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ARTIFIC~L

r ~ r E L U O E ~ E

89

S T RI P S : A New Ap p roach t o t h e

A pp l icat ion o f .Theorem Pro ving to

Problem Solv ing

Richard E Fikes

N i l s J NHsson

Stan f o r d Resea r ch n st i t u t e M en l o Pa r k Ca l i f o r n i a

Recommended by B. Raphae l

Presented at the 2nd IJCAI, Imperial College, London, England, September

1-3, 1971.

ABSTRACT

W e describe a n ew p r o b l em solver cal led STR I PS t ha t a t temp t s to ind a sequence o f opera tor s

in a sp cce o f wo r ld mode ls to t rans form a g iven in i t ia l wor ld mode l in to a mod e l in which a

g i v en goa l o rm u l a can be p r oven t o be tr u e. ST R I PS r ep resen t s a wor ld n ~ de l as an ar b i t r a r y

c o l l ec ti o n o f i r st o r d er p r e d i c a t e calculus form ula s a nd is des igned to wo rk wi th .models con

s i s t i ng o f large numbers o f formulas . I t employs a reso lu tion t h eo r em p r o v e r t o answer ques-

t io n s o f par t icular models and uses means-ends a nalys is to guide i t t o the des ired goal-sat is fy ing

mode l .

DESCRIFIIVE TERMS

Pro blem solving theo rem proving rob ot planning heuristic search.

1. Introduction

This paper describes a new problem-solving program cal led STRIPS

(STanford Research Inst i tute Problem Solver) . An init ia l vers ion of the

program has been implemented in LISP on a PDP-10 and i s be ing used in

conjunct ion wi th robot ~esearch a t SRI . ST RIP S i s a m em ber o f the c lass o f

prob lem solvers that search a space of wo rld m odels to f ind one in which a

given go al i s achieved. F or any w orld m odel , w e assume that there exists a set

1 Th e researc h reported herein was sponsore d by the Adva nced Research Projects

Ag ency and the N at ional Aeronaut ics and Space A dmin is tr~ tt ion under Contract N A S1 2-

2221 .

Art i f ic ial Inte l ligence 2 197 1), 189--208

Copyright ~ 1971 by N orth -Hol land Pub li sh ing Com pany

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1 9 0 R I C H A R D E HKE S A N D N I L S J . NILSSON

o f a p p li c a b le o p e r a t o r s , e a c h o f w h i c h t r a n s f o r m s t h e w o r l d m o d e l t o s o m e

o t h e r w o r l d m o d e l . T h e t a s k o f t h e p r o b l e m s o l v er i s t o f in d s o m e c o m p o s i -

t i o n o f o p e r a to r s t h a t t r a n s f o r m s a g i v e n i n it ia l w o r l d m o d e l i n t o o n e t h a t

sa ti sf ies som e s ta ted goa l c ond i t ion ,

T h i s f r a m e w o r k f o r p r o b l e m s o l v i n g h a s b e e n c e n t r a l t o m u c h o f t h e

research in a r t i fic ia l in te l ligence [1] . O ur pr im ary in te res t h ere i s in th e c lass

o f p r o b l e m s f a c e d b y a r o b o t i n r e -a r r a n g i n g o b j e c ts a n d i n n a v ig a t in g , i. e. ,

p r o b l e m s t h a t r e q u i r e q u it e c o m p l e x a n d g e n e r a l w o r l d m o d e l s c o m p a r e d t o

t h o s e n e e d e d i n t h e s o l u ti o n o f p u z z l e s a n d g a m e s . I n p u z z l es a n d g a m e s , a

s imple ma t r ix o r l i s t s t ruc tu re i s u sua l ly ade qua te t o r ep resen t a s t a t e o f t he

p rob lem3 . The wor ld mode l fo r a robo t p rob lem so lve r , however , mus t i n -

c l u d e a l a rg e n u m b e r o f f a ct s a n d r e l a ti o n s d e a l in g w i t h t h e p o s i ti o n o f th e

r o b o t a n d t h e p o s i ti o n s a n d a t t r i b u t e s o f v a r i o u s o b je c ts , o p e n s p a c es , a n d

bound a r i e s . In S TR IPS , a w or ld m ode l is r~p resen ted by a s et o f we l l-

fo rm ed fo rmu las (wf fs ) o f t he f i r s t-o rde r p red ica t e ca l cu lus .

Operators a re t he bas i c e l emen t s f rom which a so lu t ion is bu i l t. Fo r ro bo t

p r o b l e m s , e a c h o p e r a t o r ~ o r r e s p o n d s t o a n

action routine 2

w h o s e e x e c u t io n

causes a robo t t o t ake ce r t a in ac tions . F o r exam ple , we m igh t have a rou t in e

tha t causes i t t o go th ro ugh a doo rw ay , a rou t ine tha t causes i t t o push a box ,

a n d p e r h a p s d o z e n s o f o t he r s.

Green [4 ] imp lemen ted a p rob lem-so lv ing sys t em tha t depended exc lus -

i v e l y o n f o r m a l t h e o r e m - p r o v i n g m e t h o d s t o s e a r c h f o r t h e a p p r o p r i a t e

seque~ice of opera tors . Whi le Green ' s formula t ion represented a s igni f icant

s t ep in t he deve lopmen t o f p rob lem-so lve r s , i t su f f e red some se r ious d i sad -

v a n t ag e s c o n n e c t e d w i t h th e f r a m e p r o b l e m ' 3 th a t p r e v e n t e d it f r o m

so lv ing non t r iv i a l p rob lem s .

In STRIPS , we su rmoun t t hese d i f f i cu l t i e s by sepa ra t ing en t i r e ly t he p ro -

c es se s o f th e o r e m p r o v i n g f r o m t h o s e o f s e ar c h in g t h r o u g h a s p a ce o f w o r l d

mod e l s . Th i s s epa ra t io n a l lows us t o em ploy sepa ra t e s t r a teg i e s fo r t hese two

ac t iv i t i e s and the reby improve the ove ra l l pe r fo rmance o f t he sys t em. Thco-

r e i n - p r o v i n g m e t h o d s a r e u s e d o n l y

within

a g i v e n w o r l d m o d e l t o a n s w e r

q u e s ti o n s a b o u t i t c o n c e r n in g w h i c h o p e r a t o r s a r e a p p l i c a b l e a n d w h e t h e r o r

no t goa l s have been sat is fi ed . Fo r s ea rch ing th rou gh the space o f wo r ld

mode l s , ST RIP S uses a GPS - l ike m eans -e nd ana lys i s s t r a t egy [6 ] . Th i s com -

2 The reader should ke ep in m ind the distinction between an operator and its associated

action routine

Execution of action routines actually causes the robot to take actions.

Application of op erators to wo rld mo dels occurs during the planning (i.e., problem solving)

phase when an attempt is b eing m ade to find a sequence of operators whose associated

action rou tines will produce a desired state o f the wo rld. (See the pap ers by M unson [2]

an~l Fikes [3] for discussions of the relationships between STR IPS and the robot executive

and m onitoring functions.)

Space does not a lo w a full discussion of the frame problem ; for a thorough treatme nt,

see [5l.

r t i f i c i a l In t e l l i g e n c e 2 197 1), 189--208

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STRn~S 191

b i n a t i o n o f m e a n s - e n d s a n a ly s is a n d f o r m a l t h e o re m - p ro ,/ ~n g m e t h o d s a ll o w s

o b j e c ts w o r l d m o d e l s ) m u c h m o r e c o m p l e x a n d g e n e ra l t h a n a n y o f t h o s e

u s e d i n G P S a n d p r o v i d e s m o r e p o w e r f u l s e a r c h h eu r is ti cs t h a n t h o s e fo u n d

i n t h e o r e m - p r o v i n g p r o g r a m s .

W e p r o c e e d b y d e s c r i b i n g t h e o p e r a t i o n o f S T R I P S i n te r m s o f th e c o n -

v e n t i o n s u s e d t o r e p r e s e n t t h e s e a r c h s p a c e f o r a p r o b l e m a n d t h e s e a r c h

m eth od s used to f ind a so lu t ion . W e then d i scuss t he de t a i ls o f imp Iemen ta -

t i o n a n d p r e s e n t so m e e x a m p le s .

