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Pl Plann annin ing: g: He Heur uris isti tics cs and and CS - - PowerPoint PPT Presentation

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Pl Plann annin ing: g: He Heur uris isti tics cs and and CS CSP P Plan anni ning ng Co Computer ter Sc Science ce cpsc3 c322, 22, Lectur ture e 18 (Te Text xtbo book ok Chpt 8) 8) Febru ruary, ary, 12, 2010 CPSC

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SLIDE 1

CPSC 322, Lecture 18 Slide 1

Pl Plann annin ing: g: He Heur uris isti tics cs and and CS CSP P Plan anni ning ng

Co Computer ter Sc Science ce cpsc3 c322, 22, Lectur ture e 18 (Te Text xtbo book

  • k Chpt 8)

8)

Febru ruary, ary, 12, 2010

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SLIDE 2

CPSC 322, Lecture 18 Slide 2

Lecture cture Ov Overview view

  • Rec

ecap ap: : Pl Plan anni ning ng Rep epres esen entation tation an and d For

  • rward

ard al algo gorit ithm hm

  • Heuristics
  • CSP Planning
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SLIDE 3

CPSC 322, Lecture 11 Slide 3

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
  • Heuristic function
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SLIDE 4

CPSC 322, Lecture 2 Slide 4

Modules dules we'l 'll l cover er in th this course: se: R&Rsys sys

En Enviro ronm nmen ent Problem

Query Planning Deterministic Stochastic Search Arc Consistency Search Search Value Iteration

  • Var. Elimination

Constraint Satisfaction Logics STRIPS Belief Nets Vars + Constraints Decision Nets Markov Processes

  • Var. Elimination

Static Sequential Representation Reasoning Technique SLS

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SLIDE 5

CPSC 322, Lecture 18 Slide 5

Lecture cture Ov Overview view

  • Rec

ecap ap: : Pl Plan anni ning ng Rep epres esen entation tation an and d For

  • rward

ard al algo gorit ithm hm

  • Heuristics for forward planning
  • CSP Planning
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SLIDE 6

CPSC 322, Lecture 18 Slide 6

Heuristics uristics fo for Fo Forward ard 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 simplifi ifica catio ions ns in the representation:

  • All features are binary: T / F
  • Goals and preconditions can only be assignments to T

An And a Def. a subgoal is a particular assignment in the goal e.g., if the goal is <A=T, B=T, C=T> then….

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SLIDE 7

CPSC 322, Lecture 18 Slide 7

Heuristics uristics fo for Fo Forward ard Planning: nning: An Any y ideas? as?

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SLIDE 8

CPSC 322, Lecture 18 Slide 8

Heuristics for Forward Planning (cont’)

What kind of simplif lific icati ation

  • ns

s of the action

  • ns

s would justify tify our propos

  • sal

al for h?

a) We have removed all ……………. b) We have removed all ……………. c) We assume no action can achieve…………………..

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SLIDE 9

CPSC 322, Lecture 18 Slide 9

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

  • n 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

dele lete-lis list heuris istic tics s with forward rd plannin ing g is currently considered a very successful strategy

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SLIDE 10

Empty ty-delete delete in practice ctice

CPSC 322, Lecture 18 Slide 10

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SLIDE 11

CPSC 322, Lecture 18 Slide 11

Lecture cture Ov Overview view

  • Recap: Planning Representation and

Forward algorithm

  • Heuristics for forward planning
  • CSP

SP Pl Plan anni ning ng

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SLIDE 12

CPSC 322, Lecture 18 Slide 12

Planning anning as a CSP

  • An alternative approach to planning is to set up a

planning problem as a CSP!

  • We simply reformulate a STRIPS model as a set
  • f 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

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SLIDE 13

CPSC 322, Lecture 18 Slide 13

Planning anning as a CSP: : Variabl iables es

  • 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.

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SLIDE 14

CPSC 322, Lecture 18 Slide 14

CSP Planning: nning: Robot

  • t Exampl

mple

Variables for actions ….

action (non) occurring at that step

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SLIDE 15

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

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SLIDE 16

CPSC 322, Lecture 18 Slide 16

CSP Planning: nning: Prec. . Constraint straints s

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

PUC0

RLoc0 RHC0 PUC0 cs T F cs F T cs F F mr * F lab * F

  • ff

* F

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SLIDE 17

CPSC 322, Lecture 18 Slide 17

CSP Planning: nning: Eff ffect t 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

RHCi DelCi PUCi RHCi+1 T T T T T T F F T F T T … … … … … … … …

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SLIDE 18

CPSC 322, Lecture 18 Slide 18

CSP 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

DelMi DelCi

E.g., in the Robot domain DelM and DelC can occur in any sequence (or simultaneously) But we could change that…

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SLIDE 19

CPSC 322, Lecture 18 Slide 19

CSP 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

RHCi RHMi

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SLIDE 20

CPSC 322, Lecture 18 Slide 20

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! In order to find a plan, we expand our constraint network one layer at the time, until a solution is found Pl Plan: : all actions with assignment T

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SLIDE 21

Solve lve planning nning as s CSP: : pse seudo udo co code

CPSC 322, Lecture 18 Slide 21

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SLIDE 22

CPSC 322, Lecture 18 Slide 22

Sta tate te of th f the art t planner nner

A similar process is implemented (more efficiently) in the Graphpl plan an planner

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SLIDE 23

STR TRIPS IPS to to CSP applet let

CPSC 322, Lecture 18 Slide 23

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 will be posted next week (maybe a couple )

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SLIDE 24

CPSC 322, Lecture 4 Slide 24

Learning Goals for today’s class

You

  • u can

an:

  • Construct and justify a he

heur uris istic tic fu func ncti tion

  • n 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)

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SLIDE 25

CPSC 322, Lecture 2 Slide 25

Wh What t is coming ing next t ?

En Enviro ronm nmen ent Problem

Inference Planning Deterministic Stochastic Search Arc Consistency Search Search Value Iteration

  • Var. Elimination

Constraint Satisfaction Logics STRIPS Belief Nets Vars + Constraints Decision Nets Markov Processes

  • Var. Elimination

Static Sequential Representation Reasoning Technique SLS

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SLIDE 26

CPSC 322, Lecture 18 Slide 26

Logics gics

  • Mostly

tly only proposit sition ional al…. This is the starting point for more complex ones ….

  • Natura

ral to express knowledg dge about the world

  • What is true (boolean variables)
  • How it works (logical formulas)
  • Well understood formal properties
  • Boolean nature can be exploited for efficiency
  • ……
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SLIDE 27

CPSC 322, Lecture 18 Slide 27

Coming ming up course se element ments

As Assign gn-1 returned…… Offic fice e hours s during g break: k: Giuseppe (Wed17 ….. )

  • Sunjeet

et; ; will be available on vista chat during his hours

  • Ha

Hammad ad: : not available, but will be monitoring b-board

  • Scott

tt : regular time

  • Ken:

: next week regular hour, following week WedFeb. 24 3-4pm. Pl Please e send email il if if you pla lan to attend nd a particul icular ar offi fice ce hour

Wed, March 3: As Assign-2 2 due

  • Tw

Two program ammin ing g exerci cise ses.

  • s. St

Start t asap asap. . Work in

  • pairs. If stuck, …..

Wed, March 10 Midterm rm exam (1 hour, , regula lar r room)