A Short Report about Motion Safety

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HAL Id: inria-00101500

https://hal.inria.fr/inria-00101500v2

Submitted on 28 Sep 2006

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A Short Report about Motion Safety

Thierry Fraichard

To cite this version:

Thierry Fraichard. A Short Report about Motion Safety. [Research Report] RR-5987, INRIA. 2006,

19 p. �inria-00101500v2�

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a p p o r t

d e r e c h e r c h e

ISRN INRIA/RR--5987--FR+ENG

Thème NUM

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

A Short Report about Motion Safety

Thierry Fraichard

N° 5987

September 27, 2006

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#C=Oi/Uch;UP;}\,P;=?-JRKLVRwTV=fi/\bR;TjJ="\^¯ebiLVUc\bP|UcJ2e®g;TN\Ki=OJNJ²LV9we^L[U<>g;cUc=OJ2ei=OTLje^UcP|eb<|\,R;PYL2\^tTN=Oe,J\,P;UcP;}

ebrt\,RKL[LN9;=fRKLNR;TN= /Hb\bRh;=OiUXhK=fPw\!ªQ9we^LH,\bR>QUc¯hK\P;=4YL-2±;\bTeTV\,rt\bLVUXifJVHIJLV=O<v^LV9w=ChK=-iUXJUc\bPK_

<ebYUcP;}ªg;TV\Ki/=OJNJUXJRwJVRwe^cH rwe,J=-h1\,P eª<|\KhK=O\^LN9;=TV\,rt\bLVUXiJVHKJMLN=/< ULNJV=/RtJRwebcH }bUcb=OP

eqg;TVUc\bTNU¦v2e^Pwh¹ea<>\Ih;=/"\^fULNJs=/PIIUTN\bP;<>=OP,L-¬89;==/PIIUTN\bP;<>=OP,Ls<|\KhK=O"iOe^P i/\b<rwUP;=eag;TNU\,TVU

UcPK\,TV<e!LNU\,P N *)><e^gwJjv JV=/PtJ\,T®<>=-ebJVR;TV=O<>=/PYLNJOv°\bTi/\b<>g;RKLje!LNU\,PTN=OJVR;LNJV *)>gwTV=-hKUciLVUc\bP\^"LV9;=

R;LVR;TN=- =-JUXhK=-J®LV9;=gwebTLNUci/R;Xe^TjJC\bLN9;=hK=Oi/UcJVUc\bPK_`<e^IUPw}g;TN\Ki=-JVJ®ULNJV=/Mv LN9;=<>\Ih;=/XJ®LV9we^Le^TN=

i/\bPwJVUXhK=/TN=Oh9we4b=e>hKUcTV=-iLQU<>gwe,iLf\,PLN9;=hK=Oi/UcJVUc\bPQ9;Ucij9UXJ"LNebb=/P

89;UXJ[JV=OiLVUc\bP>= ;e^<>UcP;=OJLN9;TN=/=fi\,<><|\,P|JV=/PtJ=fi/TVULV=OTVUXe®Q9;Ucij9 v^U«IUc\bXe!LV=-hv^<e4HgwRKL2LV9;=CebiLNRwe^

TN\br$\^LNUcisJHKJLV=O< UPYLV\h;ebP;}b=OT®ebPwhqHIUc=/Xh¬ei\bccUcJVU\,P¬e!LJV\b<>=g$\bUcPYL®UcPLV9;=|RKLNR;TV=,89;=-J=>JVe^=LMH

i/TVULV=OTVUXeebTV=TN=OJVg$=OiLNU,=/cHTN=/Xe!LN=OhLN\LN9;=<>\KhK=/\^LV9;=sTV\,rt\bLVUXiJVHIJLV=O<vwLN9;=s<>\KhK=O²\b2LV9;=|=/PIIU«_

TN\bPw<|=OPYL"e^Pth>LV9;=hK=-iUXJUc\bP;_*<e^IUcP;}g;TN\Ki=-JVJO²§Pe^c¯iOebJV=OJOv,ULUcJebJNJVR;<>=Oh>LN9we!LQei/\b<>g;c=LV=®<>\KhK=/

