Hierarchical Task Network (HTN) Planning

1. Hierarchical Task Network (HTN) Planning Hai Hoang 4/17/2007

2. Reminder • JSHOP and JSHOP2 come with some sample domain files. • You CANNOT use those files. • Need to write your own.

3. HTN vs Classical • Like classical planning: • Each state of the world is represented by a set of atoms • Each action corresponds to a deterministic state transition • (block b1) (block b2) (block b3) (block b4) (on-table b1) (on b2 b1) (clear b2) (on-table b3) (on b4 b3) (clear b4)

4. HTN vs Classical • Differs: • Objective: to perform a set of tasks not a set of goals • Terms, literals, operators, actions, plans have same meaning as classical planning. • Added tasks, methods, task networks • Tasks decompose into subtasks • Constraints • Backtrack if necessary

5. Shows the order plan will be executed later Decomposition Non-primitive task method instance precond Non-primitive task primitive task primitive task operator instance operator instance precond effects precond effects s0 s1 s2

6. Tasks vs Control Rules • We saw control rules – actions NOT to consider • HTN – actions and tasks to consider

7. Control Rules • Classical planning efficiency suffers from combinatorial complexity (intractable) • Prune function detects and cuts unpromising nodes • Can improve solving: exponential to polynomial • Φ1(c,d,p) = [GOAL(in(c,p))  q GOAL(in(c,q))]  [GOAL(on(c,d)  e GOAL(on(c,e))] • No goal requiring c in another pile or on top of something else (prune if exist?) • Holds if acceptable when container c is on item d in pile p By: Steve Lee-Urban

8. Only pick up if x is on top HTN • Instead of detecting and cutting unpromising nodes • HTN methods are only applied only when the preconditions are satisfied. (:method (pick-up ?x)((clear ?x)) ((!pick-up ?x)) )

9. D1 D2 D3 D1 D2 D3 P1 P2 P3 P Domain Planner Planning procedures Domain • Domain dependent – Bridge Baron game • Domain independent – SHOP

10. HTN • Domain consists of • methods and operators (SHOP- axioms) • Problem consists of • domain, initial state, initial task network (tasks to accomplish, with some ordering of the tasks defined) • Solution • A plan: Totally ordered collection of primitive tasks (SHOP) • General HTN planner - partially ordered collection of primitive tasks.

11. TASK • Task: an expression of the form t(u1,…,un) • t is a task symbol, and each ui is a term (variable, constant, function expression (f t1 t2 tn) • (move-block ?nomove) • (move-block (list ?x . ?nomove)) • Two types of task • Non-primitive (compound) – decomposed into subtasks. • Primitive – cannot be decomposed, know how to perform directly (task name is the operator name). • (!drive-truck ?truck ?loc-from ?loc-to)

12. Methods and Operators • Defined a little differently in the textbook, but we’re more concerned with coding it in SHOP so forget the book for now (book notations later on). • Explain both with an example instead of notations. • Spent a good amount of time arranging the next slide • Help to visualize how they map to a real shop method or operator. • method as defined by SHOP (see manual) (:method h [n1] C1 T1[n2] C2 T2 … [nk] Ck Tk) • h method head – task atom with no call terms • [n1] OPTIONAL name for succeeding Ci Ti pair • C1 conjunct or tagged conjunct? Precondition list?? • T1 task list • Operator (:operator h P D A) • h head – primitive task atom with no call terms • P precondition list (logical atoms) • D delete list (logical atoms) • A add list (logical atoms)

13. Non prim preconditions Primitive task Subtasks list preconditions prim task delete list Add list Operators and Methods • Method ( decomposes into subtasks) (:method (drive-truck ?truck ?loc-from ?loc-to) ((same ?loc-from ?loc-to)) ((!do-nothing)) () ((!drive-truck ?truck ?loc-from ?loc-to))) • Notice the if else structure • Invoke non-primitive task: (drive-truck ?t ?x ?y) • Operator (achieves PRIMITIVE TASKS) (:operator (!drive-truck ?truck ?locfrom ?locto) () ((truck-at ?truck ?locfrom)) ((truck-at ?truck ?locto))) Invoke primitive task: (!drive-truck ?t ?l1 ?l2)

14. Review • Relationship between non-primitive tasks and methods • Decomposed by applying a method • Relationship between primitive tasks and operators • Primitive task is achieved by applying an operator • Important that you understand this!!!

