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Robot Creation #7
Walking Robots 3
Contents
• Quadruped Walking Robots TITAN VII &
TITAN XI for Steep Slope Operation
• Stability Criterion
• Gait Control with vision sensor
• Design of Passive Terrain Adaptive Sole
• Design of Active Terrain Adaptive Sole
• Energy efficient large obstacle climbing gait
• Dynamic Walking
• Other walking machines
Background
Construction on a steep slope
• Omni-directional locomotion
• Avoiding the damage of frame
Latest Automated Method
Developed by a Japanese Company
無足場ロックボルト工法 (大昌建設)
アンカーロックマシン(ARM01)
アンカーロックマシン(ARM06)
Requirements
1) Mobile base for the anchor-lock-bolt
machine which does not damage the ferroconcrete frames
2) Stable and posture adjustable base for the
anchor-lock-bolt machine
Construction task
of the Quadruped
Walking Robot on
a steep slope
The legged walking is good to
avoid the damage of the ferroconcrete frame
SMART SPIDER: Dante II
creeps toward Mount
Spurr’s steaming depth.
For much of the time, it
navigated without
human guidance.
Which posture is most stable?

const.
Classification of stability criteria
1. Stability Margin : McGhee, R.B. and Frank, A.A. (1968)
2. Tumble Stability Margin : K.Yoneda and S.Hirose (1996)
3. Gradient Stability Margin : S.Hirose, H.Iwasaki and
Y.Umetani (1978)
4. Tipover Stability Margin : E.G.Papadopoulos and D.A.Rey
(1996)
5. Energy Stability Margin : Dominic A.Messuri and Charles
A.Klein (1985)
6. Dynamic Energy Stability Margin : A.Ghasempoor and
N.Sepehri (1995)
Stability Margin
[McGhee, etc. 1968]
Support legs triangle
Gradient Stability Margin
[S.Hirose, etc. 1978]
 
Energy Stability Margin
[Klein, etc. 1985]
hmax
h0
mg
x
E  mg (hmax  h0 )
Which criterion is most
appropiate to evaluate the
stability of the robot on slope? (1)
(2)
Stability Margin
[McGhee, etc. 1968]
(3)
Gradient Stability Margin
[S.Hirose, etc. 1978]
Energy Stability Margin
[Klein, etc. 1985]
 
hmax
h0
mg
x
E  mg (hmax  h0 )
Comparative experiment of stability
Result of the experiment
225m m
145m m
Force from downhill side.
x
elastic m aterial
Force from uphill side.
Problem in Energy Stability Margin
E  mg (hmax  h0 )
1 2
mv
2
hmax  h0
mg(hmax  h)
NE Stability Margin
(Normalized Energy Stability Margin)
S NE  hmax  h0
Tool to derive a stable gait on slopes
SNE contour : Contour connecting the points with same SNE value
G
P
SNE contour
A gait to maximize SNE
(Intermittent crawl gait)
yyy
leg 1
leg 2
xxx
leg 3
15°
leg 4
TITAN VII
Leg length adjusting motion in wild life
Balancing by the wire suspension
By adjusting the traction force of the wires, the walking robot
can walk around the steep slope just as on the flat ground.
Wire suspended walk
system
drilling
The “Trot Gait” on a steep slope
Position controlled wires are acting as the third leg
Walking motion on the slope
of 70 degrees inclination
Development of Quadruped Steep Slope
Construction Robot TITAN XI
Design of the leg mechanism
Legs should produce large
supporting force, and at the
same time, they have to
have large motion range to
allow various motion.
Design of the leg mechanism
市販バックホウ
法面で使用するため脚機構は軽
量であること望ましい
The legs should be as lightweight
as possible
非常時には人間が直接制御でき
ることが望ましい
It can be manually controlled in
an emergency
地面から崖への移動のため、脚
は胴体上方へも伸ばせることが
必要
As it move from ground to the
slope, the motion range of the
legs should be wide.
Back Hoe
バックホウ改良型
バックホウのリンク長やシリンダ
配置などを再検討
脚ストローク
水平方向 2.0~2.5[m]
垂直方向 1.0~1.5[m]
脚先出力
3.5[ton](自重の1/2)
 x
 