\bQLV9;==/PIIUcTV\,P;<>=/PYLUXJse4!e^UcXe^r;c=bv2i\,<>g;=/LV=LV\qLN9;=gt\,UPYLLN9we!L>UL>ebcJV\¬i\,<>g;TVUXJV=OJUcPK\,TV<e!LNU\,P

ebrt\,RKL|LV9;=RKLVRwTV=<>\^LNU\,P¹\^ALV9;=<>\!IUP;}\brK]M=-iLjJ/ 89;=Tje!LVUc\bPte^c=r$=/9;UcPwh¹LV9;UXJ|UcJsLV9te!LU«CLV9;=

JNe!=/LMH¬iTNULV=/TNUXeebg;g;cU=-JQULV9gt=OT=-iLUcPK\,TV<e!LNU\,P°v°ULUXJ= Kg$=OiLN=OhLV9w=/< LV\ar$=e^XJ\TN=/c=/!e^PYLUcP

LN9;=UcPwi\,<|gw=/LV=UP;\bTN<>e^LVUc\bPi/e,J=,

89;=®JVe^=LMHiTNULV=/TNUXee^TN=Ae^ctUccRwJLVTje!LN=Oh>RwJVUcP;}LN9;=A=4Keb<>g;=C\^ e\,P;=_§hKUc<>=/PwJVU\,Pwe^tgt\,UPYL"TV\,rt\bL

A

QULV9hK\,R;r;c="UcPYLV=O}bTje!LV\,T2hKHIPwe^<>UXi/JQ¨JVR;rK]M=-iL2LV\,=/c\KiULMHe^Pwh>ebiOi=O=OTNe^LVUc\bPr$\bRwPwh;Jjv,ebPwhsQ9;Ucij9 UXJ(<>\!IUP;}e^c\bPw}®e®cUP;=-e^T2gwe^LV9°

A

UXJ[ij9webTNe,iLN=/TNUcJV=OhrIHULNJ(g$\,JVULVUc\bP

p

eb\,P;}CLV9;=Qgwe^LV9°vbU«LjJ2b=O\KiULMH

|v| ≤ v ^max

v;e^PwhULNJfe,i/i/=/c=/Tje!LVUc\bP

|a| ≤ a ^max

1 8@"F#G "F?9 #G

0\,PwJVUchK=OTs±Uc}wczQ9;=/TN=eqgt\,UPYLs\,rK]M=OiL

B

UXJse^Lsg$\,JVU«LNU\,P

p ^b

^{e^c\bP;}}

A

^-Jsgwe^LV9°

A

J9;\,R;XhP;=/,=/T h;=OiUXhK=®LV\\KiOiR;gIHg$\,JVU«LNU\,P

p ^b

JVUPwi/=U«Lf"\bR;Xhrt=UcPai\bccUcJVU\,PQULV9

B

(9)

A B

(p, v) p b

d(v) d(v, v b )

±Uc}bR;TN=>z / CP;=/_`hKUc<>=/PwJVUc\bPwebgt\,UPYLQTV\,rt\bLQ= ;e^<>g;c=b

A B

t

p v/a ^max

d(v) p b

±Uc}bR;TN=uF/89;=>Z(\,JVU«LNU\,P

×

8U<>=>Jgtebi=|\^"LV9w=|\,P;=_§hKUc<>=/PwJVU\,Pwe^(g$\bUcPYLTN\br$\^L

A

Q9;=/PU«LrwTNebb=OJ h;\!QPe^Pth¬JLV\bgtJs¨r;Rw=>i/R;TNb=\,PqLN9;=>=/¦Lj|89;=|}bTN=/=/PiR;TNb=s\bP¬LV9;=>TNU},9,Li\,TVTN=OJVgt\,Pwh;JfLV\LV9;=

I=-h\,rK]M=OiL

B

(10)

"=OiOe^RwJV=Q\^ULNJhKHIPwe^<>UXi/JOvbUL[LNebb=OJ

A

e<>UcP;Uc<R;< LVUc<>=

v/a max

LV\sJc\! h;\!QP>ebPwhJLV\bg 89;=

h;UcJLNebPwi=®LVTje4b=Oc=OhUcJ /

d(v) = v ² /2a max .

