Introduction to Humanoid Robotics by Rawichote Chalodhorn (Choppy) RoboCup soccer The brain controlled humanoid robot Outline • History of humanoid robots • Humanoid robots today • Androids • Analytical approaches of bipedal locomotion • Learning to walk through imitation • Future of humanoid robotics Atomaton: Leonardo's robot 1495 Atomaton: The Japanese tea serving doll 18th century to 19th century Honda E series Honda P series P1 P2 P3 1993 1996 1997 AIST / Kawada Industries : HRP series HRP-4C Androids • A robot that closely resembles a human • Human robot interaction Prof. Hiroshi Ishiguro ! Chapter 2 Zero-Moment Point (ZMP) The Zero-Moment Point [Vukobratovic et al. 1972] "#$!%&$'()*+!,#-%.$&!%&$+$/.$0!-!1&)-0!1-,23&)*/0!-/0!4(.$&-.*&$!+*&'$5!)6!.#$!1(%$0! 4),)7).(We)/!(/!&)1) .can(,+8!9):$' $&maintain;!(.!)/45!1&($645!7$/WhatWhat.()/$ 0!balance.#$!<$&)=> ) 7isis$/.!? )(/ZMPZMP .!as (Zero(Zero MomentMoment Point)?Point)? @<>?A!-4)/3!:(.#!-!6$:!$B-7%4$+!)6!+.*0($+!.#-.!&$')4'$0!)/!(.+!,)/,$%.8!C:(/3!.)! .#$! 6-,.;long! .#-.! .#$! %&( /,(as%-4! 3) -4!the)6! .#$! %&)D$,.! ZMP:-+! .)! +.*05! is-/0! staying0$'$4)%! 1(%$0! #*7-/)(0!4),)7).()/!,)/.&)4!1-+$0!)/!.#$!<>?;!(.!:-+!0$,(0$0!.)!,)/,$/.&-.$!-!6*44! ,#-%.$&!.)!0(+,*++!(/!0$%.#!-44!.#$!-+%$,.+!)6!.#$!<>?;!6&)7!(.+!0$6(/(.()/!-/0!,)/,$%.;! .)!(.+!-%%within4(,-1(4(.5!@(/,4*0(/ 3the!%&$'()*+!+.*0($+A! support-/0!'-&(-/.+;!-/0! 6(/-445!polygon.(.+!0$&('-.()/8! 2.1 Definition ! ZMP Vukobratovic and Stepanenco, 1972 Center of Pressure" d R •ZMP NEVER! leaves the support polygon! E(3*&$!!F8GH!<$&)=>)7$/.!?)(/.!)&(3(/-4!0$6(/(.()/!@I*2)1&-•ZMP.)'(,!"#!$%&;!GJ JKcanA8! be measured by force sensors in feet. Zero-moment point Hiro Hirukawa The Onassis Foundation Lecture Series 2006 10/88 ! GL !"#$%&'()*(%"&(+&',-.,.&/%($,0/%( !"#$%&'(&#)*&+,--./&0123'&$2(&(2&4%$25'&(1'&4$'5(4#&#$6&#33"7'6&(1'&02$3(#$(&1'4%1(& #829'&43&:'52&+1&;&-/&(2&<4')6&#$&#00"5#('&9'5342$&2=&>?3*&&+,*@/&#$6&&+,*.-/A& 2 8 6 4 & 7 ' 6 & 7 4 ' 0 ) %3 3 # 3 !!!3 4 " !!!3 6 " 3 $ 35 35 !"#$$% 6+.$ ( 2 & 8 4 & 7 %3 3 !!!3 4 " 2 8 5 4 & 7 ' 5 & 7 4 ' 0 ) %3 3 # 3 !!!3 4 " !!!3 5 " 3 $ 36 36 !"#$"% 5+.$ ( 2 & 8 4 & 7 %3 3 !!!3 4 " >?"#(42$3&&+,*../&#$6&&+,*.,/&B'5'&"3'6&#)32&8<&C1#$%&+,--D/*& ! % A&E234(42$&9'0(25&2=&'- ' ( *6; 5 ; -+ ! % A&(2(#)&(25?"'&#0(4$%&#(&'- : ")$ . ( *%6 %5 %4 + , ! 9 "($ % : : : : &A&'F('5$#)&727'$(&:( + !" , ( *. 6 . 5 . 