2 . T h e O p e r a ti o n o f S T R I P S

2 .1 . T h e P r o b le m S p a c e

Th e p r ob lem space fo r S TR IPS i s de f ined by the in it ia l wor ld m ode l , t he set

o f ava i l ab l e ope ra to r s and the i r e f f ec t s on wor ld mode l s , and the goa l s t a t e -

m e n t .

As a l r ea dy m en t ione d , S TR IPS r ep resen t s a wor ld m ode l by a s e t o f we l l-

fo r m ed fo rmulas wf fs ). Fo r example , t o desc r ibe a wo r ld mode l in wh ich the

r o b o t i s a t l o c a t io n a a n d b o x e s B a n d C a r e a t l o ca t io n s b a n d c w e w o u l d

i n c l u d e t h e f o l l o w i n g w f f s :

A T R a )

A T B , b )

AT C, c ) .

W e m i g h t a l s o in c l u d e t h e w f f

(Vu Y x Vy ) { [AT(u , x ) ^ ( x y)] ~ ~ AT u , y)}

to s ta te the gen era l ru le tha t an objec t in on e p lace i s no t in a d i f fe rent p lace .

Us ing f i r s t -o rde r p red ica t e ca l cu lus wf f s , we can r ep resen t qu i t e complex

w o r l d m o d e l s a n d c a n u s e e x i s t i n g t h e o r e m - p r o v i n g p r o g r a m s t o a n s w e r

q u e s t io n s a b o u t a m o d e l .

The ava i l ab l e ope ra to r s a r e g rouped in to f ami l i e s ca l l ed schemata . Con-

s i d e r f o r e x a m p l e t h e o p e r a t o r

goto

f o r m o v i n g t he r o b o t f r o m o n e p o i n t o n

the f loo r t o ano the r . H ere the re i s r ea l ly a d i s ti nc t op e ra to r fo r each d i ff e ren t

pa i r o f po in t s , bu t i t is conven ien t t o g rou p a l l o f these in to a f am i ly go to

m, n ) pa ram e te r i zed by the in it ia l pos i t ion4m and the f ina l pos i t i on n . W e say

t h a t g o t o m , n ) is a n o p e r a t o r

schema

w h o s e m e m b e r s a r e o b t a in e d b y s u b -

s t i tu t ing speci fic con s tan ts for the param eters rn a n d n . I n S T R I P S , w h e n a n

ope ra to r i s app l i ed to a wor ld mode l , spec i f i c cons t an t s wi l l a l r eady have

b e e n c h o s e n f o r th e o p e r a t o r p a r a m e t e r s.

Ea ch op e ra to r is de f ined by an op e ra to r desc r ip t ion cons is t ing o f two m a in

, The param etersm and n are each reallyvector-valued,but we avoid vec tor n, ,tation here

for simplicity. In general, we den ote constants by letters near the beginning of ,ae alphabet

a , b , c , . . . ) ,

param eters by letters in the midd le of the alph abet

m , n , . . . ) ,

~xtd quantified

variables by letters near the end of the alphabet x, y , z ) .

Artificial Intelh'gence2 i971 ), 189-208

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192

R I C H A R D E . F IK E S A N D N I L S J . N I L S S O N

par t s : a desc r ip t ion o f t he ef fec ts o f t he opera to r , a nd the cond i t ions under

wh ich the opera to r i s app l i cab le . The e f fec t s o f an opera to r a re s imp ly

defined by a l i s t o f wffs t ha t m us t b e ad ded to the m ode l an d a l is t o f wf fs t ha t

are n o longer t rue an d therefore mu st be dele ted . W e shal l d i scuss the process

of ca lcu la t ing these ef fects in more deta i l l a ter . I t i s convenien t to s ta te the

appl icab i l i ty condi t ion , o r precondition fo r an opera to r schema as ,~ wf f

schenu~. T o d e t e rm i n e w h e t h e r o r n o t t h e r e is a n i n st an c e o f a n o p e r a t o r

schema app l icab le to a w or ld m ode l , we mus t be ab le to p rov e tha t t he re i s an

in s t ance o f t he co r respond ing wf f schema tha t l og ica l ly fo l lows f rom the

mode l .

Fo r example , cons ider t he ques t ion o f app ly ing in s t ances o f the o pera to r

. subschema go to (m , b ) t o a w or ld m ode l con ta in ing the w f f AT R(a) , where a

and b a re cons t an ts . I f t he p recon d i t ion wf f schema o fg o t o (m , n ) is ATR(m~,

then we find tha t t he in s tance A TR (a) ca n be p roved f rom the wor ld mode l .

Thus , an appl icab le ins tance of go to(m , b) is go to(a , b ) .

I t i s impor t an t t o d i s t ingu i sh be tween the paramete r s appear ing in wf f

schem ata and ord inar y ex is ten tia l ly sn d un iversal ly quant i f ied var iab les that

may a l so appear . Cer t a in mod i f i ca t ions mus t be made to theo rem-p rov ing

p rog ram s to enab le them to han d le w f f schem ata ; t hese a re d i scussed la t e r .

G0 a l s ta t emen t s a re a l so r ep resen ted by wfl's . Fo r example , t he t a sk G et

Boxes B and C to L oca t ion a m igh t be s t a ted as the wf f:

AT(B , a) A A T(C, a) .

To summ arize , the prob lem space fo r ST RIP S is def ined by th ree en titi,s:

(1) An in i t ia l wor ld model , which i s a se t o f wffs descr ib ing the presen t

s ta te o f the w or ld .

(2) A set o f operators , includ ing a descr ip t ion of thei r ef fects and thei r

p recond i t ion wf f schemata .

(3) A goal cend i t ion s ta ted as a wff .

The p rob lem i s so lved when ST RIP S p roduces a wo r ld mode l t ha t sat is fies

the goal wff.

2 2 The Search Strategy

In a very s imple prob lem-so lv ing sys tem, we might f i r s t app ly a l l o f the

appl icab le operators to the in i t ia l wor ld model to create a se t o f successor

mode l s . We wou ld con t inue to app ly a l l app l i cab le opera to r s t o these suc-

cessors and to their descendants (say in breadth-f i rst fashion~ unt i l a model

was p roduced in wh ich the goa l fo rm u la was a theo rem. However , s ince we

env is ion uses in wh ich the num ber o f ope ra to r s app l icab le to any g iven wor ld

model might be qu i te large , such a s imple sys tem would generate an

undes ir ab ly l a rge t r ee o f wor ld m ode l s and wou ld thus be imprac ti ca l.

r t i f i c i a l I n t e l l i g e n c e 2 1 9 7 1 ) , 1 8 9 - 2 0 8

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STRWS 193

Ins tead, we have adop ted the G PS s t ra tegy of ext rac t ing d i f fe rences

be tween the p resen t wo r ld mode l and the goa l and o f ident ify ing op e ra to rs

tha t a re re leva nt to reducing these d i ffe rences [6] . Once a re levant op era to r

has been de termined , we a t tempt to so lve the subprob lem of p roduc ing a

world model to which i t i s appl icable . I f such a model i s found, then we

apply the re levant opera to i and iecons ider the or ig ina l goa l in the resul t ing

m odel . In th is sect ion , we review th is bas ic G PS search s t ra tegy as employ ed

b y STR IPS .

STRIPS beg ins by employ ing a theorem prove r to a t t empt to p rove tha t

the goa l w ff Go fol lows from the set Mo o f wtTs describing the ini tia l w orld

model . If Go does fol low from Mo, the task is t r ivial ly solved in the ini t ia l

model . Otherwise, the theorem prover wil l fa i l to f ind a proof. In this case,

the uncom ple ted pr oo f i s taken to be the d i f fe rence be tween Mo and Go.

Ne xt , opera tors tha t might be re levant to reduc ing th is d if fe rence are

sought . These a re the opera tors w hose effects on w orld mod els would enable

the proof to be cont inued. In de termining re levance , the parameters of the

op era to rs m ay be par t ia l ly or fu lly ins tant ia ted . Th e correspon ding ins tant i -

a ted precondi t ion w ffschem ata (of the re levant opera tors ) a re then taken to be

new subgoals .

Con s ider the t riv ia l ly s imple example in which the task i s for the ro bot to

go to loca t ion b . Th e goal wff is thus A TR (b) , and unless the rob ot i s a l ready

at location b, the ini t ia l pr oo f at tem pt w il l be unsuccessful. N ow , certainly

the instance goto(m, b) of the o pera tor goto(m , n) is re levant to reducing the

difference because i ts effect would al low the proof to be continued (in this

case, com ple ted) . A ccordingly , the co rresponding precon di t ion wff schema,

say AT R(m ), i s used a s a subgoal.