^Mz-

`

A

hKUcJVTN=/},ebTNhwJULNJ\!QPhKHIPwe^<>Uciij9webTNe,iLN=/TNUcJLVUXi/JOv,ULfi\,R;chhK=-iUXhK=®LV\>\Ki/iRwgYHeg$\,JVU«LNU\,PQULV9wUP LN9;=

[p ^b − d(v), p ^b [

TNebP;}b=AJVUcPwi=JRtij9gt\YJULVUc\bPtJebTV=®i\bccUcJVU\,PK_*TV=O=b2FI9;\bRwchLV9;UXJ"9we^g;g$=/P v

A

^\,R;ch

r$=UPsLVTN\bRwr;="r$=Oi/ebRwJV=UL2\,R;ch=/,=/PYLVRwebcHiTjebJV9UcPYLV\

B

P;\®<e!LVLV=/T2Q9te!L(U«L[hK\I=OJUcPLN9;="RKLVRwTV=4

8e^IUcP;}|UPYLV\e,i/i/\bR;PYL"LV9;=hKHIPweb<>UciOJ\^

A

vKLV9;=Tje^Pw}b=

[p ^b − d(v), p ^b ]

r$=Oi/\b<>=OJQ\bTNr;UchwhK=/P°

89;="JVeb<>=[i\bPticRwJUc\bPiOe^Pr$=hKTje4QPrIHCc\I\bIUPw}fe!L°LN9;=g$\,JVU«LNU\,P

×

LVUc<>=Jgtebi=\^

A

ebJ²hK=/gwUciLV=Oh UcP¬±Uc}wuIQ`LCUXJCe,JVJVR;<>=OhLN9we!L-v¯e^LfLVUc<>=sxwv

A

UXJCe^LAgt\YJULVUc\bPqxQU«LN9qb=O\KiULMH

v

^. ^9w=/P

A

rwTNebb=OJ h;\!QP e^PwhJLV\,gwJe^Ls<e KUc<R;< hK=Oi/=/c=/Tje!LNU\,P°v²ULLNTNe,i=-JeagwebTNebrt\,UXie^Tji>UcPLV9;=gt\YJULVUc\bP

×

LNU<>=

JVgwe,i=bCPti=UL®9tebJAJLV\,g;g$=Ohv$U«LCLVTjebi/=OJAeb=/TVLVUXi/eb cUPw=¦LN9;=rwR;=|iR;TNb=UP¬±Uc}wu^C89;=,=/TVLVUXi/e^

},TV=O=/PUcP;=i\,TVTN=OJVgt\,Pwh;JALV\LV9w=s I=-h¬\,rK]M=OiL

B

^. 9;=/PLN9;=hKUcJLNebPwi=>r$=LM"=/=OP

A

^{e^Pwh}

B

UXJCc=OJNJ LN9we^P

d(v)

v;LV9;=Cr;Rw=®ebPwh},TV=O=/PiRwTV,=AUcP,LN=/TjJ=-iL"=Oebij9\bLV9;=OT<>=-e^P;UcP;}LN9we!LQei/\bcUXJVU\,PQUc¯\Ki/iRwTO

89;UXJ=4Keb<>g;=aUccRwJLVTje!LN=OJ|LN9;=¨ebiLLV9we^LOvQ9;=/Pw=/b=OTeTV\,rt\bLVUXiJHKJLV=/< hKUXJTN=/}Ye^Tjh;JULNJ\!QP

h;HYPte^<>Uci|ij9webTNe,iLV=OTVUXJLVUXi/JOvwUL<e4HqhK=-iUXhK=|\bPeRKLVRwTV=i\,R;TjJ=s\^e,iLVUc\bP¬\bT®Q9;UXij9JNe!=LMHaUXJ®P;\^L

},Rwe^Tje^PYLN=/=Ohe^Pwhi\,cUXJUc\bP<e4H>LNe^,=g;ce,i==/,=/PYLVRte^cH,vK9;=/Pwi/=LV9;=tTNJLfJVe^=LMHi/TVULV=OTVUc\bPA/

À Á À Ä ¡`º 'b j£/¥'b >¥¦¡6 K¡K¤V >º^¡6¥¨º^´¤Vº,¶jº!¡*¥¨£sj¢4¡§ ;º K·'a£jº!´wj¥', ¤s¥¦¡¨

