balance control of humanoid robot for hurosot

Robot Intelligence Technology Lab.

Balance control of humanoid robot for Hurosot

Balance control of humanoid robot for Hurosot

Bum-Joo Lee, Yong-Duk Kim and Jong-Hwan Kim

Robot Intelligence Technology Lab.

KAIST

16th IFAC, Jul., 8, 2005

Robot Intelligence Technology Lab. 2

Contents

Introduction

Gait generation

First phase: walking pattern generation

Second phase: yawing moment cancellation

Balance control

Inverted pendulum model

Compensation method

Experiment

Conclusions


1. Introduction

Humanoid robot

Biped (two-legged) robot. Expected to eventually evolve into one with a human-like body and intelli

gence.

HanSaRam Meaning ‘one human being’ in Korean A humanoid robot undergoing continual design and development in the R

obot Intelligence Technology Laboratory at KAIST since 2000

Stability ZMP (Zero Moment Point) must always reside in the convex hull of all

contact points on the ground plane. ZMP: the point on the ground plane at which the total moments due to gr

ound contacts becomes zero, proposed by Vukobratovic


HSR-I, II: 2000- Easy to make and control, Lack of torque

HSR-III: 2001- 12 DC motors and 10 RC servo motors - Human-like body- No sensor feedback

HSR-IV: 2002- 12 RC servo motors - Feedback using force sensors- No upper body

HSR-V: 2003- 12 DC motors and 16 RC servo motors - Feedback using force sensors- Human-like body

HSR-VI: 2004- 12 DC motors and 13 RC servo motors - Feedback using force sensors- Improved performance

HSR-I

HSR-II

HSR-III

HSR-IV

HSR-V

HSR-VI

1. Introduction


1. Introduction


Robot (HSR-V)ZMP

Compensator

Two Phase Off-line Gait Generator

< Off-Line >

< On-Line >

ZMP Calculator

Step Time,Step Size,

Maximum Foot Height Gait Generation Using Simulator

1st Phase

Yawing Moment Cancellation

Trajectory

Compensated Reference Joint Angle

Real Joint Angle Feedback

Sensor DataMeasured ZMP Data

Reference Joint Angle

2nd Phase

2. Two Phase Off-line Gait Generation

Control architectureControl architecture


))(),(( tztxPosture vector

Hiptrajectory

Foottrajectory

zmax

xmax

Ls

xsd

xed

Hmin

Hmax

Y

Z

RL

RL

RL

RL

RL

LL

LL

LL

LL

LL

LL

LL

LL

LL

LL

3*Ls

2*Ls

2*Ls

Ls

Ls


First phase: walking pattern generation First phase: walking pattern generation


sss

dss

ssfbsas

m

deffea

TTtL

TTtL

TtLLL

Ttx

TtLL

t

tx

2

2

))cos(1()sin(2

))cos(1()sin(

00

)( max

a

a

easfb

eaeff

a

L

L

LL

H

LL

L

tz)cos()sin(

)cos()sin(

)( max

LffLfb

La

2*Ls

Hmaxse

xmax x

Z

Gait generation (Huang 2000)Gait generation (Huang 2000)

1) Foot trajectory




ssds

ms

deds

sd

TtxL

TtL

TtxL

tx

tx

0

)(

s

m

d

TtH

TtH

TtH

tH

tz

min

max

min

min 0

)(

Xsd

Xed

z

x

Xsd

2) Hip trajectory


Interpolate at

Match velocity and acceleration values at every via points.

Calculate the trajectories of ankle and hip joints.

3rd order spline interpolation3rd order spline interpolation

)()()()( 32jjjjjjjj ttdttcttbats ],[ 1jj tt




Z

Y

Xn

ipii

n

i

i

i

i

pii

n

ipii

n

iipii

T

T

T

g

rrm

z

y

x

rrm

TGrrmrrrm

0

0

)(

)(

TermMoment Yawing :

)(

})({

)(

})({

n

iiZMPiiZMPiiZ

ii

iiiiiiZMP

ii

iiiiiiZMP

xyyyxxmT

gzm

yzmygzmy

gzm

xzmxgzmx

0 YX TT

ZMP equation:

Second phase: yawing moment compensationSecond phase: yawing moment compensation



XTrajectory of arm- COG

< Real arm model > < Simplified arm model >

yx

X

Z

o Y

Z

o

< Sagittal plane > < Frontal plane >

o

Z



0

2

12

0

,

xymM

xym

xyyyxxm

xyxyyyxyxxm

xyyyxxmT

a

a

n

iiZMPiiZMPii

aZMPaaZMPaa

n

aaiiZMPiiZMPiiZ

rl

ym

Mx

a 0

C.O.G. arm to origin coordinate local fromnt displaceme : , yx

Off-line yawing moment cancellation:

Above equation can be solved by numerical double integration.


3. On-line Balance control

< Simplified upper body model >v

Y

AlAl ML ,

AuAu ML ,

TT ML ,

SlSl ML ,

X

YZ

o

Z

o X

Y

UU ML ,

X

YZ

o

Z

o

Inverted Pendulum Model

< Lumped upper body model >

Robot modeling for online compensationRobot modeling for online compensation



}2

1

2

)cos()cos({

})cos()cos(){sin(

)()(

))((})(({})({

)()(

})({})({

)(

})({

2222

2

gglmM

lmM

MM

MM

gzmgzm

xxzzmxzmxxgzzmxgzm

gzmgzm

xzmxzmxgzmxgzmx

M

M

gzm

xzmxgzmx

ub

ua

aA

bB

uiuuii

upupuui

iiiupupuiui

ii

uiuuii

uuuui

iiiuuuiui

ii

ZMPd

A

B

ii

iiiiiiZMPo

On-line compensation equation



time sampling :

valuepast time sampling one :

valuecurrent :

value predicted :

equation oncompensati momentum axis : )(),,(

equation Difference equation alDifferenti

equation aldifferentiorder 2ndlinear -Non )(),,(

gait line-off by predefined:,

1

1

1111

Ts

Yegf

egf

MMeM

M

MM

MM

exx

n

n

n

nnnn

BAA

B

aA

bB

ZMPoZMPd

Desired ZMP Measured ZMPerror

e = xZMPd - xZMPm

X

Y

o

Continued



.obtained is angle torso axis-

method Cardano by Solved

equation.order 3rd is equation oncompensati momentum axis-

polynomialorder 3rd:

ly,continuous change onaccelerati and velosity position,error that Assuming

2

1

211

1

11

X

Y

θ

T

T

n

s

nnnn

s

nnn

Continued


4. Experiments

Two phase off-line gait generation


4. Experiments

Online Balance Control


4. Experiments

ZMP trajectory without compensation (pre-designed ZMPx = 15mm)

(a) ZMP trajectory (5 degree tilt)

(b) waist angle trajectory.


4. Experiments

ZMP trajectory with compensation ( at 5 degree tilt)

(b) waist angle trajectory.

(a) ZMP trajectory.


4. Experiments

Ongoing research: HuroSot


5. Conclusions

This paper has presented an overview of research development in humanoid robot HanSaRam.

The off-line gait generation method and the on-line compensation algorithm was proposed. By putting arm-swinging motion in the off-line gait generation

stage, the yawing moment could be cancelled. ZMP compensation has been accomplished by moving the upper

body front and rear in on-line walking.

balance control of humanoid robot for hurosot

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