www.cs.washington.edu - UW Robotics and State Estimation Lab
Transcription
www.cs.washington.edu - UW Robotics and State Estimation Lab
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; 'A ; = A = ; A ; ; A ? ? ; A ? ; ? ?A = ; A ; A @; 0.4 0.35 Certain position 0.3 P(d) 0.25 0.2 0.15 Uncertain position 0.1 0.05 0 0 100 200 300 400 500 distance d [cm] %6@ BC D < 1 ( $/ (FEG*-H JILK 0 #" = ; A 3 ; 69:$ M( 1 ( #9N ; A &8'0"`<%1A1A>@+(>@!B2?%!>A9)2%B)<"JP m +h&84(2%>AK!'N&,$d!4,E2%4(9+("1@"<7&8>A%B+(<T'0""E!/01A9DM"`&(p-)>@<T2p90>A+,&82%B)<=" 2%<=<!4,9)>AB)K&8G&8'0"9)>A+h&84,>AD)/0&(>A!B6%$!>@3P=OB0$d%4,&8/0B2J&8"=1@H%U:&(')>A+Ef!/)1@9s4("=+(/)1&*>AB`$d4,"+I/)"=BI&(1@H`-)>A<TI>AB0K &8:*1A%B)K*4("2%9)>AB0K!+t"+,-."=<>32J1A1@Hi')"=Bk&(')"-.!+,>@&(>A!B"=+,&(>A62J&8>@!B>A+o/)B)<"=4,&82%>ABj+(/0<T'G2%+t>@G B =>AK!/04( " RP U`_0P BV<!BN&84(2%+,&i&(F&(')>A+=U t 1 Dvm +("=1A"<7&8+i&8')" /h?:>@4,&8/)2%1 3G"C2J+(/)4,""BN&8+/)+(>@B)K2_<!B)+,"4h?%2l&8>@?%"4,/)1A" i$|jn?rwy|7|Qwy|QUx l7|Q7x;;`| *|7dz%7 * | )P 97 m%d } x*~(~ } 2 nz%7E* |RQTSMUWVYXZUm* )P wy|7|z\[ 2 2 P C `2 N2KH A bL>@3!] 2 e H ^ /2143)@B1NAB3%9:14;OFa_DF9 9:38@ @M;'`4e aNaDdI 7OdO\;c4A^3/b [38AMDdG38I+@C98e b6RPR%e ) 4 U& "=4("%Ut&(')"_-)4(%D2%D)>@1A>@&qHs&('2J&&(')"_+("=B)+(%4k4,"=&(/)4(B)+2%<=<!4,9)>AB0K`&8m>@&(+9)>@+,&84,>AD)/&8>A%Bp2?J2%1A/)" 132J4(K!"=4E&8'2JB 2>A+*K!>?!"BVDNH - A ] bB>@3 :eXC Y 2 bL>@3 A }elS b6RP s e CE2 >AK%/)4("DRPVU Tcb2Ne2%B)9 =>@K!/)4,"DRP U c T bdD e9)"=-)>A<7&&8'0"G" 2%-)1A"9)>A+h&84,>AD)/0&(>A!B0+%$ 1A>@B)"+=P Q*')"j<!4,4("=+(-M!B)9)>@B)K?J2%1@/)"+ A bB>@3!] 2:e#2%4,"k-01A%&,&8"9V2%+i+,!1A>@9s1A>AB0"+P = 1 1 0.9 0.8 m2%+r92%+('0"9 >@3 0.8 0.6 proability proability 0.7 0.5 0.4 0.6 0.4 0.3 0.2 0.2 0.1 0 0 50 100 150 200 250 300 350 400 450 0 5"500 698 0 50 100 150 200 250 300 350 400 450 5 500 : 8 distance [cm] distance [cm] 5>AK)P-RPVU ) T P>@4,&8/)2%1o"C2%+,/)4("=6"=BN&;2)Pi>@$a&8'0"k-M!