1 21 5$9#%5 ?5" B 8 ? " 9 "9? ? $9#%

e,ij¹LN\ª±U}tz¬r;RKLaebJNJR;<>UcP;} P;\! LN9we!L

B

UcJ<>\!YUcP;}LN\ LN9;=¬c=¦LQU«LN9 eªi\bPtJMLje^PYLb=O\Ki/U«LMH

v ^b ≤ v max

|§PLV9wUcJJVU«LNRwe!LNU\,P°v°ULLNebb=OJ®<>\bTN=sLV9webPJLNe4HIUcP;}\bRKL\^LV9;=

[p ^b − d(v), p ^b ]

g$\,JVU«LNU\,P Tje^Pw}b=LN\},Rwe^Tje^PYLN=/=LN9;=JVe^=LMH\^

A

§PwhK=O=OhvR;P;c=OJNJ

A

JV9;U¦LNJ>UcPªTN=/,=/TjJ=RwP,LNUQULTV=-ebij9;=-Je

,=/c\KiULMHe!Lfc=OebJLQ=OWYRweb¯LV\

v ^b

vwe>i\bccUcJVU\,PQULV9

B

QUcc°\Ki/iRwTO

×

8U<>=Jgtebi=C\^

A

e^c\!fJLV\hK=/LV=OT_

<>UcP;=sLV9;=|TNebP;}b=\^[\,TVr;UXh;hK=OP¬g$\,JVU«LNU\,PwJCUP¬LV9;UXJi/ebJV=b±Uc}whK=Og;UciLNJCLV9w=sZ(\,JVULVUc\bP

×

8Uc<>=sJVgwebi/=

\b

A

`L|UXJ>ebJNJRw<|=-hLV9we^LOve^LsLNU<>=x;v

A

UXJ|e!L>gt\YJULVUc\bP¹x¬QU«LN9¹,=/c\Ii/U«LMH

v

89;=r;cR;=iR;TNb=

TN=/gwTV=-J=OP,LjJQLN9;=|LVTje!]M=OiLV\,TVH\bcc\!=-harIH

A

Q9;=/PULJV\!fJ®hK\!QP°v°JLV\,gwJe^PwhJ9wU«¦LjJCUcPTV=Ob=/TjJV=e!L

<e IUc<Rw< e,i/i/=/c=/Tje!LVUc\bP>R;PYLNU$U«LTN=Oebij9w=OJ2,=/c\Ii/U«LMH

v ^b

UL"UXJ<>e,hK=fR;g\^LM"\gwebTNebrt\,UXife^Tji/Je^Pwhe

cUcP;=J=O}b<>=/PYL89;=},TV=O=/PiR;TNb=TN=/gwTV=-J=OP,LjJLV9;=LNTNe^]M=OiLV\bTNH>\bcc\!=-hrIH

B

<>\!YUcP;}e!LAi/\bPwJLNebPYL

,=/c\KiULMH

v ^b

^. 9;=/PLV9w=>h;UcJLNebPwi=|rt=/LM=O=/P

A

^ebPwh

B

UXJc=OJNJALN9we^P

d(v, v ^b )

v°LV9;=>r;cR;=e^Pwh}bTN=/=OP i/R;TNb=®UPYLV=OTNJV=OiLQ=Oebij9\^LN9;=/TQ<>=-e^P;UcP;}|LV9we^LAe>i\bccUcJVU\,PQUcc\IiOiR;T-2`LAi/ebPr$==OJLNebr;cUcJV9;=OhLV9te!L /

d(v, v ^b ) = (v + v ^b ) ² /2a ^max .

^6ub

8e^IUcP;}UPYLN\ ebi/i/\bR;PYLr$\^LN9ªLN9;=¬hKHIPweb<>UciOJ\^

A

e^PwhªLV9w=¬hKHIPwe^<>UXiULMH¹\b

B

v"LV9;=¬TNebP;}b=

[p b − d(v, v b ), p b ]

r$=Oi/\b<>=OJ"\,TVr;UXh;hK=OP¨±U}tz-

89;UXJ(= ;eb<|gw=UccRwJLVTje!LV=-J²LV9;=¨e,iL(LV9we^LOv^Q9w=/P;=Ob=/T2e®TN\br$\^LVUXi"JHKJLV=/< hKUcJVTN=/},ebTNhwJ°LN9;="¨ebiL2LN9we!L

ebP\brK]M=-iLAUXJAe,iLVRte^cH<|\!IUcP;}wvwU«L®<>e4HhK=Oi/Uch;=\bPqe|RKLNR;TN=si\,R;TjJ=\^[e,iLVUc\bP\,TAQ9;UXij9qJVe^=LMHUcJ

Pw\^LQ}bRwebTNebPYLV=/=-hebPwhi/\bcUXJVU\,P<e4HLje^b=g;Xebi/==/b=OPYLVRwebcHbvK9;=OPwi=®LN9;=J=-i\,PwhJNe!=/LMHiTNULV=/TNUc\bPA/

(11)