4 + !"#$%&'()*(%"&(+&'9 ,-.,.&/%(&3 $,0/%( * 9 9 9 9 % &A&'F('5$#)&=250'&9( + ( *<6 <5 <4 + &3 ' ' 9 9 9 9 % A&E234(42$&B1'5'&+9&43&#0(4$%& * ( *=6 = 5 =4 + !"#$%&'(&#)*&+,--./&0123'&' $2(&(2&4%$25'&(1'&4$'5(4#&#$6&#33"7'6&(1'&02$3(#$(&1'4%1(& # " #829'&43&:'52&+1&;&-/&(2&<4')6&#$&#00"5#('&9'5342$&2=&>?3*&&+,*@/&#$6&&+,*.-/A& & !"#$%&'()*(%"&(+&',-.,.&/%($,0/%( G4%"5'&&,*HA&I'=4$4(42$3&2=&9'0(253&=25&#&B#)J4$%&7'01#$437&+#6#E('6&=527&K#J#$4314&>?(@A*L&.@H@/*& 2 8 6 4 & 7 ' 6 & 7 4 ' 0 ) !"#$%&'(&#)*&+,--./&0123'&$2(&(2&%4%$25'&3 3 #(1'&3 !4$'5(4#&!!3 #$6&4 " #33"7!!!3 '6&(1'&6 "02$3(#$(&3 $ 351'4%1(&35 !"#$$% 6+.$ ( 2 & K#J#$4314&#829'&43&:'52&+>?(@A*&+.@H@/&1&;&-/&E5'3'$('6&(2&<4')6&#$&#00"5#('&#&6'549#(42$&9'5342$&2=&>?3*&&=25&8(1'&+,*@/&#$6&&4CMN&& 7 +,*.-/A&'?"#(42$3&B1401&4$0)"6'6& %3 3 !!!3 4 " 'F('5$#)& =250'3& #$6& 727'$(3& #002564$%& (2& (1'& 9'0(253O& 6'=4$4(42$3& #3& 312B$& 4$& 2 82 6 4 & 7 ' 6 & 7 4 ' 0 ) %3 3 # 3 !!!3 4 " !!!3 6 " 3 $ 35 35 !"#$$% 6 ( 83 #53 !!4!3 & 7 4 "' !!5!3 & 7 5 "&43 $' 0 36)36 +/01&2- -"#3*&P$4(4#))<L&(1'&=2))2B4$%&+.$Derivation%3 '?"#(42$&2 2=& of72(42$& the#(& ZMP#$&#584(5#5<&E24$(&2$&(1'& !"#$"% 5+.$ ( 8 4 & 7 & %3 3 !!!3 2 4 " 8 4 & 7 %3 3 !!!3 4 " %52"$6&'-43&6'=4$'6L&B1401&43&#0?"45'6&2 8<&#EE)<4$%&6OQ)'78'5(&E54$04E)'A& 8 5 4 & 7 ' 5 & 7 4 ' 0 ) [Takanishi et al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ectors of a walking mechanism" G4%"5'&&,*HA&I'=4$4(42$3&2=&9'0(253&=25&#&B#)J4$%&7'01#$437&+#6#E('6&=527&K#J#$4314&>?(@A*L&.@H@/*& & & DU G4%"5'K#J#$4314&&&,*HA&I'=>?(4$4@A(4*&2+.@H@/&$3&2=&9E5'3'$('6&'0(253&=25#&&#6'549#(42$&&B#)J4$%&=25&7'(1'&01#CMN&$437&'?"#(42$3&+#6#E('6&B1401&=527&K4$0)"6'6&#J#$4314&>?(@A*L&.@H@/*& 'F('5$#)& =250'3& #$6& 727'$(3& #002564$%& (2& (1'& 9'0(253O& 6'=4$4(42$3& #3& 312B$& 4$& K#J#$4314&+/01&2->?(-"#3@A*&*&P$4(4#))<L&+.@H@/&(1'&E5'3'$('6&=2))2B4$%&#&'?"#(42$&6'549#(42$&2=&72(42$&=25&#(&(1'&#$&CMN&#584(5#5<&'?"#(42$3&E24$(&2$&(1'&B1401&4$0)"6'6& %52"$6&'-43&6'=4$'6L&B1401&43&#0?"45'6&8<&#EE)<4$%&6OQ)'78'5(&E54$04E)'A& 'F('5$#)& =250'3& #$6& 727'$(3& #002564$%& (2& (1'& 9'0(253O& 6'=4$4(42$3& #3& 312B$& 4$& 2 : 9 9 +/01&2- -"#3!"#$4%*&P$4(4#))<L& %#(1'&83 !&3=2))2B4$%&' 6", !!&!3 & 0"$'?"#(42$&& . ' %, 2=&' %72(42$&#!* ' 6",#(&+ #$&$( 5#584(5#5<&& E24$(&2$&(1'& 3 : 9 %52"$6&'-43&6'=4$'6L&B1401&43&#0?"45'6&8<&#EE)<4$%&6OQ)'78'5(&E54$04E)'A& Q3&7'$(42$'6&'#5)4'5L&(1'&CMN&43&(1'&E24$(&4$&B1401&(1'&1254:2$(#)&027E2$'$(3&2=&(1'& 727'$(& #5'& '?"