+,>@&8>@!Bs>A+*IB)iBVi>@&8'bn2NeE1A <="4h&T2%>@BI&qH%P = 2JB)9bnD e#')>@K!' 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B !/)41 :<C2J1A> 2J&8> !B &=<T')B)> : / ;2%B)9&8'I/)+ 1 D '2%9 9 =& =4 >A B =9U:<C2%/)+,>AB)Kk&8 ' 4 !D%&& k&!/0<T'&8 ' 7&T2%1 -)1A2J&(#$ %4 %$/%B#"0'0>AD)>&CP Q*')4 )%&( ' 4< !1@1A>@+(> %B)+G =4 <2%/)+ 9DNH~'2%4(9#2%4 -)4 !D)1 6+pbn+,/)<T' 2%+1 D2J&,& =4,HS - =4TeP{Q* ' s4 `2%>@B)>AB0Kp&q c<!1A1@>A+(> !B)+j =4 V<C2%/0+ 9~DNHSw 2Ci+_>AB{&( ' s'2%B)9:vq<4(2J$}& =9 62%-U0i')>@<T' >@B)>@&(>32%1@1@H_1A2%<T =9p+ /=+(+ BN&8>A2%01 !D)+,&82%<1 ;>AB0#$ %462J&8> !BP : 21 E / = - , & % % '& b |7Hk2%+(-<7&J$ D {>A+a>&8+a2%D)>@1A>&qH&KB=482J&?:>@4,&8/)2%1!+=B)+%454C2%9)>@B)K!+0=?B>@$I&8'u4%D%&9=+ B%&IB{i'= 4u>@&a>A+fbd<%P[$ P :PVU$jbn2Net2%B)96 Pb P Ie,e7PQ>A1@1A/)+h&8482l&&('f>6-!4h&T2%B)<3%$)<!B)+,>A9=4(>AB0K &8' BN&(>A4k D 1A>= $ >AB)+h&2%9%$ ,/)+,&r26+,>AB)K!1+,&(>62J&JU"-)>A4,>A<C2J1A1@H6<6-2J49 D & 2%Bc2%-0-)4N2J<T'i')>A<T'4!B01@HV<!B0+(>A9 4(+&('65 7 87 4%D%&r-%+(>@&(>!BSb2%4,K6 2" ,b ne(e& K= B 4(2J& ?:>A4,&(/2%1!+ B)+!44C 2J9)>AB)K%+PQ*')>A+52%-)-)4N2%<T'k<C2%BkDu &('!/)K!'N&9:02%+a&8' 1%K!>A<2%1%<!/)BN&= 4(-2%4h& : D >: &8'm 1:<C2J1A> 2J&8>!B<-!B BN&>A+_B%&-)4!D2%D0>A1A>@+,&(>A<2JB)9 ,/0+,&` 2J>ABN&T2%>@B)+_2c+(>@B)K!1 +h&8>` 2J&% P /)4#" -= 4(> BN&(+>AB09)>A<2J& &8')2J& D +>ABN& K!4(2J&8>!Bj>A+a+82;:#= 45i'= Bg&8'f 4!DJ&5>@+5B%&< 4h&T2%>@B 2%D!/0&>@&(+i1:<C2J&(>!BP >@K!/)4 :P $ & +('i+r26 2%-.: 2F'2%1@1@E2CHs>AB.!/)4/)B)>? 4,+(>&qHmD)/)>A1@9)>AB0KF2%1!B0K 1 R SR UT ODP 5 1 1 = 1 Z R O P 5 $Q C 5 UU _ i>@&('y-!+,>@&8>!B{-)4!D2%D)>@1A>&8>=+P B|&8')>@+ "02-)1s&8'V4!D%&+,&T2J4,&=9~i>&8'~<-)1=&m>@K!B!4(2%B)< 2% D !/0&u>@&(++,&T2J4,&8>@B)Kj - %+(>@&(> !B2%B09`9)/i&j&8'+hH=&84hH-:.