STRIPS works on a subgoal us ing the same technique . Suppose the pre-

con dit ion wff schem a G is selected as the f irs t subgoal to be w ork ed on .

STRIPS again uses a theorem prover in an a t tdmpt to f ind ins tances of G

tha t fo l low from th e in i tia l world model Mo. H ere aga in , there a re two poss i-

b i l i t ies . I f no proof can be found, STRIPS uses the incomple te proof as a

di f fe rence , and se ts up (sub) subgoals corresponding to the i r precondi t ion

wffs . I f STRIPS does f ind an ins tance of G tha t fo l lows f rom Mo, then the

correspond ing o pera tor instance i s used to t,~ansform Mo in to a new wo rld

m odel M1. In ou r previous s imple example , the subgoal w ff schema G w as

AT R(m ) . I f the in it ia l mode l con ta ins the wffAT R(a ) , then a n ins tance o f G - -

nam ely A TR (a) can be proved f rom M o. In th is case, the correspond ing op-

era tor ins tance goto(a , b) i s appl ied to Mo to produce the new model , MI.

ST RI PS then con t inues by a t tempt ing to p rove Go f rom M I . In our example,

Go t r iv ia lly fo l lows f rom M~ and we are through . H ow ever , i f no pr oo f could

be found, subgoals for th is problem would be se t up and the process would

continue.

r t i j~ ia l In t e l l i gence 2 1971) , 189-208

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94

R I C H A R D E . F I K E S A N D N I L S J. N I L S S O N

The hierarchy of goal , subgoals , and models genera ted by the search

process is represen ted by a

search tree.

Each node of the search t ree has the

form ~world model~, go a l l i s t )) , an d represents the problem of t ry ing to

achieve the sub-goals on the goal l is t in order) f rom the indica ted w or ld

model .

A n example of such a search t ree is shown in Fig . 1 . Th e top nod e Mo,

Go)) represents the m ain task of achieving goal Go from wo rld mod el Mo.

' , '%

I

I o c'%'% ',

P

( 1 , ( % , % ) )1 i ( = , ( % 0 % ) )

%

I

( 3 ( c ; l ' C o ) ~

F I o . 1 . A t y p i c a l S T R I P S s e a r c h t r e e .

In this case, two aRernat ive subgoa ls Ga and Gb are se t up . These a re add ed

to the front o f the goal lists in the tw o successor nodes. Pursuing on e o f these

subgoals, supp ose th at in the n od e Mo, Ga, Go)), goa l Go is satisf ied in M o;

the corresponding opera tor , say

OPo,

i s then ap pl ied to Mo to y ield M1. Thus,

a long th is branch, the problem is now to satisfy goa l Go f rom M l , an d th is

problem is represented by the node M I, Go)) . Alon g the o ther pa th , suppose

Gc is set up as a subgo al for achieving

Gb

and thus the nod e Mo, Go,

Gb, Go))

is created . S up po se Gc is satisfied in -44o an d thu s

OPc

is appl ied to M o yield-

ing M2. Now STR IPS mu st s ti ll so lve the subproblem

Gb

before a t temp t ing

the main goal Go. Thus, the resul t of applying

OPc

i s to replace Mo by M2

and to remove Gc f rom the goal l is t to produ ce the node M2, Gb, Go)).

r t i f i c i a l I n t e l l i g e n c e

2 197 1), 189-20{,

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s 3 3 ~ J p s 1 9 5

T h i s p r o c e s s c o n t i n u e s u n t i l S T R I P S p r o d u c e s t h e n o d e ( M , , ( G o ) ) . H e r e

s u p p o s e G o c a n b e p r o v e d d i r e c tl y f r o m M , s o t h a t th i s n o d e i s te r m i n a l . T h e

s o l u t i o n s e q u e n c e o f o p e r a t o r s is t h u s OP t, OPb, OPe).

T h i s e x a m p l e s e a r c h t r e e i n d i c a t e s c l e a r l y t h a t w h e n a n o p e r a t o r i s f o u n d

t o b e r e le v a n t, it is n o t k n o w n w h e r e it w i l l o c c u r i n t h e c o m p l e t e d p l a n ; t h a t

i s , i t m a y b e a p p l i c a b l e t o t h e i n i t ia l m o d e l a n d t h e r e fo r e b e t h e f ir st o p e r a t o r

a p p l i e d , i ts e f fe c t s m a y i m p l y t h e g o a l s o t h a t i t i s t h e l a s t o p e r a t o r a p p l i e d ,

o r i t m a y b e s o m e i n t e r m e d i a t e s te p t o w a r d t h e g o a l . T h i s f le x i b le s e a r c h

s tr a t eg y e m b o d i e d i n S T R I P S c o m b i n e s m a n y o f t h e a d v a n ta g e s o f b o t h

f o r w a r d s e a r c h ( f r o m t h e i n i t i a l m o d e l t o w a r d t h e g o a l ) a n d b a c k w a r d

s e a r c h ( fr o m t h e g o a l t o w a r d t h e i n it ia l m o d e l ) .

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I

F ] o . 2 . F l o w c h a r t f o r S T R I P S .

W h e n e v e r S T R I P S g e n e r a t e s a s u c c e s s o r n o d e , i t i m m e d i a t e l y t e s t s t o s e e

i f th e f ir st g o a l o n t h e g o a l l i st is s a ti sf ie d i n th e n e w n o d e s m o d e l . I f so , t h e

c o r r e s p o n d i n g o p e r a t o r i s a p p l ie d , g e n e r a t in g a n e w s u c c e s s o r n o d e ; i f n o t ,

r t i f i c i a l I n t e l l i g e n c e

2 1971) , 189- 208

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196

RICHARD E. lIKES AND NILS J. NILSSON

the d i f fe rence ( i . e . , the uncomple ted proof) i s s to red wi th the node . Excep t

fo r those suc c e sso r node s ge ne ra te d a s a r e su l t o f a pp ly ing ope ra to r s , the

p roc e ss o f suc c e sso r ge ne ra t ion i s a s fo l lows : STRIPS se le c t s a node a nd

uses the d i f fe rence s to red wi th the node to se lec t a re levan t opera to r . I t uses

the p re c ond i t ion o f th i s op e ra to r to ge ne ra te a ne w suc ce ssor . ( I f a l l o f the

nod e s suc ce sso rs ha ve a l re a dy be e n ge ne ra te d , S TR IPS se le c ts some o th e r

node s t i l l h a v ing unc omple te d suc c e sso rs . ) A f lowc ha r t summa r iz ing the

ST RIP S se a rc h p roc e ss is shown in F ig . 2 .

ST RIP S ha s a he u r i s t ic me c ha n i sm to se le c t node s w i th unc om ple te d suc -

c e sso rs to w ork o n ne x t . Fo r th i s pu r pos e we u se a n e va lua t ion func t ion tha t

t a k e s i n t o a c c o u n t s u c h f a c t o rs a s t h e n u m b e r o f r e m a i n i n g g o a ls o n t h e g o a l

l is t , t h e num be r a nd type s o f p re d ic a te s in the re m a in ing goa l fo rmu la s , a n d

the com plex i ty o f the d i ffe rence a t tac hed to the node .

3. Implementation

3.1. Theorem Proving with Param eters

In th i s se ct ion , we d isc uss the m ore im por ta n t de ta il s o f ou r imp le m e n ta t ion

o f S T R I P S ; w e b e g i n b y d e s c r i b i n g t h e a u t o m a t i c t h e o r e m - p r o v i n g c o m -

pone n t .

STRIPS use s the re so lu t ion the o re m-p rove r QA3 .5 [7 ] whe n a t t e mp t ing

to p rove go a l a nd sub -goa l wff s. We a ssum e tha t the re a de r i s f a mi l i a r w i th

re so lu t ion p ro o f t e c hn ique s fo r the p re d ic a te c a lc u lu s [1 ]. The se t e c hn ique s

m us t be e x te nded to ha nd le the pa ra m e te r s oc c u r r ing in wf f sc he ma s ; we

discuss these extensions next .

