Forward-Planning. - Can be used with Strips or Situation Semantics

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1 CSE560 Class 14: 1 P. Heeman, 2010 Planning Summary Strips: - Ations speified with preonditions, add and delete list - Ations are not part of the logi Situation Semantis: - Add situation variables to derived and primitive relations - do funtion takes ation + situation, points to new situation - poss prediate defines situations in whih an ation is possible - Primitive prediates have + hange axioms whih state when they start being true + frame axiosms whih state when they ontinue to be true + Both are ondition on what ation just ourred CSE560 Class 14: 2 P. Heeman, 2010 Continued Planning as Resolution - Sine Situation Semantis entirely expressed in logi, an use theorem prover to find situation in whih goal is true + Representation of situation with do funtion gives plan - Not very effiient even with breadth-first searh + Interation between subgoals means a lot of baktraking Forward-Planning - Can be used with Strips or Situation Semantis - with initial world in frontier, find worlds that an be reahed by performing an ation - Need to do breadth-first searh, due to yles CSE560 Class 14: 3 P. Heeman, 2010 Overview Bakward Strips Planner Improvements POP Algorithm Example

2 CSE560 Class 14: 4 P. Heeman, 2010 Bakward Strips Planner Can do bakward searh from goal - Don t have to blindly searh for world where goal is true - Find ations to make goal true Strips Planner input: goal-list Goals, initial world W output: list of ations P, final world plan = [] while Goals: G = Goals[0] Goals = Goals[1:] if G is not true in W find ation A whose effet ahieves G add A to beginning of plan all planner on preonditions of A with W returning plan P and world W append P to end of plan P, append A to end of plan P set W to W apply add/delete list of A to W CSE560 Class 14: 5 P. Heeman, 2010 Example Blok World: stak(c,a) move blok C from on table to ontop of A unstak(c,a) move blok C from ontop of A onto table - initial world: ontable(a), on(,a), ontable(b) Goal: on(a,b) and on(b,) a b Sussman Anomoly CSE560 Class 14: 6 P. Heeman, 2010 Interations Planning for on(a,b) on(b,) - Stak a onto b, requires unstaking from a first - Stak b onto, requires unstaking a from b first - Final plan is unstak(,a) stak(a,b) unstak(a,b) stak(b,) If we swith the order of the goals: - Stak b onto, no preonditions - Stak a onto b + Must first have a lear, unstak a + Must first have lear, unstak b - Final plan is stak(b,) unstak(b,) unstak(,a) stak(a,b) Subgoals an have interations - Subsequent ations an undo previously ahieved goals - Planning for eah subgoal individually is problemati

3 CSE560 Class 14: 7 P. Heeman, 2010 Bakward Strips Planner Improvements POP Algorithm Example Overview CSE560 Class 14: 8 P. Heeman, 2010 Improvement 1: Clobberers Clobberers: - Say ationain partial plan has preondition - We might have planned forto be true sine true in initial world - We might later add an ation beforeawith effet More general ase - We added ationbto ahievefora - We add in ationj betweenbandawith effet Lets remember why ations are added in! - Don t allow subsequent ations to be lobberers Russell and Norvig, Artiifial Intelligene: A Modern Approah, 1995 has an exellent writeup of this approah. CSE560 Class 14: 9 P. Heeman, 2010 Causal Links Keep trak of why ations were added to plan Example: two ausal links - stak added to plan to ahieve on(a,b) - lear(a) of on(a,b) to be done by initial We an add a new ation anywhere, as long as doesn t violate existing ausal links Causal links: - Give ations a name (e.g. a1, a2, et) - Reord preondition, ation that needs it & ation that establishes it Keep both ausal links and ation list Causal Link lear(a) lear(a) lear(b) ontable(a) stak(a,b) on(a,b)!lear(b) Causal Link on(a,b)

