Plan anni ning ng: : He Heur urist stics cs an and C d CSP Pl Plann annin ing g Computer ter Sc Science ce cpsc3 c322 22, , Lectur ture e 18 (Te Text xtbo book ok Chpt 8) 8) Oct, ct, 17, 2012 CPSC 322, Lecture 18 Slide 1
Lecture cture Ov Overview view • Rec ecap ap: : Pla lann nnin ing g Rep epres esen entation tation an and d For orward ard al algo gorit ithm hm • Heuristics • CSP Planning CPSC 322, Lecture 18 Slide 2
Sta tandard ndard Search rch vs. . Specific cific R&R system tems Constraint Satisfaction (Problems): • State: assignments of values to a subset of the variables • Successor function: assign values to a “free” variable • Goal test: set of constraints • Solution: possible world that satisfies the constraints • Heuristic function: none (all solutions at the same distance from start) Planning : • State • Successor function • Goal test • Solution • Heuristic function Inference • State • Successor function • Goal test • Solution CPSC 322, Lecture 11 Slide 3 • Heuristic function
Modules dules we'l 'll l cover er in th this course: se: R&Rsys sys Enviro En ronm nmen ent Stochastic Deterministic Problem Arc Consistency Search Constraint Vars + Satisfaction Constraints SLS Static Belief Nets Logics Query Var. Elimination Search Decision Nets Sequential STRIPS Var. Elimination Planning Markov Processes Search Representation Value Iteration Reasoning CPSC 322, Lecture 2 Slide 4 Technique
Lecture cture Ov Overview view • Rec ecap ap: : Pla lann nnin ing g Rep epres esen entation tation an and d For orward ard al algo gorit ithm hm • Heuristics for forward planning • CSP Planning CPSC 322, Lecture 18 Slide 5
Heuristics uristics fo for Fo Forward ard Pl Planning nning Heuris istic tic funct ctio ion: n: estimate of the distance form a state to the goal In planning this is the………………. Tw Two simplific ificatio ations ns in the representation: • All features are binary: T / F • Goals and preconditions can only be assignments to T And a De An Def. a subgoal is a particular assignment in the goal e.g., if the goal is <A=T, B=T, C=T> then…. CPSC 322, Lecture 18 Slide 6
Heuristics uristics fo for Fo Forward ard Planning: nning: An Any y ideas? as? CPSC 322, Lecture 18 Slide 7
Heuristics for Forward Planning (cont’) What kind of simplifi lifica catio tions ns of the actions ons wo would justify tify our propos osal al for h? a) We have removed all ……………. b) We have removed all ……………. c) We assume no action can achieve………………….. CPSC 322, Lecture 18 Slide 8
Heuristics uristics fo for Fo Forward ard Planning: nning: empty pty-delet elete-list list • We only relax the problem according to (…….) i.e., we remove all the effects that make a variable F Ac Action on a effects cts (B= B= F , C= T ) • Bu But then how do we compute te the heuristic? stic? …………………………………………. This is often fast enough to be worthwhile • empty-de delete lete-lis list heurist istics ics with forwa ward rd planning ing is currently considered a very successful strategy CPSC 322, Lecture 18 Slide 9
Em Empty ty-delete delete in practice ctice CPSC 322, Lecture 18 Slide 10
Fi Final nal Comment ment • You should view Forward Planning as one of the basic planning techniques (we’ll see another one after the break) • By itself, it cannot go far, but it can work very well in combination with other techniques, for specific domains • See, for instance, descriptions of competing planners in the presentation of results for the 2008 planning competition (posted in the class schedule)
Lecture cture Ov Overview view • Recap: Planning Representation and Forward algorithm • Heuristics for forward planning • CSP Pla lann nnin ing CPSC 322, Lecture 18 Slide 12
Pl Planning anning as s a CSP SP • An alternative approach to planning is to set up a planning problem as a CSP! • We simply reformulate a STRIPS model as a set of variables and constraints • Once this is done we can even express additional aspects of our problem (as additional constraints) e.g., see Practice Exercise UBC commuting “ careAboutEnvironment ” constraint CPSC 322, Lecture 18 Slide 13
Pl Planning anning as s a CSP SP: : Va Variables iables • We need to “unroll the plan” for a fixed number of steps: this is called the horizon • To do this with a horizon of k: • construct a CSP variable for each STRIPS variable at each time step from 0 to k • construct a boolean CSP variable for each STRIPS action at each time step from 0 to k - 1. CPSC 322, Lecture 18 Slide 14