15. STN and HTN • STN – Simple Task Network (simplified version of HTN) • TFD – Total-order Forward Decomposition (used in SHOP) • Example later Input: tasks are totally ordered Output: totally ordered plan • PFD – Partial-order Forward Decomposition (SHOP2) • Example later Input: tasks are partially ordered Output: totally ordered plan • HTN – generalization of STN • More freedom about how to construct the task networks. • Can use other decomposition procedures not just forward-decomposition. • Like Partial-order planning combined with STN Input: partial-order tasks Output: The resulting plan is partially ordered

16. Task Network • STN w = (U, E) - an acyclic graph U – set of task nodes E – set of edges • HTN w = (U, C) U – set of task nodes C – set of constraints (allow for generic task networks). Different planning procedures.

17. STN • STN method: 4-tuple m = (name(m), task(m), precond(m), subtasks(m)) • name(m): an expression of the form n(x1,…,xn) • n – name of the method – method symbol • x1,…,xnare parameters - variable symbols • task(m): a nonprimitive task • task that this method could apply to • In SHOP, the task is the head of the method. • precond(m): preconditions (literals) • subtasks(m): a sequenceof tasks t1, …, tk do-nothing(p,q) task: move-stack(p,q) precond: top(pallet,p) subtasks: ()

18. Pseudo-code for TFD Applying an operator Changing the state Randomly pick an applicable method Decompose method into tasks

19. DWR • Move the containers, preserving ordering • Use loc1 as example.

20. Total Order Tasks (SHOP- STD)

21. Example TFD Goal: move-each-twice Move-stack(p1a, p1b) Move-stack(p1b, p1c) Stack 2 and 3 empty.

22. Partially Ordered tasks (SHOP2 - PFD)

23. PFD Example

24. TFD & PFD • STN doesn’t allow parallel execution, but can interleave steps (PFD) • At the end the resulting plan is totally ordered (both TFD & PFD)

25. SHOP & SHOP2 • SHOP: Simple Hierarchical Ordered Planner • SHOP is basically TFD STN • SHOP2 is PFD STN – mainly with the addition of the unordered keyword for the task list. Note: resulting plan is still a totally-ordered task list.

26. Prefix Notation • Domain and problem file are in Lisp like format. • 7 + 3 • (+ 7 3) • p(a,?x) -> (p a ?x) • Any volunteer? p(f (a,b), ?y) • Answer: (p (f a b) ?y) • (call + 3 7)

27. Axioms (Horn clauses) • (:- a C1 C2 C3 … Cn) • a is true if C1 is true, else if C1 is false and C2 is true, or else if C1 to Cn-1 is false and Cn is true. • (:- (same ?x ?x) nil) • (same 5 5) • (same 5 7)

28. Above Example • (:- (above ?a ?b) ((on ?a ?b))) • (:- (above ?a ?b) ((on ?a ?c) (above ?c ?b))) • S0 = (on 1 2) (on 2 3) (on 3 4) • Is (above 1 4) true? • (on 1 2) (above 2 4) • (on 1 2) (on 2 3) (above 3 4) • (on 1 2) (on 2 3) (on 3 4) • When all conjuncts are true, (above 1 4) is true.

29. JSHOP • Domain file: operators, methods, axioms • Problem file: initial state, initial task list (goals) • On Vega in /home/hah3/jshop • To run one of the sample problem java umd.cs.shop.JSJshop logistic/logistic.shp logistic/Log_ran_problems_10.shp 1 all > output.txt java –jar shop.jar logistic/logistic.shp logistic/Log_ran_problems_10.shp 1 all > output.txt java umd.cs.shop.JSJshop domainfile problemfile logLevel numofplan

30. For reference: • JSHOP manual in the jshop directory • http://www.cs.umd.edu/~nau/papers/shop-ijcai99.pdf • Contact me hah3@lehigh.edu