The ge ne ra l s i tua t ion i s tha t we ha ve som e goa l wf f sc he m a G (p ), sa y , tha t

i s to be p rove d f ro m a se t M o f c la use s whe re ~ i s a se t o f sc he ma pa ra me te r s .

Fo l lowing the ge ne ra l s t r a te gy o f r e so lu t ion the o re m p rove rs , we a t t e m p t to

p rove ~he inc ons is t e ncy o f the se t ( M U ~ G(p ) ) . Th a t i s, we a t t e m p t to

f ind an ins tance p o f ~ fo r which ( M U ~ G( ,~ )} i s inconsis ten t .

W e ha ve be en a b le to u se the s t a nda rd un i f ic a t ion a lgo r i thm o f the re so lu -

t ion m e thod to c o m pu te the a pp ro p r ia t e in sta nc e s o f sc he m a va r ia b le s du r ing

the se arc h fo r a p ro o f Th i s a lgo r i thm ha s the a dva n ta ge tha t i t f inds the m os t

genera l ins tances o f pa ram ete rs needed to e f fec t un i f ica t ion . T o use the un i f i -

c a t ion a lgo r i thm we m us t spe c ify how i t is to t r e a t pa ra me te r s . The fo l lowing

subs t i tu t ion type s a re a l lowa b le c om pone n t s o f the ou tpu t o f the m od i f i ed

un i f ic a t ion a lg o r i thm :

T e r ms th a t c a n b e s u b s t i t u t e d f o r a v ar ia b le var iab les , constan ts , pa ra -

me te r s , a nd func t ione l t e rms no t c on ta in ing the va r i a b le

T e r m s th a t c a n b e s u b s t i t u t e d f o r a p a r a m e te r c ons ta n t s , pa ra me te r s ,

a nd func t iona l t e rms no t c on ta in ing Sko le m func t ions , va r i a b le s , o r

the pa ra me te r .

r t i f i c i a l In t e l li g e n c e 2 (1971), 189-208

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STgtPS 197

The fa c t tha t the sa me pa ra m e te r m a y ha ve mu l t ip le oc c u r re nc e s in a se t o f

c la use s de ma nds a no the r mod i f i c a t ion to the the o re m p rove r . Suppose tw~

c lause s C t a nd C2 re so lve to fo rm c la use C a nd tha t in the p roc e ss some t e rm

t i s subs t i tu te d fo r pa ra m e te r p , The n w e m us t m a ke su re tha t p i s r e p la c e d

by t in a l l o f the clauses tha t a re descend ants o f C.

3 2 Op erator Descriptions and Applications

We ha ve a l re a dy me n t ione d tha t to de f ine a n ope ra to r , we mus t s t a t e the

precondi t ions under which i t i s app l icab le and i t s e f fec ts on a wor ld mode l

sc he ma . P re c ond i t ions a re s t a t e d a s wf f sc he ma ta . F o r e xa mple , suppose

G ~ ) i s the ope ra to r p re c ond i t ion sc he ma o f a n ope ra to r O(~) , p i s a se t o f

pa ra m e te r s , a nd M i s a w or ld mode l . The n i f p i s a c ons ta n t in s ta nc e o f p

fo r wh ic h {M U ~ G(p )} i s c on t ra d ic to ry , the n STR IPS c a n a pp ly ope ra to r

O ~ ) t o w o rl d m o d e l M .

We ne x t ne e d a wa y to s t a t e the e f fe c t s o f ope ra to r a pp l i c a t ion on wor ld

m ode ls . These e f fec ts a re s imp ly desc r ibed by tw o l i st s. On the

dele te l i s t

w e

spe c i fy those c l a use s in the o r ig ina l mode l tha t migh t no longe r be t rue in

t h e n e w m o d e l. O n t h e a d d l i s t a re those cl a use s tha t m igh t no t ha ve be e n t rue

in the o r ig ina l mod e l bu t a re t rue in the ne w m ode l .

Fo r e xa mple , c ons ide r a n ope ra to r push (k , m , n ) fo r push ing ob jec t k

f ro m m to n . Such a n o pe ra to r m igh t be de sc r ibe d a s fo l lows :

p u s h k , m , n )

Pr e c o n d i t i o n :

de le t e l i s t

a d d l i s t

A T R ( m )

A A T ( k , m )

A T R ( m ) ;

A T ( k , m )

A T R ( n ) ;

A T( k , n ) .

The p a ra m e te r s o f a n ope ra to r sc he ma a re in s ta n ti a te d by c ons ta n t s a t

the t im e o f ope ra to r a pp l i c a t ion . Som e in s ta n t ia t ions a re m a de w h ile de -

c id ing wha t in s t a nc e s o f a n ope ra to r sc he ma a re r e l e va n t to r e duc ing a

d i f fe rence , and the res t a re m ade whi le dec id ing wh a t ins tances o f an oper-

a to r a re a pp l i c a b le in a g ive n wor ld mode l . Thus , whe n the a dd a nd de le te

l i s t s a re u se d to c re a te ne w wor ld mode l s , a l l pa ta a ,~c r s oc c u r r ing in the m

wil l have been rep laced by constan ts .

(W e c a n m a ke c e r ta in m od i fi c at ions to ST RIP S to a l low i t to a pp ly ope r -

a to r s w i th un in s ta n t i a t e d pa ra me te r s . The se a pp l i ca t ions w il l p roduc e wor ld

mode l sc he ma ta . Th i s ge ne ra l i z a t ion c ompl ic a te s some wha t the s imp le a dd

a nd de le te - l i s t ru le s fo r c ompu t ing ne w wor ld mode l s a nd ne e ds fu r the r

s t u d y . )

Art i f zc ia l In te ll genea 7

1971) , 189-208

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98 I n C H e D E . F IK E S A N D N IL S J . N IL S SO N

Fo r ce r ta in ope ra to r s i t is conven ien t t o be ab l e mere ly t o speci fy t he f orm

o f c lauses t o be de l e t ed . Fo r exam ple , one o f t he e ff ec ts o f a ro bo t goto oper -

a t o r m u s t b e t o d e l e t e i n f o r m a t i o n a b o u t t h e d i r e c t i o n t h a t t h e r o b o t w a s

or ig ina l l y f ac ing even thoug h such in fo rm a t ion m igh t no t hav e been r epre -

s e n te d b y o n e o f th e p a r a m e t e r s o f th e o p e r a t o r . I n t h is c a s e w e w o u l d i n -

c lu d e t h e a t o m F A C I N G ( I ; ) o n th e d e le t e li st o f g o t o w i t h th e c o n v e n t io n t h a t

a n y a t o m o f t h e f o r m F A C I N G ( S ) , r e ga r d le s s o f t h e v a lu e o f , w o u l d b e

deleted.

When an ope ra to r desc r ip t i on i s wr i t t en , i t may no t be poss ib l e t o name

exp li ci tl y a l l t he a to m s tha t shou ld a pp ea r on t he de l e te li st . Fo r example , i t

may be t he case t ha t a wor ld mode l con t a ins c l auses t ha t a r e de r ived f rom

o t h e r c la u se s i n t h e m o d e l. T h u s , f r o m A T ( B I , a ) a n d f r o m A T ( B 2 , a + A ) ,

we migh t de rive NE X TT O (BI , 132) an d inser t it i n to the mo de l . N ow, i f one

of the c lauses on wh ich the der ived c lause depen ds i s de le ted , then the der ived

clause mu st a l so be d e le ted .

W e deal wi th th i s pro blem by d ef in ing a se t o f pr im i t ive predica tes (e.g .,

AT , A TR ) an d r e l a t ing a l l o the r p red i ca t e s t o t h i s p r imi t ive se t. I n pa r t i cu l a r,

we r equ i r e the de l e t e l is t o f an op e ra to r desc r ip ti on t o i nd i ca t e a l l t he a tom s

con ta in ing p r imi t i ve p red i ca te s t ha t sh ou ld b e de l e ted when the o pe ra to r i s

app l i ed . A l so , we r equ i r e t ha t any nonpr imi t i ve c l ause i n t he wor ld mode l

have a s soc ia t ed wi th i t t hose p r imi t i ve c lauses on wh ich i t s va l i d i ty depends .

(A pr imi t ive c lause i s one which conta ins ~nly pr imi t ive predica tes . ) For

example , t he c l ause NEXTTO(BI , B2) would have a s soc i a t ed wi th i t t he

c lauses AT (BI , a ) an d AT(B2, a +A ) .