A B t

p t ¹

t ²

p ¹

p ² d(v, b b ) p b

±Uc}bR;TN= /|89;=gt\YJULVUc\bP

×

LNU<>=Jgwe,i=\bQLV9;=\bP;=/_`hKUc<>=/PwJVUc\bPweb[gt\,UPYLTN\br$\^L

A

^Q9;=/P ULsrwTNebb=OJ h;\!QP°v°JMLN\bgwJebPwhJV9;U¦LNJUcPTN=/,=/TjJ=sR;PYLVUc2U«LTN=Oe,ij9;=OJCb=O\KiULMH

v b

rwR;=i/R;TV,=s\,P¬LN9;=>=/¦Lj|89;=

},TV=O=/PiR;TNb=\bPLV9w=TVUc}b9YLfi\,TVTN=OJVgt\,Pwh;JLV\|LN9;=\brK]M=-iL

B

<>\!IUcP;}|e^LAi\,PwJMLje^PYLb=/c\KiULMH

v b

(12)

À Á À Ä wº 'b j£/¥'b s¥¦¡6 K¡K¤V >º^¡6¥¨º^´"¤Vº,¶Nº^¡6¥¨£¢4¡` wºK·'£jº!´wj¥', ¤¡w

t

p B

p b

t e

t l

t h

A

! "

A

#

! "

±Uc}bR;TN=//2dfe^Pw}b=\^gt\YJVJVUrw=®LVUc<>=LV\i/\bcUXJUc\bP

1 $ %4# ?'& 7#(

`P;=/=-hK=Ohar$=bv¯LN9;=|g;TV=OIU\,RwJQLM"\= ;eb<|gw=-JA9we4,=TN=/b=-e^c=OhLN9;=¨e,iL®LV9we^L®JNe!=/LMHUXJCP;\^LJUc<>g;cHe

<e^LLV=OTA\b[b=/=Og;UcP;}>LV9;=sTV\,rt\bLVUXiJVHIJLV=O<e4e4HTN\b< i\,cUXJUc\bPqJLNe^LV=OJOQ`LCUXJQRwPwh;e^<>=OP,Lje^²LV\,=/=Og

LN9;=>TV\,rt\bLVUXisJVHKJMLN=/< e4e4HTV\,< JMLje!LV=-J®LV9we^L®=Ob=OP,LNRwe^ccHaHYUc=/Xhei/\bcUXJUc\bPe!LJV\b<>=sg$\bUcPYLUPLV9;=

R;LVR;TN=bf8²\LV9te!LC=OPwhv$TV=-ebJV\bP;UcP;}e^r$\bR;LfLV9;=RKLVRwTV=sUcJATV=-W,RwUTN=Oh 0\,<|UcP;}i/TVULV=OTVUc\bPa=4Igw\,TV=-JLV9;=

Uc<>gwebiLQ\^LV9;==4YLN=/PYLQLV\>Q9;UXij9LV9;=RKLNR;TN=UcJQ=4Kg;\,TV=-h

=LRwJi\bPtJUXhK=/T(LN9;=fJVU«LNRwe!LNU\,P|Q9w=/TN=

A

9we,JLV\hK=-iUXhK=QQ9;=/LV9;=OT2LV\\Ki/i/R;gIHse®g$\,JVU«LNU\,P|c\Ki/e^LV=Oh

QULV9wUP¬LV9;=>Tje^P;},=

[p ^b − d(v, v ^b ), p ^b ]

\bgt\YJULVUc\bPtJf\,TVr;UXh;hK=OP*)2¤¡²LV9;=><>\!IUPw}\brK]M=-iL

B

§PqLV9wUcJ iOebJV=bvYi\bccUcJVU\,PhK\I=OJP;\^L[Lje^,=fg;Xebi=ATVUc}b9YLP;\!v,U«L"9we^gwgt=OPwJ[Xe!LN=/Te^L"eLNU<>=CUPwJLNebPYL[LV9we^L"hK=Ogt=OPwh;J

\,PLV9;=RKLVRwTV=rt=O9we4IU\,R;T\^

A

vQ¥¨ Q9;=/LV9;=OTUL|ebiOi=O=OTNe^LV=OJ\bTsh;=Oi=O=OTNe^LV=-J¨±Uc}wY =/L

[t ^e , t ^l ]

r$=qLN9;=TNebP;}b=q\bLVUc<>=UcPwJLNe^PYLjJQ9;=OP i\,cUXJUc\bP1QUccALje^b=g;Xebi=, "\^LN9

t ^e

^ebPwh

t ^l

ebTV=¬=OebJVUcH h;=LV=OTV<>UcP;=Oha¨TV\I\bLNJ[\b°eWYRwebhKTje!LNUcif=OWYRwe!LNU\,Pt(©AJNJVR;<>UP;}P;\! LV9we^L