 1
y
J
 1
 z

 1
特長
胴体の上下に適当な可動範囲
過不足のない脚出力
x
 2
y
 2
z
 2
x   1
 3   L1

y  
0
 3  
x  
 0
 3  
0
 2
L2
0

0 

0 

 3 

L3 
Conventional
Back Hoe Type
Couple Drive type
Improved Back Hoe
Prototype leg of TITAN XI
Coupled Drive Type with New Omni-directional Gripper
Selected Leg Mechanism
Improved Back Hoe Type
Feature
Item
Mass [kg]
480
Length [m]
3.7
Stroke
(Horizontal) [m]
2.0 (1.0--3.0)
Stroke (Vertical)
[m]
1.0 (1.0--2.0)
Output [kN]
35
I → II → III → IV → V → VI → VII
Winch with Tension Sensor
• Wires are driven by hydraulic motor.
• The winch can rotate around the pivot and the wire
traction force can be measured by load cell.
• Maximum measurable load is 10[t]. Wire length is
about 100[m].
Drill
• Drilling is done by hydraulic
motor.
• Orientation of the drill can be
adjusted by the legs motion.
I → II → III → IV → V → VI → VII
Crawler and Engine
外側
エンジンリフト上
Study of MARS
(Map Realization System)
Map generation using knowledge
Detection of frame for
map generation
Viewpoint
Simulation: detection of frame on undulated terrain
Raw data
Center line
Segment
Estimated frames
Terrain adaptive walk
by using the laser range finder mounted on the robot
測量技術を用いた自己位置同定法
Localization using 3D laser sensor
Introduction of the off-the-shelf 3D laser sensor
Total Station (TOPCON Co.)
Feature of the TS
1. Measuring range is more than 2
km.
2. High accuracy(±4-5 mm in
x,y,z directions for 1000 m
away)
3. Automatic searching ability of
the corner cube.
I → II → III → IV → V → VI → VII
Map generation by using 3D laser sensor
As the worker have to survey the site beforehand, he can place the corner
cube at the cross points of the flame and measure the 3D position and
makes the map.
Worker
マーカ
Total Station
I → II → III → IV → V → VI → VII
Map Generation
Real Site
Map formed by the
cross point data
Measurement of position and
orientation of the robot
Corner cube mirror
• Position of the
center of rotation
• Vector of rotation
axis
Posture sensor
One axis posture
Measure the position of rotating
corner cube by the Total Station
6 dof position
and orientation
Measured rotating corner cube of the robot
Gait control
TITAN XI
Preliminary experiment of the ground
On going development of TITAN XI
On going development of TITAN XI
Sole Design
足裏の設計
Adaptation to the Rough Terrain
Typical Conventional Foot Design
TITAN VII
Terrain Adaptive Sole with
Connected Differential Mechanism
Tactile Sensor for the Foot
TITAN XI Foot Design
Round Foot
Simple
Contact point moves
Universal Joint
Ball Joint
Wide motion range
High center of rotation
and easy to sprain
Low center of rotation
Limited motion range
Final mechanism of TITAN XI
I → II → III → IV → V → VI → VII
Objective of the research
Soft and rigid foot
Requirement of the Foot
Softness: Terrain Adaptive
Rigidness: Wide support range
Related study 1
(Ogata,2004)
Related Study 2
能動的に路面に合わせて形状を固定する足先機構
寸法
248x322
X113 mm
重量
2.9 kg
適応可能段差
±20 mm
アクチュエータ
ソレノイド
セミアクティブ支持多角形確保機構WS-5(早稲田,2005)
能動型の問題点
• 素早い適応動作や軽量でコンパクトな構成が困難
• 耐環境性、耐久性が乏しい
斜面や凹凸を含む不整地に受動的に適応できる足先機構の開発
PATAS1
諸元
直径
高さ
遊脚時
Φ140 mm
60 mm
支持脚時
Φ165 mm
40 mm
重量
200g
変形機構
• 弾性体によって対向する指機構を連結し
高い対地適応性を実現
変形機構
• 全ての指機構が紐で連結され連動して路面に合わせて変形
• 指機構が全て接地する事で変形動作が完了し固定動作へ移行
固定機構
指機構に取り付けられたブレー
キプレートを重ね合わせ
自重を利用して中心軸で押し
付けることで形状を固定
Brake plates
Comparison
conventional
flat sole &
PATAS2
4足歩行ロボット“TITAN XII”
Length:1.1[m]
Width:1.7[m]
Height:0.65[m]
Weight:100[kg]
DOF: 20
80
基礎動作実験
Active
Ankle