By us ing these convent ions , we can be assured tha t pr imi t ive c lauses wi l l

be cor r ec t l y de l e t ed dur ing ope ra to r app l i ca t i ons , and tha t t he va l i d i t y o f

nonpr imi t ive c l auses can be de t e rmined w henever t hey a re used i n a d educ-

t i on by check ing to see i f a l l o f t he p r imi t i ve c l auses on which t he non-

pr imi tive c lause depe nds are s t i ll in the w or ld m odel .

3 3 Com puting Differences and Relevant Op erators

STRIPS uses th G P S s tr a te g y o f a t te m p t i n g t o a p p l y t h o s e o p e r a t o rs t h a t

a r e r e l evan t t o r educ ing a d i f f e r ence be tween a wor ld mode l and a goa l o r

subgoa l . W e use the t heo rem prov er a s a key pa r t o f t h i s mechan ism.

Suppose we have j us t c r ea t ed a new n ode i n t he sea rch t r ee represen ted by

M , Gt, G a _ t , . . . , Go)). The

t heorem prover i s ca l l ed t o a t t empt t o f i nd a

con t r ad i c t i on fo r t he se t {M U ~ Gt} . I f on e ca n be found , t he ope ra to r ~

whose p recon d i t i on was Gs is app l i ed t o M an d the p rocess con t inues .

Here , t hough , we a re i n t e r es t ed i n t he case i n which no con t r ad i c t i on i s

ob t a ined a f t e r inves t ing som e prespec if ied am ou nt o f t heorem -prov ing e f fo r t.

The uncom ple t ed p r oo f P i s r ep resen ted by t he se t o f c lauses t ha t fo rm the

r t i f i c i a l I n t e l l i g e n c e 2 19 71 ), 18.9--208

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STRI PS

]

nega t ion o f the goal wff, p lus a l l o f thei r de scendan ts ( i f any) , l ess any c lauses

el iminated by ed i t ing s t ra teg ies ( such as subsumpt ion and pred icate evalua-

t ion ) . W e t ak e P to be the d if fe revee be tween M and Gl and a t t a ch P :to the

node. s

La te r , i n a t t em p t ing to com pu te a successo r to th is node w i th incomple te

p r oo f P a t t ached , w e f ir st m us t sel ec t a r e l evan t opera to r . The ques t fo r

re l evan t opera to r s p roceeds in two s teps. In the f i r s t s tep an o rdered l is t o f

cand ida te o pera to r s i s c reat ed . The se lec tion o f cand ida te op era to r s i s based

on a s imple com par ison of the pred icates in the d i fference c lauses wi th those

on the ad d l i s t s o f the ope rator descr ip t ions . Fo r example , i f the d i fference

con ta ined a c l ause hav ing in i t t he nega t ion o f a pos i t ion p red ica te A T, then

t h e o p e r a t o r

pus

wo uld be considered as a cand idate fo r th i s d i fference.

The second s tep in f ind ing an operator re levant to a g iven d i f ference in -

vo lves em p loy ing the theo rem p rover to de t e rmine i f c lauses on the add l is t o f

a cand ida te ope ra to r can be u sed to r eso lve aw ay c lauses in the d if fe rence

( i.e. , to see i f t ire p ro of ca n be con t inued bas ed on the effects o f the operator ) .

I f t he the o rem p rover can in f ac t p roduce new reso lven ts tha t a re descen-

dan t s o f t he ad d l is t c l auses, t hen the cand ida te o pera to r (p roper ly in st an t-

ia ted) i s considered to be a re ievant opera tor fo r the d i fference se t.

No te tha t t he cons idera t ion o f one cand id~ . t e opera to r schema may p ro -

duce several re leva nt o pe rato r ins tances . F or example , i f the d if ference se t

con ta in s the un i t c lauses ~ A TR (a) and ~ ATR (b) , t hen the re a re two re le -

van t i n s tances o f go to (m, n ), namely go to (m, a ) and go to (m, b ) . Each new

reso lven t that i s a descendant o f the operator ' s add l i s t c lauses i s used to

fo rm a r e l evan t i n s tance o f t he opera to r b y app ly ing to the o pera to r ' s pa ra -

mete r s t he same subs t i tu t ions tha t w ere m ade du r ing the p rod uc t ion o f t he

resolvent .

3 4 Eff ic ient lRepresentafion of W orld M ode ls

A pr imary des ign i s sue in the imp lemen ta t ion o f a sy s t em such as STRIP5

is ho w t o sa t i s fy the s to rag e requirements o f a search tree in which each no de

may con ta in a d i f f e ren t wor ld mode l . We wou ld l i ke to u se STRIPS in a

robo t o r ques t ion -answer ing env i ronmen t where the in i t i a l wor ld mode l

m ay consis t o f hu ndre ds of wffs. F or such ap pl ica t ions i t is in feas ib le to

recopy com ple t e ly a w or ld m ode l each t ime a new m ode l is p roduced by

app l i ca t ion o f an opera to r .

W e have dea l t wi th thi s p rob lem in ST RIPS by fi rs t a ssuming tha t m os t o f the

wi t s in a p rob lem ' s i , i t i a l w or ld mode l wi ll no t be changed by the app l i ca t ion

o f opera to r s . T h i s i s ce r t a in ly true fo r t he c lass o f robo t p rob lem s wi th wh ich

we a re c u r ren t ly concerned . Fo r these p rob lems m os t o f t he wffs in a mode l

descr ibe room s, wal l s, doors , an d ob jects, o r specify general p roper t ies o f the

s I f P i s v e r y l a r g e w e c a n h e u r i s ti c a l ly se le c t s o m e p a r t o f P a s t h e

difference

r t i f i c~ l In t el li gence

2 1971 ) , 189 - 20 8

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20 0 RICHARD E. lIKES AND ~ J. NILSSON

wor ld , wh ich a re t rue in a l l mode l s . The on ly wffs t ha t m igh t be change d in

th is rob e t e nv i ronm en t a re the ones tha t desc r ibe the s t a tu s o f t he robo t an d

any ob jec ts wh ich i t man ipu la t es .

Given th i s as sumpt ion , we have imp lemen ted th~ fo l lowing scheme fo r

hand l ing m u l tip le wo r ld m ode ls . Al l t he wffs fo r a l l wo r ld m ode l s a re s to red

in a common memory s t ructure . Associa ted wi th each wf l ( i .e . , c lause) i s a

v isib il ity f lag, an d QA 3.5 has be en m odif ied to con sider on ly c lauses f rom the

m em ory s t ruc tu re tha t a re m arke d as v is ib le . Hence , we can def ine a pa r -

t icu la r wor ld m ode l fo r QA 3 .5 by m ark ing tha t m ode l ' s c lauses v is ib le an d

al l o ther c lauses inv is ib le . When c lauses are en tered in to the in i t ia l wor ld

mode l , t hey a re a l l m arked as v is ib le . C lauses tha t a re no t changed rem ain

v is ib le th rougho u t S TR IPS ' sea rch fo r a so lu tion .

Each wor ld m ode l p roduced by S TR IPS i s de fined by two c l ause li sts . The

f ir st li st , DE LE TI O N S, names a l l those c lauses from the in it ia l wor ld mode l

that are no longer p resen t in the model being def ined . The second l i s t ,

ADDITIONS, names a l l t hose c l auses in the mode l be ing def ined tha t a re

not a l so in the in i t ia l model . These l i s t s represen t the changes in the in i t ia l

m ode l needed to fo rm the m ode l be ing defined , an d ou r assum pt ion imp l i es

they wi ll con ta in on ly a sm al l num ber of c lauses.

To specify a g iven wor ld mode l to Q A3.5 , S TR IPS m ark s v is ib le the c lauses

on the mode l ' s ADDITIONS l i s t and marks inv i s ib l e the c l auses on the

mode l ' s DELETIONS l i s t . When the ca l l t o QA3 .5 i s comple t ed , t he v i s i -

b i l ity mark ings of these c lauses are re turne d to the i r p rev ious se t tings .