CSP SP Pl Planning: nning: Robot ot Ex Example mple Variables for actions …. action (non) occurring at that step CPSC 322, Lecture 18 Slide 15
CSP SP Pl Planning: nning: In Initia tial l and Go Goal l Constrai straints nts • initial state constraints constrain the state variables at time 0 • goal constraints constrain the state variables at time k CPSC 322, Lecture 18 Slide 16
CSP SP Pl Planning: nning: Pr Prec. c. Constrai straints nts As usual, we have to express the precond nditions itions and effects ects of actions: • precondition constraints • hold between state variables at time t and action variables at time t • specify when actions may be taken RLoc 0 RHC 0 PUC 0 cs T F cs F T PUC 0 cs F F mr * F lab * F off * F CPSC 322, Lecture 18 Slide 17
CSP SP Pl Planning: nning: Ef Effe fect ct Constraints straints • effect constraints • between state variables at time t , action variables at time t and state variables at time t + 1 • explain how a state variable at time t + 1 is affected by the action(s) taken at time t and by its own value at time t RHC i DelC i PUC i RHC i+1 T T T T T T F F T F T T … … … … … … … … CPSC 322, Lecture 18 Slide 18
CSP SP Pl Planning: nning: Constraints straints Contd. td. Other constraints we may want are action constraints: • specify which actions cannot occur simultaneously • these are sometimes called mutual exclusion (mutex) constraints E.g., in the Robot domain DelM i DelC i DelM and DelC can occur in any sequence (or simultaneously) But we could change that… CPSC 322, Lecture 18 Slide 19
CSP SP Pl Planning: nning: Constraints straints Contd. td. Other constraints we may want are state constraints • hold between variables at the same time step • they can capture physical constraints of the system (robot cannot hold coffee and mail) • they can encode maintenance goals RHC i RHM i CPSC 322, Lecture 18 Slide 20
CSP Pl CS P Plan anni ning: ng: So Solving ing the he pr prob oblem em Map STRIPS Representation for horizon 1, 2, 3, …, until solution found Run arc consistency and search or stochastic local search! k = 0 Is State 0 a goal? If yes, DONE! If no, 21
CSP Pl CS P Plan anni ning: ng: So Solving ing the he pr prob oblem em Map STRIPS Representation for horizon k =1 Run arc consistency and search or stochastic local search! k = 1 Is State 1 a goal If yes, DONE! If no, 22
CS CSP Pl P Plan anni ning: ng: So Solving ing the he pr prob oblem em Map STRIPS Representation for horizon k = 2 Run arc consistency, search, stochastic local search! k = 2: Is State 2 a goal If yes, DONE! 23 If no….continue
CSP Planning: nning: Solving ving th the problem blem Map STRIPS Representation for horizon: Run arc consis istenc ncy, search ch, stoch chas astic ic local l searc rch! Pl Plan: : all actions with assignment T In order to find a plan, we expand our constraint network one layer at the time, until a solution is found CPSC 322, Lecture 18 Slide 24
Solve lve planning nning as s CSP: : pse seudo udo co code CPSC 322, Lecture 18 Slide 25
Sta tate te of th f the art t planner nner A similar process is implemented (more efficiently) in the Graphpl plan an planner CPSC 322, Lecture 18 Slide 26
STR TRIPS IPS to to CSP applet let Allows you: • to specify a planning problem in STRIPS • to map it into a CSP for a given horizon • the CSP translation is automatically loaded into the CSP applet where it can be solved Practice exercise using STRIPS to CSP is available on AIspace CPSC 322, Lecture 6 Slide 27
Learning Goals for today’s class You ou can an: • Construct and justify a he heur uris istic tic fu func ncti tion on for forward planning. • Translate a planning problem represented in STRIPS into a corresponding CSP problem (and vice versa) • Solve a planning problem with CPS by expanding the horizon (new one) CPSC 322, Lecture 4 Slide 28
Wh What t is coming ing next t ? Textboo tbook k Ch Chpt 5.1- Enviro En ronm nmen ent 5.1.1 1 – 5.2 Stochastic Deterministic Problem Arc Consistency Search Constraint Vars + Satisfaction Constraints SLS Static Belief Nets Logics Inference Var. Elimination Search Decision Nets Sequential STRIPS Var. Elimination Planning Markov Processes Search Representation Value Iteration Reasoning CPSC 322, Lecture 2 Slide 29 Technique
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