&8'<!4,4(>@9!4 &8'4!DJ&f')2%+fB%&uDB 2%D)1 & F/)B)> I / 1Hs 9 =& 4 6>@ B ;>@&(+*1 :<C2J&(> !BP Invisible obstacle a b Z & , 6 )( ( $ $/621 1 ; = ; #9/9: #9N !B,>A9=4(>(/2 (>!BG=B4!D>(4(/)1HF2 1<2 8>!BG132JD=19":n2J<>AB0Kk4,>AKD 2(>AK%B(1A>@K81H0>AK=4)4%D2%D)>@1A>qH1:<C2 (>!Br132%D19:n2%<=>AB)K: P -4!u2%90?J2%BT2JK3: 1 D > !DN?> D 0> "62 "> #$@>A; %A> 9`2 )4 N2%&< m< !B'(>A 9 4#"0<(,>@?%@H):<C2 (>!B ; BcK = B 4( 2 8>@B) K g?:>A*4 2 += B %4;4 C2J9)>AB)K U 1 D ,T2%; %; D -B 8>A2 +:<C 2 (> !B>AB 2%<=< )B U .")>A<TI>AB0/ K i< %B=4,?J 2 8>? j?:>A4 2 0 B !4i4 2%9)>AB0K)P 1 maximum likelihood probability 0.8 0.6 µ DWA 0.4 0.2 0 0 ( $ 9 , $/621 EG*-H GI K 0 3 100 200 300 400 500 distance d [cm] 69/$ M( 1 ( #9 )( >1 )9/ , , ( $/ 1D$ #9 $/621 *1 23 0 #9 $ & ( $ . R7 ( 6$/621821 # ? ; ; A A GA Q4%U#<!B(>5%6/ 8 = 7@K6 R P $UV(6 ; A = ; A bL>[3\C 2:e#7/%5 :#69;:<76>=%?6 7?7?@)#7?:<77A"A'&= B%C7?-#B66756=& P -$(6C#5>=%5D7?E A bB>@3 C 2:e (?C=F:(6=@%5 G:%6+= <BF= 7?' bH= 7? 1 D ;eU %6F=!75I7?!57*67A'7? A>=%56?(7@(J%*7)= ?J%PKL=M6%<U (= "7#N7@ %7 <5/=6=B&6 7 :O=%PJ-@%?(6= /=3?@)6F= 57?@b#)="Q6=?@#7?Q7RBF= I e =K7?57BF= %5SAJ-#:(67BF= 7?%U (6F= 1 D 7T@%?(6= I=C6F=57?@M>= U6V:%?R6A :W6XB75'7?@)P = 6 1 D (66U6A>= =7@?;(=? $ Y6A>=A77ZJ//B66(B(<BF= 7?P A UU T %6 # $ ; %$ ? 4 F < 9/ , #$ ? 87@6 :P $ $-=Q>= =%(? AJ 6AC7?@ 6#J<A675 =6=B& SB77? =F:75>=?B%P @=7?oU /6A = E' =B%5 7?QB66756r7';.?7?@ 7PI*&=6*7?'@ Jv 7P7 ?PjQ #&= 6@VI<BF= 7?':#6 D Y(6-%7P(6/?Q967@.(6!?S9 : R75-:! B6675 6=PSQ ;6 %=5 % 6 =FJ ? 7B3>= 9;6A/??J B(B%:WJ B(76B(C:%?(5 6%=7?:<77A .A=B% Sb}O> %5 e#A'5 ?B %6=7?ZJ 7? 7 77 ? 7= =F: 75 (5 J V67BI 7P7 ?+:7& A=B% /)=,6 (5 AJ E? ?vxO (5 6 (B(&= ?@ JP = R 1 number of considered positions 1.4 1.2 time [sec] 1 0.8 0.6 0.4 0.2 0 0 20 40 60 14000 1 12000 0.98 10000 0.96 probability 1.6 8000 6000 0.94 0.92 4000 2000 0.9 0 0.88 698 80 100 120 140 160 180 57 200 time [sec]] 0 20 40 60 :8 80 100 120 140 160 180 5" 200 time [sec]] 0 20 40 60 80 100 120 140 160 180 5 200 8 time [sec]] #B * 0 C & 9 > 69 8$ R 1 9 $ ( #1A%$ 9/$ M( 1 ( #9 *-,@0 1 )&, 9 7 ( 6$/621 ( 21 ( 9 #1 * N0 ()&R& 8)9: , , $ R 21 ( 9 A7 ( 6$/621 ( ; = ; <= ; = ; ; ? A ; ; A = 87@6 P $ bH=Ne_vVbOBCe7*6= ;76=?3=(B(+:6 7B%7(?;7(?.