4 CSE560 Class 14: 10 P. Heeman, 2010 Improvement 2: Partial Order Do we need to deide full ordering of ations when planning? For forward planners (initial word to goal state) - We needed to hek if ation is true in the urrent world For regressive planners with ausal links - Why not allow new ations to go anywhere, rather than always at front Let s inlude ordering onstraints - Minimum restritions on where ations an go - Causal link implies an ordering onstraint - If new ation potentially violates a ausal link, add ordering onstraint CSE560 Class 14: 11 P. Heeman, 2010 Example Putting on shoes and soks - Ations: right, left, right, left - Partial plan speifies right before right and left before left Note ompatness by not ommitting to ordering How many linearizations are there for this plan? Partial Order Plan: On On On, On CSE560 Class 14: 12 P. Heeman, 2010 Totally Ordered Total Order Plans:

5 CSE560 Class 14: 13 P. Heeman, 2010 Bakward Strips Planner Improvements POP Algorithm Example Overview CSE560 Class 14: 14 P. Heeman, 2010 Partial Order Planners Path of least ommittment - Don t deide ordering until neesary (make sure there is a solution) with a simple inomplete plan - Find unahieved preondition - Add ation (or reuse ation already in plan) to ahieve preondition - Add ausal link - When lobberer (fig a), add ordering onstraint to make fig b or fig S 1 S 3 L S 1 S 3 L S 1 S 2 S 2 S 2 S 3 L (a) (b) () CSE560 Class 14: 15 P. Heeman, 2010 Representation A plan is a data struture onsisting of - A set of plan stepss 1...S n + Eah step of form Name:step(Head,Effet,Preonditions) + Name bound to a unique identifier so that we an ensure we an uniquely refer to eah step - A set of ordering onstraints, e.g. S i S j,s i befores j + Just keep ordering onstraints of the step names - A set of ausal links, e.g. S i S j : S i ahievesfors j + reord the purposes of eah step: a purpose of S i is to ahieve the preondition ofs j

6 CSE560 Class 14: 16 P. Heeman, 2010 Initial and Final Plans Initial Plan - Steps start:step(start,initial world state,null) finish:step(finish,null,goal) - Orderings: {start finish} - Links: {} Final plan: need not be fully ordered - Why arbitrarily hoose one solution over another - Some agents an perform ations in parallel - Plan might be a subplan of a bigger plan At(Home) Sells(SM,Banana) Sells(SM,Milk) Sells(HWS,Drill) Have(Drill) Have(Milk) Have(Banana) At(Home) CSE560 Class 14: 17 P. Heeman, 2010 Complete Consistent Plans Complete: - Every preondition of every step ahieved by some step - A steps i ahieves a preonditionof steps j if +S i S j and effets(s i) + There is no lobbering step S k suh that effets(s k), where S i S k S j in some linearization of the plan - Note: must hek all possible linearizations of the plan - Reason about onsisteny of set of time points Inomplete: - not all preonditions ahieved Consistent: - No ontraditions in the ordering CSE560 Class 14: 18 P. Heeman, 2010 Algorithm Always work from a onsistent plan with no lobberers CHOOSE an unahieved preondition CHOOSE effet of an existing step to ahieve it - Add ausal link and ordering onstraint OR CHOOSE a new step S j to ahieve preondition - Add ausal link and ordering onstraint Resolve threats - For ANY CLOBBERERS to any ausal links i S j + DEMOTE: make S preede S i + PROMOTE: make S ome after S j Repeat until omplete, baktrak on failure

7 CSE560 Class 14: 19 P. Heeman, 2010 Bakward Strips Planner Improvements POP Algorithm Example Overview CSE560 Class 14: 20 P. Heeman, 2010 Example Add buy ations to ahieve the three goals: have milk, bread & drill - Note ordering onstraints fore all ations to be after start At(s), Sells(s,Drill) At(s), Sells(s,Milk) At(s), Sells(s,Bananas) Buy(Drill) Buy(Milk) Buy(Bananas) Have(Drill), Have(Milk), Have(Bananas), At(Home) Add ausal links from initial state to sells preonditions At(HWS), Sells(HWS,Drill) At(SM), Sells(SM,Milk) At(SM), Sells(SM,Bananas) Buy(Drill) Buy(Milk) Buy(Bananas) Have(Drill), Have(Milk), Have(Bananas), At(Home) CSE560 Class 14: 21 P. Heeman, 2010 Example Continued - Add go(hws) to satisfy preondition on buy(drill) and go(sm) for buy(milk) - Not shown here are the at(x) effets of go - Any lobberers yet? At(x) Go(HWS) At(x) Go(SM) At(HWS), Sells(HWS,Drill) At(SM), Sells(SM,Milk) At(SM), Sells(SM,Bananas) Buy(Drill) Buy(Milk) Buy(Bananas) Have(Drill), Have(Milk), Have(Bananas), At(Home)