#)&2 (2&:'52*& R4(1& (143& 02$3(5#4$(L&(1'&#"(1253&7264=<&>?*&&+,*.D/&#$6& : 9 9 !"#$4%5'(54'9' &+"34$%%&347#E8)'3&!7&#3(1''76#"(,40#!)!&&!23 E&'5#0(42$3/&"$& .(1'&'S&%#$6&,T&027' %E2$'$(3&#!* 2=&'(1'&6",CMNA&+ $( 5 & 3 : 9 Q3&7'$(42$'6&'#5)4'5L&(1'&CMN&43&(1'&E24$(&4$&B1401&(1'&1254:2$(#)&027E2$'$(3&2=&(1'& 727'$(& #5'& '?"#)& (2&:'52*& R4(1& (143& 02$3(5#4$(L&(1'&#"(1253&7264=<&>?*&&+,*.D/&#$6& & DU 5'(54'9'&+"34$%&347E)'&7#(1'7#(40#)&2E'5#(42$3/&(1'&S&#$6&T&027E2$'$(3&2=&(1'&CMNA& & DU Derivation of the ZMP !"#$%&'()*(%"&(+&',-.,.&/%($,0/%( ZMP equations with external forces and moments 3 : 7 2 ) 9 ( 7 ) 9 2 ) . 6 ) ( 1 * ' 1 '4 4 # 4 !!!4 2 " !!!4 7 " 4 $ ' 6 5 '1 % &5 !"#$%& 7+.$ + 3 ! : 2 ) 9 ( 8 1 '4 4 !!!4 2 " '1 2 !"#$%&'()*(%"&(+&',-.,.&/%($,0/%( [Takanishi et al., 1989] 3 : 7 2 ) 9 ( 7 ) 9 2 ) . 6 ) ( 1 * ' 1 '4 4 # 4 !!!4 2 " !!!4 5 " 4 $ ' 6 7 '1 % &7 !"#$)& 5+.$ + 3 ! !"#$%&'(&#)*&+,--./&0123'&$2(&(2&4%$25'&(1'&:4$'5(4#&2 ) 9#$6&(#33"78'16&(1'&02$3(#$(&1'4%1(& '4 4 !!!4 2 " '1 2 #829'&43&:'52&+1&;&-/&(2&<4')6&#$&#00"5#('&9'5342$&2=&>?3*&&+,*@/&#$6&&+,*.-/A& "#$%!&''()&*#!+&%!,%-.!$/!A%-0-(&1! simplified%2,.$-% version!34!2#-!&,2#)(%! of ZMP&/.! equations)2#-(!(-%-&(*#-(%!56$(;<( 2 8 6 4 & 7 ' 6 & 7 4 ' 0 ) =>?7!8998:!;&(<!=!>#--7!899?:!"&<&/$%#$%3 3 #(;<(=>?3 !!!3 7!899@AB!4 " !!!3 6 " 3 $ 35 35 !"#$$% 6+.$ ( 2 & 8 4 & 7 %3 3 !!!3 4 " [Huang et al., 2001] 2 8 5 4 & 7 ' 5 & 7 4 ' 0 ) %3 3 # 3 !!!3 4 " !!!3 5 " 3 $ 36 36 !"#$"% 5+.$ ( 2 & 8 4 & 7 %3 3 !!!3 4 " >?"#(42$3&&+,*../&#$6&&+,*.,/&B'5'&"3'6&#)32&8<&C1#$%&+,--D/*& ! % A&E234(42$&9'0(25&2=&'- ' ( *6; 5 ; -+ ! % A&(2(#)&(25?"'&#0(4$%&#(&'- : ")$ . ( *%6 %5 %4 + , ! 9 "($ % : : : : &A&'F('5$#)&727'$(&:( + !" , ( *. 6 . 5 . 4 + 9 &3 * 9 9 9 9 % &A&'F('5$#)&=250'&9( + ( *<6 <5 <4 + &3 ' ' 9 9 9 9 % A&E234(42$&B1'5'&+9&43&#0(4$%& * ( *=6 = 5 =4 + ' # " & G4%"5'&&,*HA&I'=4$4(42$3&2=&9'0(253&=25&#&B#)J4$%&7'01#$437&+#6#E('6&=527&K#J#$4314&>?(@A*L&.@H@/*& K#J#$4314&>?(@A*&+.@H@/&E5'3'$('6&#&6'549#(42$&=25&(1'&CMN&'?"#(42$3&B1401&4$0)"6'6& 'F('5$#)& =250'3& #$6& 727'$(3& #002564$%& (2& (1'& 9'0(253O& 6'=4$4(42$3& #3& 312B$& 4$& +/01&2- -"#3*&P$4(4#))<L&(1'&=2))2B4$%&'?"#(42$&2=&72(42$&#(&#$&#584(5#5<&E24$(&2$&(1'& %52"$6&'-43&6'=4$'6L&B1401&43&#0?"45'6&8<&#EE)<4$%&6OQ)'78'5(&E54$04E)'A& 2 : 9 9 !"#$4% %#83 !&3 ' 6", !!&!3 & 0"$& .