Wide motion
range
Roll:±69°
Pitch:±90°

Large payload

Dust proof
What kind of posture should be
selected in climbing motion?
Rising motion
H0=0.3m H1=0.7m
J2 &J3 of one leg is considered
Open Dynamics Engine(ODE).
Joint torque leg width relation
Joint2
Joint3
86
Power consumption leg width relation
Joint2
脚幅y=0.29
Joint3
脚幅y=1.18
Internal force
When the legs have to be placed at a place where negative
power should be produced, application of internal force
should be considered
Joint torque internal force relation
Joint 2
No internal force
Joint 3
With internal force 100N
Internal force consumed power relation
Joint 2
内力なし
Joint 3
内力100N
90
On going study
We should find optimum posture and gait
control method which prevents the generation
of negative power consumption and let the
actuators being driven in most effectively way.
Dynamic Walking
•
•
•
•
WABOT (Waseda University)
P2 ASHIMO (HONDA)
Marc Raibert (MIT)
Marc Raibert (Boston Dynamics)
Key Word: ZMP(Zero Moment Point)
by Prof. Miomir Vukobratovic
A supporting point on the ground which allows to
generate required motion of the body by the reaction
force of the point and with zero moment.
胴体の希望の運動を床反力だけでゼロのモーメントで支える
ことが可能な床の上の作用点
reaction force
acceleration
force
mg
ZMP
ZMP
ZMP
ZMP
この範囲しか存在し得ない
(圧縮力のみの場合)
In the acceleration motion by the hind wheel
後輪で前向きの力を受けるとき(加速している)
ZMP
In the acceleration motion by the hind wheel
後輪で前向きの力を受けるとき(加速している)
ZMP
Acceleration
direction of
the rod
Reaction moment
of the body
ZMP without rotation
ZMP with rotation
Balancing motion by the rod in tightrope walking
Acceleration
direction of the rod
Virtual ZMP
Reaction Moment of the body
Constant Velocity
mα
mg
Acceleration
Decceleration
ZMP
H
CG trajectory
Solve the differential equation 微分方程式を解く
x
x
ma
x
mg = H
H
g
mg
x
x=
ma = mx
H
0
ZMP
In case CG moves
along the horizontal
line with height H
x = x となるのは?
t
e
t
x= e
x=
Solve the differential equation 微分方程式を解く
x
x
ma
x
mg = H
H
g
mg
x
x=
ma = mx
H
0
ZMP
x = A x となるのは?
x=
e
At
x = Ae
At
Solve the differential equation 微分方程式を解く
x
x
ma
x
mg = H
H
g
mg
x
x=
ma = mx
H
0
ZMP
x = A x となるのは?
x=
e
At
e
±√ A t
x = Ae
x = A x となるのは?
x=
At
Solve the differential equation 微分方程式を解く
x
x
ma
x
mg = H
H
g
mg
x=
x
x=
ma = mx
H
e
g
t
±
H
0
ZMP
x = A x となるのは?
x=
e
At
e
±√ A t
x = Ae
x = A x となるのは?
x=
At
Solve the differential equation 微分方程式を解く
x
x
ma
x
mg = H
H
mg
ma = mx
g
x
x=
H
x=
e
g
t
±
H
General solution 一般解
0
(いろいろな場合を包括した表現)
ZMP
x = C1
e
g t
H
+ C2
g t
H
e
x
Hyperbolic function
双曲線関数
t
Dynamic Gait Control for the Trot
Sideway Swaying Gait 左右揺動歩容
Center of Gravity CG
Support leg
Swing leg
ZMP
CG trajectory following
the hyperbolic curve
ZMP trajectory following
the supporting-legsconnecting diagonal lines