8 CSE560 Class 14: 22 P. Heeman, 2010 Variables When hoosing an ation, don t need to instantiate all variables - Example: Choose move(a,b,c) to ahieve on(a,x,), but don t are what B is Wait with instantiating B until we have to Hene, fewer ation instanes to onsider Don t have to distinguish between move(a,d,) and move(a,e,), et Use variable onstraints, like Prolog - On baktraking need to undo variable onstraints, like Prolog - Can use Prolog s variable substitutions Could imagine more ompliated onstraints - Don t allow variable to be bound with something - Only allow value to be from a speified set CSE560 Class 14: 23 P. Heeman, 2010 Variables and Threats After adding first ausal link, we have at(x) as an effet and at(home) as a ausal link Should this be onsidered a threat? Approahes: - Add onstraintx home, not easy in Prolog - Consider threat if unifiable at(x) = at(home) + Will this still give us a omplete algorithm? - Consider threat if exat math at(x) == at(home) + After any operation that bind variables, need to hek for lobberers CSE560 Class 14: 24 P. Heeman, 2010 Example Continued - Add ausal link for at(home) for go(hws). Any lobberers? - Add ausal link for at(home) for go(sm). Any Clobberers? At(Home) Go(HWS) At(Home) Go(SM) At(HWS), Sells(HWS,Drill) At(SM), Sells(SM,Milk) At(SM), Sells(SM,Bananas) Buy(Drill) Buy(Milk) Buy(Bananas) Have(Drill), Have(Milk), Have(Bananas), At(Home)

9 CSE560 Class 14: 25 P. Heeman, 2010 Example Continued If we used at(home) from start node to satisfy the preondition of go(hws), we an t use it for go(sm) Other options for at(x) preondtion of go(sm) are - Introdue another go ation - Use effet of go(hws) At(Home) Go(HWS) At(HWS), Sells(HWS,Drill) At(SM), Sells(SM,Milk) At(SM), Sells(SM,Bananas) Buy(Drill) Buy(Milk) Buy(Bananas) Have(Drill), Have(Milk), Have(Bananas), At(Home) At(HWS) Go(SM) At(SM) Go(Home) CSE560 Class 14: 26 P. Heeman, 2010 Final Plan At(Home) Go(HWS) At(HWS) Sells(HWS,Drill) Buy(Drill) At(HWS) Go(SM) At(SM) Sells(SM,Milk) Buy(Milk) At(SM) Sells(SM,Ban.) Buy(Ban.) At(SM) Go(Home) Have(Milk) At(Home) Have(Ban.) Have(Drill) CSE560 Class 14: 27 P. Heeman, 2010 Properties of Algorithm Algorithm has hoie points - Can do depth first or breadth first searh Is algorithm sound and omplete? - If there is a solution, there is a sequene of hoies that will find plan If there is no plan, will it stop? - No Will depth first planner always find plan? - Could get stuk down wrong path - But, sine searhing over partial plans, many fewer wrong paths Will breadth first planner always find plan (if there is one)? - Yes. Sine partial plans, muh smaller searh spae.

10 CSE560 Class 14: 28 P. Heeman, 2010 Choie Points CHOOSE an unahieved preondition CHOOSE effet of an existing step to ahieve it OR CHOOSE a add new steps j to ahieve preondition For ANY CLOBBERERS to any ausal links i S j DEMOTE: makes preedes i PROMOTE: makes ome afters j Lots of hoie points. If we an elminiate some - less baktraking for depth-first and less breadth for breadth-first Are all hoose points needed for ompleteness? - Does it matter the order we resolve threats? - Does order of piking unahieved preonditions matter?