A

hK=-iUXhK=OJU«LjJ2RKLNR;TV=C<>\^LVUc\bP rIHTV=-JMLNTVUXiLNUPw}U«LjJATN=Oe,J\,P;UPw}sLN\e>tP;U«LN=LNU<>=_`9;\,TVUc/\,P

t ^h < t ^l

^LN9;=/P

A

<e4Hb=OTVH=O(hK=-iUch;=LV\

\KiOiR;gIHLN9;UXJfg$\,JVU«LNU\,Pr$=OiOe^RwJV=bv;TV\,<ULNJQg$\bUcPYLA\^2IUc=/v;ULAUXJfg$\,JNJUcr;c=LV\e4b\,Uchi\,cUXJUc\bPQULV9

B

¨R;gLN\

t ^h

vILV9w=h;=Oi=O=OTNe^LVUcP;}LNTNe^]M=OiLN\bTNH>UcJi\,cUXJUc\bPK_*TN=/=-²§PtiTN=OebJVUcP;}LV9w=CLNU<>=®9;\bTNUc/\bPhK\I=OJ"P;\^L JV\bcb=sLV9w=|gwTV\,r;=O< r$=Oi/ebRwJV=bv°UcP}b=/Pw=/Tje^*v¯LV9;=|RKLNR;TV=i/\bcUXJVU\,Pi\,R;Xh¬9webg;g$=/Pe!LeLVUc<|=UcPwJLNebP,L

(13)

ebTVrwU«LNTNebTVUcHq¨e^Tse4e4HqUcPYLV\LV9w=RKLNR;TV=¨hK=Ogt=OPwhKUcP;}q\,PLV9;=hKHIPwe^<>UXii/e^gte^r;UcULVUc=OJ\^

A

^{e^PthLV9;=}

R;LVR;TN=rt=O9we4IU\,R;T\^

B

§PLN9;UXJTN=OJVgt=-iL-v,ULUXJebTV},R;=OhsLN9we!L-vYQ9w=/P;=Ob=/TeTV\,rt\bLVUXifJVHIJLV=O< hK=Oi/UchK=-J[ULNJRKLVRwTV=C<|\bLVUc\bPrIH

TN=OJLVTNUXiLVUcP;}QULNJ²TV=-ebJV\bP;UcP;}"LV\CewP;ULV=LVUc<|=/_*9w\bTNUO\bP°v4i\,cUcJVUc\bP<e4HCg$\^LN=/PYLVUXe^cH®9webg;gt=OPr$=/Hb\,Pwh®LV9wUcJ

LNU<>=/_*9;\,TVUc/\,PebPwhJVe^=LMHiOe^P;P;\bLQrt=},Rwe^Tje^PYLV=O=Ohe,i/i/\bTjhKUPw}bcHbvI9;=/Pti=LV9w=LV9;UcTNhJNe!=LMHiTNU«LN=/TNU\,PA/

À Á À Ä $ wº ', N£/¥'b ¥¦¡6A K¡K¤V º!¡*¥¨º!´ q¤Vº,¶jº!¡*¥¨£j¢4¡§ ;º K·'¤V j4/º!´ º!µ! /¤!´

89;=-J=LN9;TN=/=iTNU«LN=/TNUce ebTV=}b=OP;=/Tje^ebPwhvhK=Ogt=OPwhKUcP;} \bP½LV9w= iUcTNi/R;<JMLje^Pwi/=OJOv®e Pwe4IUc},e^LVUc\bP

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Unité de recherche INRIA Rhône-Alpes

655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France)

Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France)

Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)

A Short Report about Motion Safety

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A Short Report about Motion Safety

Thierry Fraichard

To cite this version:

Thierry Fraichard. A Short Report about Motion Safety. [Research Report] RR-5987, INRIA. 2006,

19 p. �inria-00101500v2�

a p p o r t

d e r e c h e r c h e

ISRN INRIA/RR--5987--FR+ENG

Thème NUM

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

A Short Report about Motion Safety

Thierry Fraichard

N° 5987

September 27, 2006

∗

∗

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