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1 The flexible cotrol of the Quadruped Walkig Robot by Positio-Based Impedace Cotrol
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4 HONDA ASIMO SONY SDR-3X McGhee The OSU Hexapod ReCUS 1980 Waldro ASV Whitaker AmblerHalme MECANT 1,000kg Brooks Muybridge 1960 Mosher Walkig Truck McGhee Phoy Poy 1979 PV
5 6 TITANNINJA 7 8 TITAN 8 TITAN 9 TITAN Tekke Patrush 10 AIBO JROB ZMP ZMP ZMP ZMP ZMP Free Gait
6 Fig.1.1 Stability margi 36 Fig ZMP 3 TITAN 4 5 3
7 Float Force sesor Ma Quadruped Walkig Robot Fig.1.1 Quadruped Walkig Robot image 4
8 ZMP ZMP Zero Momet Poit(ZMP) ZMP 37 Fig.2.1 ZMP ZMP ZMP Fig.2.1 Cotrol image of ZMP type ad Pedulum type 5
9 ZMP Fig.2.2 Swig leg Swig leg Ceter of gravity Supportig leg Supportig leg Ceter of gravity Support polygo Fig.2.2 Support polygo 23 1 Fig2.3 T 1 Tg Tg β = (1) T 6
10 0.75 3/4 Leg Support phase Swig phase Fig2.3 Walk cycle 24 ZMP ZMP 7
11 2 ZMP
12 Duty factor Supportig leg Table.1 classificatio of Gait Leg phase Leg phase (Right ad Left)(Frot ad Rear) Gait Velocity of walk or 4 Crawl Slow Trot Pace Bouce Quick 25 Tipover Stability Margi Eergy Stability Margi Dyamic Eergy Stability Margi NE 1440RSM 16 0 Leg.2 Leg.1 Ceter of gravity Stability margi Leg.4 Leg.3 Fig.2.3 Stability margi 9
13 3 4 TITAN Fig.3.1 Y X Z 3 Leg.1 X 100 Y 200 Leg.2 X 100 Y 200 Leg.3 X 100 Y 200 Leg.4 X 100 Y -200 Coordiate system of mai part Y Z X Coordiate system of leg Fig.3.1 Coordiate system 10
14 32 TITAN l l 243 l2 3 1 Z Y X 2 Joit 2 3 Joit 3 Joit 1 L3 1 L1 L2 Fig.3.2 Simplified leg mechaism 33 Joit ( l + l cosθ l θ ) X = cosθ + (2) cos ( l + l cosθ l θ ) Y = siθ + (3) cos 3 3 Z = l + θ (4) 2 siθ 2 l3 si 3 11
15 θ = arcta Y 1 X (5) θ θ 2 3 = arcta Z l l ± arccos 2 2 l X cosθ1 1 2l2 2 3 X ( l ) l2 l3 + cosθ 1 + Z 1 = θ 2 ± π + arccos 2l2l3 X ( ) cosθ l1 + Z 1 ( ) + X 2 2 cosθ l 1 1 Z 2 (7) (6) 34 Fig.3.3 TITAN Leg 1 Leg Leg 3 Leg 4 90 Fig.3.3 Movable agle 12
16 Leg.4 Leg.1 Leg.3 Leg.2 Swig leg Swig leg Gravity move Swig leg Swig leg Gravity move Gravity move Swig leg Swig leg Gravity move Swig leg Swig leg Fig.4.1 Walk sequece 13
17 m/s Y β Liftig Placig Z 100 Y 100 Z 100 Liftig Placig T 1 = T3 = 0.25msec T 2 = 50msec Liftig 100 Placig T1 T2 T3 T Fig.4.2 swig phase 14
18 Ceter of gravity Quadruped Walkig Robot Ky Cy Cx Kx Cz Kz My Mx Mz Fig.5.1 Virtual mechaical impedace 15
19 52 F = M Pg + C Pg + K( Pg Pg0) (8) 0 F Pg Pg Pg Pg M C K Pg Pg Pg 1 = (9) dt Pg Pg Pg 1 = (10) dt dt Pg 1 Pg F Pg Pg 1 Pg Pg 1 1 = m + C + K( Pg Pg 0 dt dt ) (11) Pg 1 Pg 1 Pg 2 = (12) dt Pg
20 Pg = F M + dt ( Pg Pg ) 1 M dt C dt Pg + C dt + K 1 + KPg 0 (13) Pg Pg = Pg Pg 1 (14) Pg Pf i P i Fig.5.2 TITAN Positio Based Impedace Cotrol Robot Pg Robot TITAN Titech Robot Driver Positio Based Impedace Cotrol Positio cotrol system of Robot Pg Pfi Titech Robot Driver Robot F Pi Fig.5.2 System of Quadruped Walkig Robot 17
21 TITAN 54 18