W h e n a n o p e r a t o r is a p p l ie d t o a w o r l d mo d e l, t h e D E L E T I O N S l is t o f t h e

n e w w o r l d mo d e l i s a c .) py o f t h e D E L E T I O N S l i st o f t h e o l d mo d e l p lu s

any c l auses f rom the in i t i a l mode l t ha t e re de l e t ed by the opera to r . The

ADDITIONS l i s t o f t he new mode l cons i s t s o f t he c l auses f rom the o ld

mo d e l 's A D D I T I O N S lis t, a s t r a ns f o rme d b y th e o p e r a t o r , p lu s t he c l a u s e s

f rom the opera to r ' s add l is t.

3 5 An Example

Tracing th rough the main po in ts o f a s imple example helps to i l lus t ra te the

var ious mechan isms in STR IPS . Suppose we wan t a rob o t t o ga ther t oge ther

three ob jects and tha t the in i tia l w or ld mo del is g iven by :

M o . A T B O X , b ) .

AT(BOX2, c )

A T t B O X 3 , d )

Th e goal wff describ ing this task= is

Go : (3x ) [AT (~O X I , x ) ^ AT(BO X2, x )

^ AT (BO X3 , x)] .

r t i f ic i a l I n t e l li g e n c e 2 1971), 189-208

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s r tn , s 201

It* . neg a ted form i s

~ G o : ~ A T ( B O X 1 , z ) v ~ A T ( B O X 2 , x )

v ~ A T B O X 3 , x ) .

( In ~ Go , t he t e rm x i s a un ive r sa l ly quan t i f ied v a r i a b l e . )

W e a d m i t t h e fo l lo w i n g o p e r a t o r s :

(1) p u s h k , m , n ) : R ob o t pu shes ob jec t k f rom p lace m to p l ace n .

Precond i t ion : A T ( k , m ) A A T R ( m )

N e g a t e d p r e c o n d i ti o n : ~

A T ( k , m ) v ~ A T R ( m )

D e l e t e l i s t : A T R ( m )

A T ( k , m )

A d d l is t: A T ( k , n )

A T R ( n )

(2)

g o t o m , n ) :

Robo t goes f rom p lace m to p l ace n .

Precond i t ion : A T R ( m )

N e g a t e d p r e c o n d i ti o n :

~ A T R ( m )

Dele t e l i s t :

A T R ( m )

A d d l i s t : A T R ( n ) .

F o l l o w i n g t h e f l o w c h a r t o f

F i g . 2 , S T R I P S

f i rs t creates the ini t ia l node

M o , G o ) )

a n d a t t e m p t s t o

f i n d a

con t r ad i c t i on to

{ M o U ~ G o } .

Thi s

a t t em pt i s unsuccessfu l; suppo se the incom ple t e p ro o f is :

-,, A T ( B O X I , x ) v ~ A T ( B O X 2 , x ) v ~ A T ( B O X 3 , x )

A T ( B O X I , c) v ~ A T ( B O X 3 . c ) ~ /

,,, A T (B O X 2 , b ) v A T (B O X 3 , b) ~ ]

v

~ A T ( B O X I , a ) v ~ A T ( B O X 2 , d )

W e a t t ach th is incom ple t e p r oo f to t he node an d then se lec t t he no de to have

a successo r compu ted .

T he on ly cand ida t e op e ra to r i s push (k , m , n ). Us ing the ad d l is t c lause

A T ( k , n ) , w e ca n c o n t in u e t h e u n c o m p l e t e d p r o o f in o n e o f s e v e ra l w a y s

depe nd ing on the subs t i tu t i ons m ade fo r k ~n d n . Each o f t hese subs t it u t ions

p rod uces a r e l evan t in s t ance o f push . O ne o f these is :

O P I :

p u s h ( B O X 2 ,

m , b )

g iven by the subs t i t u t i ons BOX2 fo r k and b fo r n . I t s a s soc i a t ed p recond i -

t i on ( i n nega ted fo rm) i s :

~ G ~ : - - A T ( B O X 2 , m ) v ~ A T R ( m ) .

A rtificial Intelligence 2 1971) , 189-208

15

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2 2

R I C H A R D E . l I K E S A N D N I L S J . N I L S S O N

Suppose

OPI

i s se lec ted and used to c rea te a successor node . (La ter in the

search process ano ther successor us ing o ne of the o tL er re levant ins tances of

push migh t be com puted i f ou r o r ig ina l se lec t ion d id no t l ead to a so lu t ion . )

Select ing

OPI

l e ads to the com puta t ion o f the succes so r node (Mo, (GI , Go)) .

STR IPS nex t a t t em pts to f ind a co n t rad ic t ion fo r {M o tJ ~ G l} . The un-

comp le ted p ro of (dif fe rence) a t t ached to the n ode co n ta ins :

~ A T (B O X 2 . m ) v ~ A T R ( m )

A T (B O X 2, e) ~ ~ R ( a )

~ A T R c ) ~ A T B O X 2 , a )

When th is node i s la te r se lec ted to have a successor computed , one of the

candida te opera tors i s g o t o m , n ) . Th e re levan t in s tance i s de te rmined to be

OP :

go to (m,

c )

with (nega ted) precondi t ion

~ G z : A TR ( m ) .

Th is re levan t ope ra to r results in th e successor nod e (M o, (6;2, G~, Go)) .

Ne s t ST RIPS de te rmines tha t (M o t3 ,-- G2) i s con t radic tory wi th m = a .

Thus , S TR IPS app l ie s the ope ra to r go to (a , c ) to Mo to y ie ld

A TR ( c ) /

M , - A T ( B O X I , b ) .

AT(BOX2, c )

A T( B O X 3 , d )

Th e successor n ode i s (M ~, (G~, Go)) . Imm edia te ly , ST RIP S de te rmines tha t

M ~ U ~

Go) is cont rad ic tory w i th

m -

c . Thus , STRIPS appl ies the oper-

a to r push(BOX 2, c , b) to y ie ld

A T R ( b )

M z : A T( B O X 1 , b )

A T( B O X 2 , b )

AT(BOX 3, d )

Th e resul ting successor node i s (M2, (Go)), and thus ST RIP S recons iders the

or ig ina l p rob lem bu t now beg inn ing wi th wor ld m ode l M z . The re s t o f the

solu t ion proceeds in s imi la r fash ion .

Ou r implem en ta t ion o f STR IPS eas ily p roduces the so lu t ion {go to (a, c ),

push(BO X2, c , b), goto(b , d) , push(BO X3 , d , b)} . ( Inc identa lly , G reen ' s

theorem-prov ing p rob lem-so lve r [4] has no t been ab le to ob ta in a so lu t ion

to th is vers ion of the 3-Boxes prob lem . I t d id so lve a s impler vers ion o f the

prob lem des igned to requ i re o n ly two ope ra to r app l i ca tions .)

r t i f ic i a l In t e l l i g e n c e

2 1971) , 189-208

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s 1 ~ n s 2 0 3

4 . E x a m p l e P r o b le m s S e l v e d b y S T R I P S

S T R I P S h a s b e e n d e s i g n e d t o b e a g e n e ra l -p u r p o se p r o b l e m s o lv e r f o r r o b o t

t a s k s a n d t h u s m u s t b e a b le t o w o r k w i t h a v a r ie t y o f o p e r a t o r s a n d w i t h a

w o r l d m o d e l c o n t a i n i n g a l ar g e n u m b e r o f f a c t s a n d r e la t io n s . T h i s s e c t io n

I i I I1 ~

i

i | l

~ l l

8

[

c ~ ~

: j

N

N -

i i

FIo . 3 . R oo m plan for the robot tasks.

t t

J

i

A r t i f i c i a l I n t e l h g e n c e 2 1971) , 189-208

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20 4 RICHA RD E. lIKES AND NIL S J. NILSSON

d e s c r ib e s i ts p e r f o r m a n c e o n t h r e e d i ff e r e n t ta s k s . T h e i n i t i a l w o r l d m o d e l f o r

a l l t hr e e t a sk s c o n s i s ts o f a c o r r i d o r w i t h f o u r r o o m s a n d d o o r w a y s s e e

F i g . 3 ) a n d i s d e s c r i b e d b y t h e l i s t o f a x i o m s i n T a b l e 1 . I n i t i a l l y , t h e r o b o t

TABLE 1 . Formula t ion fo r STRIPS T a s k s .