Dynamic walk of TITAN VI
Hyperbolic trajectory of the CG can be observed by the track of light
Trot gait of Hyperion 3
Prof. Kan Yoneda, Chiba Inst. Tech.
TITAN XIII
倒立振子が倒れていくとき、ZMPはどこにあるか。
When the inverted pendulum is falling down, where should the ZMP
locates?
1.
A
2.
B
3.
C
4.
D
A
B
C
D
ZMP (Zero Moment Point, by M. Vukobratovic )
胴体の希望の運動をゼロのモーメントで支えることで生成できる地上の点
A supporting point on the ground which allows to generate required motion of
the body by the manner of zero moment .
ZMP (Zero Moment Point)
reaction force
reaction force
acceleration
force
mg
mg
ZMP
ZMP
reaction force
acceleration
force
mg
Be notice!
ZMP
Zero moment point makes
Mx and My zero, but Mz is
remained non-zero value.
Marc Raibert (CMU. USA)
Miomir Vukobratovic
(MIT, Boston Dynamics)
(Mihailo Pupin Institute Yugoslavia )
Designer of MIT hopping robot
1981 RoManSy Symp. Poland
Advocator of ZMP
人間型は最適な2足歩行形態か
Is humanoid shape the best
biped walking?
典型的な二足歩行ロボット
Typical Biped
<Working>
立ったまま作業しようとすると、常にバラン
ス制御が必要
Posture control is required to do something
while standing.
<Walking>
歩行時にヨー軸回りの回転を防ぐ制御
が必要
Prevention control of yaw angle rotation
is required in the walking motion.
恐竜型二足歩行ロボット
Dinosaur-like biped robot
首をマニピュレータに利用 ⇒作業性
Neck can be a manipulator.
尻尾を第三脚として利用 ⇒静的安定性
Tail can be the third leg for stable standing.
上体補償運動 ⇒ 動的安定性
Horizontally long body increase the inertia
around yaw axis and makes the dynamic
stability control easy.
“Troody”, MIT Leg Lab.
Unfortunately I have never seen the motion of this
robot
TITRUS-III
Weight:
DOF:
2001
Dimensions: W130 x H150 x L480 mm
1.4 kg ( Body: 720g, Head: 200g, Tail: 180g, Leg: 84g)
Actuator: RC Servo Motor x 10
10 ( Leg: 2 x 2 DOF, Arm: 2 x 2 DOF , Head: 2 DOF)
Sensor: no sensor
Leg Mechanism
A ct iv e Joint
P assiv e Joint
2 DOF
干渉駆動による高出力重量比の機構
High output driving mechanism with
Coupled Drive
Neck and Tail Mechanism
2 DOF
Active Revolute Joint
Passive Ball Joint
Passive Universal Joint
Static Walk of the TITRUS III
Dynamic Walk of the TITRUS III
Tripod standing
&
handling motion
Dynamic model of the TITRUS III
Related Studies on Walking
Passive Walk
Mike Hall Delft University
Anything else?
Chebyshev linkage
チェビシェフリンク機構
Chebyshev linkage
チェビシェフリンク機構
新しいマシンは以下のいずれかに分類される
New machine can be classified into two groups
まだ“おもちゃ”のように見える未来機械
A future machine which looks like a toy
未来機械のように見える“おもちゃ”
A toy which looks like a future machine
機械についての本質的な長所と短所に関する的確な洞察を行えるようにすることに
よって、数多くの「未来機械のように見えるおもちゃ」群の中から、「まだおもちゃにしか
見えない未来機械」を見出せるようにすべきである。
Try to acquire the ability to find the intrinsic merits and demerits of new
machines and properly distinguish toy-like future machine out of future-machinelike toys.
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