22 Start Force Sesig Walk Plaig orbit of the ceter of gravity Make a foot positio If foot positio i movable area? No Program stop Yes Joit agle plaig by iverse kiematics Out put Fig.6.1 Cotrol flow 19
23 62 IFS-67M25A 50-I40 PC Table.2 Receiverboard F Force ceser PC Fig.6.2Simulatio system Table.2 Specificatio of F/T Sesor IFS-67M25A 50-I40NITTA Measuremet bouds of X ad Y directio 200[N] Measuremet bouds of Z directio 400[N] Measuremet bouds of each axis momet 12.5[Nm] Diameter 67[] Height 25[] Weight 180[g] Data output cycle 8000[Hz] 20
24 63 Leg1 1 Support polygo Y Leg2 2 Y-itercepts Stability margi X Ceter of Gravity Fig.6.3 Relatio betwee a support polygo ad a stability margi S y = mx + 15 S 2 = (16) 2 1+ m y1 y2 m = (17) x x 1 2 Y = y 1 + mx 1 (18) 21
25 S Y X 64 C M K M 1kgfC 100NS/ K 100N/ C MS-DOS 22
26 X 85 Y 70 Z 30 Lifted leg Supportig leg Ceter of gravity Support polygo Before After Fig.7.1 Chage of Support polygo 23
27 72 F Fig.7.2 Orbit chage at X directio G G T Pg G = (19) Pg G Pg G = (20) Fl Fg 24
28 G Fl ( 1 β )T (21) Pf i Fg G β T (22) Pf i X 25 Y 25 Y Fig.7.3 F Fig.7.3 Orbit chage at Y directio 25
29 8 X Fig.8.1,8.2 Y X Fig.8.1 Fig.8.2 Fig.8.3,8.4 X Y Fig.8.5 Fig.8.6 Fig.8.7 Z Fig.8.8 X Fig.8.9 Y Fig XY Fig
30 Fig.8.1 Stability margi at 3 legs support Fig.8.2 Stability margi at 4 legs support 27
31 Fig.8.3 Orbit chage o X directio Fig.8.4 Orbit chage o Y directio 28
32 Fig.8.5 Locus of Ceter of gravity by itermittet crawl gait Fig.8.6 Stability margi of itermittet crawl gait Fig.8.7 Leg positio of itermittet crawl gait o Z directio 29
33 Fig.8.8 Orbit o X directio Fig.8.9 Orbit o Y directio 30
34 Fig8.10 Leg positio of leg.1 ad leg.4 o X directio Fig8.11 Leg positio of leg.2 ad leg.3 o X directio Fig8.12 Leg positio o Y directio 31
35 Fig8.13 Leg positio of leg.1 ad leg.4 o X directio Fig8.14 Leg positio of leg.2 ad leg.3 o X directio Fig8.15 Leg positio o Y directio 32
36 Fig.8.16 Ceter of gravity ad force o X directio Fig.8.16 Ceter of gravity ad force o Y directio Fig.8.16 Ceter of gravity ad force o Z directio 33
37 9 1 34
38 10 35
39 1 "4 " Vol.16No.5pp "YT " C Vol.62No.593pp "YT " C Vol.62No.601pp " C Vol.62No.596pp " " C Vol.60No.575pp " " C Vol.61No.589pp " NINJA-1 " C 57540pp " " Vol.18No.2pp " TITAN " Vol.17No.8pp " Vol.16No.8pp "4 " Vol.3No.4 pp " MARS " Vol.4No.3pp " MARS " Vol.6No.1pp "3 - -" '02 (ROBMEC'02) Ju "3 " 13 Mar "3 " 18 vol.1, pp Sep " 4 36
40 " Vol.9No.7pp "4 " Vol.2No.6 pp "4 " Vol.4 No.4pp "4 " Vol.9No.3pp " 13 pp " Vol.17 No.2pp " 4 " Vol.16 No.3 pp "4 " Vol.18No.6pp " Vol.6No.2pp " 4 " Vol.9No.6pp " 3 " Vol.4No.3pp " 4 TITAN " Vol.9No.4pp "3D GDA " Vol.13No.5pp "3 " 20 Sep "4 " Vol.12No.7pp " Vol.18No.3pp " Vol.14No.7pp " " Vol.13No.7pp
41 " R.B. McGheead A.A. Frak"O the Stability Properties of Quadruped Creepig Gaits"Math. Bioscieces Vol.3pp [] ". " pp " Vol.16 No.8pp "" Vol.16 No.5pp "" Vol.16 No.7pp
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