Initial Wo rld M od el

VxVyVz)[CONN ECTS x ,y,z )=~ CC N N E CTS x,z ,y)]

C O N N E ~ R I , R O O M I , R O O M S )

C O N N E ~ R 2 , R OO M 2, R OO M 5)

CONNECTS (DOOR3,ROOM3,ROOMS )

CONNECTS (DOOR4,ROOM4,ROOMS )

LOCINROO M(f , ROOM 4)

AT BOXl,a)

AT(BOX2,b)

AT(BOX3,c)

A T ( L I G H T S W l T C H , d )

ATROBOT(e)

TYPE(BOXI,BOX)

TYPE(BOX2,BOX)

TYPE(BOX3,BOX)

TYP E( IM,DOOR)

TYP E(D3 ,DOOR)

TYP E(D2 ,DOOR)

T Y P E ( D I , D O O R )

I N R O O M ( B O X I , R O O M D

I N R O O M ( B O X 2 , R O O M I )

I N R O O M B O X 3 , R O O M I )

I N R O O M R O B O T , R O O M 1 )

I N R O O M ( L I G H T S W I T C H I , R O O M 1

PUSHABLF.(BOXI)

PUSHABLE(BOX2)

PUSHABLE(BOX3)

O N F L O O R

S T A T U S ( L I G H T S W I T C H I , O F F )

T Y P E ( L I G H T S W I T C H I , L I G H T S W I T C H )

Operators

gotol m): Rob ot goes to coordinate location m.

Preconditions:

(ONF LO OR) A (3x )[ INROO M(ROBO T,x) A LO CINROOM(m,x) ]

Dele te l is t: ATR OBO T( ) ,NEX TTO (ROBO T, )

A d d l i s t :

ATROBOT(m)

g6,o2 m): Robot goes next to item m.

Preconditions:

(ON FLO OR ) ^ {(3x) [INROOM (ROBOT,x) A INROO M(m,x)] V (3x)(3y)

[INRO OM (ROB OT ,x) A CONN ECTS(m,x,y)]}

Dele te l is t: ATR OB OT ( ) ,NEXT rO(RO BO T, )

A d d l i s t : NEXTTO (ROBOT, m)

pushto m,n): robo t pushes object m next[to item n

Precondition:

PUSHA BLE(m) ON FL OO R A NEX TTO(RO BOT ,m) {(~lx)[INROOM(m,x)

^ INROO M(n,x)] v Ox 3y)[ INR OO M (m,x) A CONNECTS(n,x ,y)]}

De le te l is t: AT ROB OT ( ) N EX Tr O (ROBOT ) NE XT I 'O ( ,m)

A T ( m S ) N E X T T O fm )

A d d l i s t : N E X T T O m , n )

NEXTTO n,m)

N E X T F O ( R O B O T ,m)

Artificial Intelligence 2 (1971), 189-208

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STRIPS 2 5

t u rnon l i gh t m ) : robo t turn s o n lightswitch m.

Precondition: {(3n)[TYPE(n,BOX) A ON(R OBO T, n) A NEXTO (n,m)I}

A TYPE(m, L IGHTSW ITCH)

Delete l is t : STATU S(re,OFF)

A dd lis t: STATUS(re,ON)

d i m b o n b o x m ) :

Rob ot climbs up on box m.

Preconditions:

ON i L OO R A TYPE(re,BOX) A NEXTFO(ROB OT,m)

Delete l is t: ATRO BO T($) ,ONFLG OR

A dd lis t : ON(ROB OT#n)

c l im b o f f b o x m ) :

Ro bot climbs off box m.

Preconditions:

TYPE(re,BOX) A ON(RO BOT,m)

Delete list: O N(RO BO T, m)

A d d l is t: O N F L O O R

oo t hrudoar k , l , m ) : Ro bot goes through door k from room I into room m.

Preconditions:

NEXTTO (ROBOT, R) A

C O N N E C T S ~ , k , I , m )

A I N R O O M ( R O B O T ,0 A O N F L O O R

Delete l is t : ATROBO T($),NEXTTO(ROBOT,$),INROOM (ROBOT, $)

Add l is t: INROOM (ROBOT,m)

T a s k s

1 . Turn on t he l igh t sw i tch

Go al wfl ': STATUSOLIGH TSWITCHI,ON)

STR IPS solution: {goto2(BOXl),climbonbox(BOXl),climboffbox(BO Xl),

pushto(BOXI,LIGHTSWlTCHl) ,c l imbonbox(BOXl) ,

turnonl ight(LIGHTSWITCHI)}

2 . P u s h t h r e e b o x e s t o g e t h er

Goa l w ff: NEXTTO (BOXI,BOX2) A NEXTTO (BOX2,BOX3)

STRIPS solution: {goto2(BOX2),pushto(BOX2,BOXl),goto2(BOX3),pushto

(BOX3,BOX2)}

3 . G o t o a l oca t ion i n ano t her room

Goa l w ff : ATR OBO T(f)

STR IPS solution: {goto2(DOORl), gothrudoor(DO OR 1,ROO M 1 ROOM S),

gogo2(DOO R4),gothrudoor(DOOR 4,ROOMS,ROOM 4),

gotol(f)}

is i n R O O M I a t lo c a t io n e . A l s o in R O O M I a r e th r e e bo x e s a n d a l ig h t sw i t ch :

B O X I a t lo c a t i o n a , B O X 2 a t l o c a t i o n b, a n d B O X 3 a t lo c a t i o n c ; a n d a l ig h t -

s w i tc h , L I G H T S W I T C H I a t l o ca t io n d . T h e l ig h ts w i tc h is h i g h o n a w a ll o u t

o f n o r m a l r e a c h o f t h t ~ ob ot.

T h e f ir st t a sk is t o t u r n o n t h e l i g ht sw i t c h. T h e r o b o t c a n s o lv e t h is p r o b l e m

b y g o i n g t o o n e o f t h e t h r e e b t , xe s , p u s h i n g i t t o t h e l i g h t sw i t c h , c l im b i n g o n

t h e b o x e a n d t u r n i n g o i l t h e li g h t3 w i t ch . T h e s c t: o n d t a s k i s t o p u s h t h e t h r e e

b o x e s i n R O O M I t o g e t h e r . ( T h i s t a s k i s a m o r e r e a li s ti c e l ab o ra t _i o n o f t h e

6 Th; task is a robot version of the so-called M onk ey and Banana s problem. STR IPS

can solve the problem even though the current SRI robot is incapable of climbing boxes

and turning on lightswitches.

Art i f i c ia l In te ll igence 2 (1971), 189-208

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2 0 6 m C n A a D E ~ A N D N I t S J. Ng,SSON

t h r e e- b o x p r o b l e m u s e d a s a n e x a m p l e i n t h e l a st s e ct io n . ) T h e t h i r d t a s k i s f o r

t h e r o b o t t o g o t o a d e s i g n at e d l o c a t io n , f , i n R O O M 4 .

T h e o p e r a t o r s t h a t a r e g i v e n t o S T R I P S t o s o l v e t h e s e p r o b l e m s a r e

d e s c ri b e d i n T a b l e 1. F o r c o n v e n i e n c e w e d e fi n e t w o " g o t o " o p e r a t o r s , g o t o l

a n d g o to 2 . T h e o p e r a t o r g o t o l ( m ) t a k e s t h e r o b o t t o a n y

c o o r d i n a t e

l o c a t i o n

m i n th e s a m e r o o m a s t h e r o b o t . T h e o p e r a t o r g o t o 2 ( m ) t a k es t h e r o b o t n e x t

t o a n y

i t e m m

( e .g . , ~ igh tswit ch , do or , o r box) i n t he sam e roo m as t he rob o t .

T h e o p e r a t o r p u s h t o ( m , n) p u s h e s a n y p u s h a b l e o b j e c t m n e x t to a n y

i t e m n

( e.g ., li gh ts w i tc h , d o o r o r b o x ) i n t h e s a m e r o o m a s t h e r o b o t . A d d i t i o n a l ly ,

w e h a v e o p e r a t o r s f o r t u r n i n g o n l ig h t sw i tc h e s, g o i n g t h r o u g h d o o r w a y s , a n d

c l im b i n g o n a n d o f f b o x e s. T h e p r e c i s e f o r m u l a t i o n o f th e p r e c o n d i t io n s a n d

the e f fect s o f t hese o pe ra t3 r s i s con ta ined in Tab le 1.

TASLE 2 . Pe r fo rm ance o f ST RIP S on " Ih ree Tasks .

