3 a1a1 a2a2 a3a3 g4g4 g5g5 s0s0 a4a4 a5a5

3. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 3 Outline l The Graphplan algorithm l Constructing planning graphs u example l Mutual exclusion u example (continued) l Doing solution extraction u example (continued) l Discussion

4. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 4 Graphplan procedure Graphplan: l for k = 0, 1, 2, … u Graph expansion: »create a “planning graph” that contains k “levels” u Check whether the planning graph satisfies a necessary (but insufficient) condition for plan existence u If it does, then »do solution extraction: backward search, modified to consider only the actions in the planning graph if we find a solution, then return it possible literals in state s i possible actions in state s i relaxed problem

5. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 5 state-level i effects Maintenance actions: propagate literals to the next level. These represent what happens if no action in the final plan affects the literal. state-level i-1 state-level 0 (the literals true in s 0 ) The Planning Graph l Alternating layers of ground literals and actions u All actions that might possibly occur at each time step u All of the literals asserted by those actions action-level i preconditions

6. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 6 Example »due to Dan Weld (U. of Washington) l Suppose you want to prepare dinner as a surprise for your sweetheart (who is asleep) s 0 = {garbage, cleanHands, quiet} g = {dinner, present,  garbage} ActionPreconditions Effects cook() cleanHandsdinner wrap() quietpresent carry() none  garbage,  cleanHands dolly() none  garbage,  quiet Also have the maintenance actions: one for each literal

7. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 7 Example (continued) state-level 0: {all atoms in s 0 } U {negations of all atoms not in s 0 } l action-level 1: {all actions whose prconditions are satisfied in s 0 } l state-level 1: {all effects of all of the actions in action-level 1} ActionPreconditionsEffects cook() cleanHandsdinner wrap() quietpresent carry() none  garbage,  cleanHands dolly() none  garbage,  quiet Also have the maintenance actions  dinner  present  dinner  present state-level 0state-level 1action-level 1

8. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 8 Mutual Exclusion l Two actions at the same action-level are mutex if u Inconsistent effects: an effect of one negates an effect of the other u Interference: one deletes a precondition of the other u Competing needs: they have mutually exclusive preconditions l Otherwise they don’t interfere with each other u Both may appear in a solution plan l Two literals at the same state-level are mutex if u Inconsistent support: one is the negation of the other, or all ways of achieving them are pairwise mutex

9. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 9 Example (continued) l Augment the graph to indicate mutexes l carry is mutex with the maintenance action for garbage (inconsistent effects) l dolly is mutex with wrap u interference l ~quiet is mutex with present u inconsistent support l each of cook and wrap is mutex with a maintenance operation ActionPreconditionsEffects cook() cleanHandsdinner wrap() quietpresent carry() none  garbage,  cleanHands dolly() none  garbage,  quiet Also have the maintenance actions  dinner  present  dinner  present state-level 0state-level 1action-level 1

10. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 10  dinner  present  dinner  present Example (continued) l Check to see whether there’s a possible plan l Recall that the goal is  {  garbage, dinner, present} l Note that u All are prossible in s 1 u None are mutex with each other l Thus, there’s a chance that a plan exists l Try to find it u Solution extraction state-level 0state-level 1action-level 1

11. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 11 Solution Extraction procedure Solution-extraction(g,j) if j=0 then return the solution for each literal l in g nondeterministically choose an action to use in state s j–1 to achieve l if any pair of chosen actions are mutex then backtrack g’ := {the preconditions of the chosen actions} Solution-extraction(g’, j–1) end Solution-extraction The level of the state s j The set of goals we are trying to achieve state- level i-1 action- level i state- level i A real action or a maintenance action

12. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 12 Example (continued) l Two sets of actions for the goals at state-level 1 l Neither works: both sets contain actions that are mutex  dinner  present  dinner  present state-level 0state-level 1action-level 1

13. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 13 Recall what the algorithm does procedure Graphplan: l for k = 0, 1, 2, … u Graph expansion: »create a “planning graph” that contains k “levels” u Check whether the planning graph satisfies a necessary (but insufficient) condition for plan existence u If it does, then »do solution extraction: backward search, modified to consider only the actions in the planning graph if we find a solution, then return it

14. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 14 Example (continued) l Go back and do more graph expansion l Generate another action-level and another state-level  dinner  present  dinner  present  dinner  present state-level 0state-level 1action-level 1state-level 2action-level 2

15. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 15 Example (continued) l Solution extraction l Twelve combinations at level 4  Three ways to achieve  garb u Two ways to achieve dinner u Two ways to achieve present  dinner  present  dinner  present  dinner  present state-level 0state-level 1action-level 1state-level 2action-level 2

16. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 16 Example (continued) l Several of the combinations look OK at level 2 l Here’s one of them  dinner  present  dinner  present  dinner  present state-level 0state-level 1action-level 1state-level 2action-level 2

17. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 17 Example (continued) l Call Solution- Extraction recursively at level 2 l It succeeds l Solution whose parallel length is 2  dinner  present  dinner  present  dinner  present state-level 0state-level 1action-level 1state-level 2action-level 2

18. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 18 Comparison with PSP l Unlike PSP, Graphplan creates ground instances of everything u Many of them may be irrelevant l But the backward-search part of Graphplan—which is the hard part—will only look at the actions in the planning graph u smaller search space than PSP; thus faster

19. Dana Nau: Lecture slides for Automated Planning Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/ 19 History l Before Graphplan came out, most planning researchers were working on PSP-like planners u POP, SNLP, UCPOP, etc. l Graphplan caused a sensation because it was so much faster l Many subsequent planning systems have used ideas from it u IPP, STAN, GraphHTN, SGP, Blackbox, Medic, TGP, LPG l Several of them are much faster than the original Graphplan