= 7? : D 5'67?@-'7 #"(67%?PpQ+#"'%67%?C%4= A $ &'& (B?5'/=?5 "Iv = "7 7?S GO>@6 %E6 (6 ( %?M #7 :W6 9A (@7??'7?+ @ : #"(67%?P 87@'6 P$ cbH=!e 5(7BVK M7 M? (B (= 6J- 3B #=BF= ?S7?B(57?@ '& 6 %=57?@( ;: E:76>=+%?'6=P : (?47?Q 9A %@7??7?@ =R #6 AR7! #"6 (JQ'?B (6&= 7?D=A 'I7PR 77 ?U =3BF= ?4B%=? AMB '' (5 7? %=?7!U P 9 %B ?5= P K EB (6=7?ZJ;7?; M 7P7 ? @6 7 !:#6 5V %6 7?7?'@C=B%=?3A %B ( = *!? %@ %BV&=A' gbO (!>= ? & P UK %B%8 e7PQ7L7L5 E :O=BV = E /?PJ/B ?75 (6 <BF= 7 ? 7P36 A>=A'77PZJ=A : I=CB %6=7?6 % 5 :#6UB 7?'@ K:<76>=T (? 6=B%B 65'7?@C 6 Ptb :P IeP ?)7 " (67 (?.L 6 % ` 5 U= ( U v P Q ?< #A (6 ;:B ?'75 %6 (53 <BF= 7 ?7! %5)7? 7@6 P $ `bWA e7PUB%=?)A (? %6 %U.7 ?. #A %6"5 %B(6 %= (I= E6 A" 5>= %"7 7P7 ?,%7 = 7 ?;=?5 .7TB .J;B ?: (6@ (K = ?. #A %$ 6 : (">=?<U &'& <BF= 7 ?= P 87@6 P$ bOB e5 %'7B( C %5 6 A>=A77Z6 J : B ?75 %6 %5D <BF= 7 ?' P I 5 A #? %5S>= / V: %?D @Q 9?. #A %! 6 :! % B%= 7 ? 5 (B%6 %= ( U (5#6 A>=A77PZ J :> 7P7 ?8B ?: (6@ (L= + %U P & = : %68 %8=? & (B ?'5 P = R F_ 1 = @R _ R 5 SR ]T 'R I= ?= T R _ <R F_ ); UU `R < ) ! ? 7B&>='%6 "5(B%67A%5=I.J<A675=6=B&/B77?9=F:75>=?B .BF= (5 D %'7B& / 7?%@6= ("A %?6K5>= &==?5 5>= &=-:W6 ='6(:<7PJ '7%5.)= 7?./B77?;=F:75v =?B ;;(J 75F= :9'6U(B&?7 .7U9@(?%6= R:<76= %?66F= 57?@ A>=%5,? = )= : (?.:<76 ?%? #7P7?%;:C6A6%= 7P:E =-7((7)= %5 7?@6'6 7 %?&= 7 ?:+7P7?)6A>=A77PZJ@675' R:<76= F=6(?=6I@%?(6= %5; 7?'@=B ?' %6*: = 7P: E6 j'7B& (?'6 %>= M6 A=G: 75'"B 77 ?f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c M )M % =< P H = Q! UU% 4 F < 5>=FJ Z5>=FJ,%6= 7?>= B* $ V:(6 07? (?.:<76?%? 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