Num ber of o perator

Time taken Number of n o d e s appl ica t ion s

(in seconds) On solution In search On solution In search

To ta Theorem -proving tyath tree path tree

Turn on the

iightswitch 113.1 83.0 13 21 6 6

Push three

boxes together 66.0 49.6 9 9 4 4

G o to a locat",n

in ano ther room 123.0 104.9 11 12 5 5

W e a l so l is t i n Tab le 1 t he goa l wf fs fo r t he th ree t a sk s a nd the so lu t ions

o b t a i n e d b y S T R I P S . S o m e p e r f o r m a n c e f i g u r e s f o r t h e s e s o l u t i o n s a r e

s h o w n i n T a b l e 2 . I n T a b l e 2 , t h e f ig u re s i n th e " T i m e T a k e n " c o l u m n r e p r e -

s e n t th e C P U t i m e ( e x c lu d in g g a r b a g e c o l le c ti o n ) u s e d b y S T R I P S i n f in d i n g

a s o l ut io n . A l t h o u g h s o m e p a r t s o f o u r p r o g r a m a r e c o m p i l e d , m o s t o f t h e

t i m e i s s p e n t r u n n i n g i n t e r p r e t i v e c o d e ; h e n c e , w e d o n o t a t t a c h m u c h

imp or t ance to t hese times . We n o te t h a t i n a l l c a ses m os t o f t he t ime i s spen t

d o i n g t h e o r e m p r o v i n g ( i n Q A 3 .5 ) .

T h e n e x t c o l u m n s o f T a b l e 2 in d i c a t e t h e n u m b e r o f n o d e s g e n e r at e d a n d

t h e n u m b e r o f o p e r a t o r a p p l i c a t i o n s b o t h i n t h e s e a r c h t r e e a n d a l o n g t h e

s o l u ti o n p a t h . ( R e c a l l f r o m F i g. 2 t h a t s o m e s u c c e ss o r n o d e s d o n o t c o r r e s -

p o n d t o o p e r a t o r a p p l i c a t i o n s . ) W e s e e f r o m t h e s e f i g u r e s t h a t t h e g e n e r a l

sea rch heur i s t i c s bu i l t i n to STRIPS p rov ide a h igh ly d i r ec t ed sea rch toward

the goa l . These heu r i s t i c s p re sen t ly g ive the sea rch a l a rge "dep th - f i r s t "

c o m p o n e n t , a n d f o r t h i s r e a s o n S T R I P S o b t a i n s a n i n t e r e s t i n g b u t n o n -

o p t i m a l s o l u t io n t o t h e " t u r n o n t h e l ig h t - sw i t c h " p r o b l e m .

rtbqcial Intelligence 2 (1971), 189--208

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slmn,s

2 7

5 Future P lans and Prob lem s

Th e cu rren t implem entat ion of STR IPS ca n be ex tended in several d i rect ions .

The se ex tens ions wi ll be the sub ject o f m uch of ou r p rob lem -so lv ing research

act iv i ties in the im m ediate fu ture . W e m ent ion some of these brief ly .

W e have seen tha t ST RIPS cons t ruc t s a p rob lem-so lv ing t r ee whose nedes

rep resen t subp rob lems . In a p rob lem-so lv ing p rocess o f t h i s so r t , the re m us t

be a mechan i sm to dec ide wh ich node to w ork on next . Cur ren t ly , we use an

eva lua t ion func t ion tha t i nco rpo ra t es such f ac to r s as t he number and the

es t imated d i f f icu l ty o f the remain ing subgoals , the cos t o f the operators

appl ied so far , and the complex i ty of the curren t d i f ference. We expect to

devote a good deal o f ef for t to dev is ing and exper iment ing wi th var ious

evaluat ion funct ions and o ther o rder ing techniques .

A no th er a rea fo r fu tu re r esea rch concerns the syn thesi s o f more complex

procedures than those consis t ing of s imple l inear sequences of operators .

Specif ica lly, we w ant to be ab le to g enerate p roced ures involv ing iter~tion (or

recurs ion) and condi t ional b ranching . In shor t , we would l ike STRIPS to be

ab le to generate c om pute r p rograms. Several researchers [4 , 8 , 9 ] have

a l ready cons idered the p rob lem o f au tom at i c p rog ram syn thes is and we

expec t t o be ab le to u se som e o f the i r ideas in STRIPS .

W e are a l so in teres ted i t, ge t t ing ST R IPS to lea rn by hav ing i t define

new o perators fo r i t se l f on the bas is o f p rev ious prob lem so lu t ions . These new

ope rator s co u ld then be used to so lve even m ore d i ff icult p rob lems. I t w ould

be im por t an t t o be ab le to genera li ze to pa ram ete r s any cons t an t s appear ing

in a new ope ra to r ; o the rwise , t he new opera to r lwou ld no t be genera l eneu gh

to w arra n t sav ing. On~ appro ach [10] that appears p rom is ing is to modify

ST R IP S so th at i t so l,~cs every prob lem presen ted to i t in term s uf general-

ized parameters ra ther than in terms of constan ts appear ing in the speci f ic

pro ble m s ta tem ents . H ew i t t [11] d iscusses a re la ted process tha t he cal ls

p roce du ra l abs t r ac t ion . He suggest s t ha t , f rom a f ew in s t a n t s o f a p ro -

cedure , a gen eral vers ion can somet imes be syn thesized .

Th i s t ype o f lea rn ing p rov ides pa r t o f ou r r a t iona le fo r w ork ing on au to -

m at ic p rob lem so lvers such as STR IPS. Som e researchers have ques t ioned the

value of sys tems for au tomat ical ly chain ing together operators in to h igher-

level p rocedures tha t themselves could have been ha nd cod ed qu i te eas ily

in the f i rs t p lace. The i r v iewpoin t seems to be that a rob ot sys tem should be

p rov ided a p r io r i wi th a r eper to i r e o f a l l o f the op era to r s and p rocedu res tha t

i t w il l ever need.

W e agree that i t is des irab le to p rov ide a p r io r i a large num ber of specia l ized

operators , bu t such a reper to i re wi l l never theless be f in i te . To accompl ish

tasks jus t o u ts ide the bou nd ary o f a p r io r i ab i l it ies requi res a p rocess fo r

cha in ing toge ther ex i s t ing opera to r s i n to more complex ones . We a re in -

teres ted in a system wh ose operator reper to i re ~ .an gr ow in th is fash ion .

r t i f t c i a l In t e l l i g e n c e 2 1971), 189-208

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20 8 RICHARD E. FIKES AND NIL S J. NILSSON

C l e a r l y o n e m u s t n o t g i v e s u c h a s y s te m a p r o b l e m t o o f a r a w a y f r o m t h e

b o u n d a r y o f k n o w n a b i li ti es , b e c a u s e th e c o m b i n a t o r i c s o f s e ar c h w ill t h e n

m a k e a s o l u t i o n u n l ik e ly . H o w e v e r , a t r u l y i n t e l l i g e n t s y s te m o u g h t

a l w a y s t o b e a b l e t o s o lv e s l ig h t l y m o r e d if fi cu l t p r o b l e m s t h a n a n y i t h a s

s o l ve d be f o r e .

ACKNOWLEDGEMENT

The development of the ideas embodied in STRIPS has been the result of the combined

efforts of the present authors, Bertrmn Raphael, Thomas Garvey, John Mtmson, a:~d

Richard W aldinger, all m embers of the A rtificial Intelligence Gr ou p at SR L

Th e research reported herein was sponso red by the Advanced Research Projects Agen cy

an d th e Nat ional Aeronautics and Space Administration under C ontract NAS12-2221.

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ment.

Proc. 2n d Int l . Jo int Conf. Artif icial Intelligence,

London, England (September

13, 1971).

3. Fikes, R. E. M onitored execution of robo t plans produced by ST RIPS .

Proc. IF IP 71,

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Artificial Intelligence, Washington, D.C. (May 1969).

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GP S: A Case Stud y in G eneral ity an d Problem Solving.

A C M

M onograph Series. Academic Press, New Y ork , New Y ork , 1969.

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Research Institute Artificial Intell igence G rou p Technical N ote 15, Menlo P ark,

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lnt l. Conf. Artificial Intelligence,

Washington, D.C. (May 1969).

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chusetts Institute of Technology, Cambridge, Massachusetts (August 1970).

Artificial Intelligence

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