on humanoid control - hellas · 2010-11-05 · on humanoid control hiro hirukawa humanoid robotics...

11//8888Hiro Hirukawa The Onassis Foundation Lecture Series 2006

On Humanoid ControlOn Humanoid Control

HiroHiro HirukawaHirukawaHumanoid Robotics GroupHumanoid Robotics Group

Intelligent Systems InstituteIntelligent Systems InstituteAIST, JapanAIST, Japan

Implies thatImplies thatWalking on a flat floor and rough terrainWalking on a flat floor and rough terrainGoing up and down stairs and laddersGoing up and down stairs and laddersLying down, crawling and getting upLying down, crawling and getting upFalling down safely and getting upFalling down safely and getting upOpening and closing doorsOpening and closing doors

Humanoids move on two, three or four feet.Humanoids move on two, three or four feet.

Humanoids can move the Humanoids can move the environment for humansenvironment for humans

Humanoid as a Controlled Plant Humanoid as a Controlled Plant

A humanoid robot is a multiA humanoid robot is a multi--link structure that is not fixed link structure that is not fixed to the environment and moves to the environment and moves in the environment and/or in the environment and/or moves the environment by moves the environment by the the contact forcecontact force between the between the robot and the environment in robot and the environment in the gravity field.the gravity field.

Humanoid Control ProblemHumanoid Control Problem

When the initial and final configurations of a When the initial and final configurations of a humanoid robot is given, find motions of humanoid robot is given, find motions of the robot that can transfer it from the initial the robot that can transfer it from the initial configuration to the final configuration configuration to the final configuration through through a sequence of the contact statesa sequence of the contact states..

Control AlgorithmsControl Algorithms

Inverted Pendulum Scheme Inverted Pendulum Scheme 1.1. Plan motions of the robotPlan motions of the robot2.2. Change the position of the next footprint to Change the position of the next footprint to

keep the planned configuration of the robotkeep the planned configuration of the robot

ZMP (Zero Moment Point) based SchemeZMP (Zero Moment Point) based Scheme1.1. Plan a sequence of footprints.Plan a sequence of footprints.2.2. Change the configuration of the robot to Change the configuration of the robot to

keep the planned sequence of the footprintskeep the planned sequence of the footprints

Motions vs. Contact ForceMotions vs. Contact Force

( )G CM − =g p f&&

( )G G CMp g p L τ× − − =

Contact force

Contact torque

Position of the center of the gravity

Angular momentum about the COG

[Gubina, Hemami and McGee 1974]

Inverted Pendulum SchemeInverted Pendulum Scheme

Footprints may have a constraint

[Vukobratovic and Stepanenko 1972]

And more….

ZMP based SchemeZMP based Scheme

What is ZMP (Zero Moment Point)?What is ZMP (Zero Moment Point)?

Vukobratovic and Stepanenco, 1972

Center of Pressure

•ZMP NEVER leaves the support polygon!•ZMP can be measured by force sensors in feet.

How ZMP is used?How ZMP is used?

When the ZMP is When the ZMP is insideinside the the support polygon, the contact support polygon, the contact between the feet and the between the feet and the floor should be kept.floor should be kept.

When the contact is kept, the When the contact is kept, the posture of the robot should posture of the robot should be kept without falling down.be kept without falling down.

0 1 2 3 4 5 6 7

-0.1-0.05

time [s]

Trajectory of the center of mass

From the ZMP to the COGFrom the ZMP to the COG

0 1 2 3 4 5 6 7

-0.1-0.05

00.050.1

time [s]

zmp ref

Target ZMP pattern

Motions vs. Contact ForceMotions vs. Contact Force

( )G CM − =g p f&&

( )G G CMp g p L τ× − − =

Contact force

Contact torque

Position of the center of the gravity

Angular momentum about the COG

CartCart--Table ModelTable Model

• A running cart on a mass-less table• The table has a small support area

O0ZMP =

The ZMP of the CartThe ZMP of the Cart--Table ModelTable Model

0ZMPτ =

ZMP hMg x x Mxzτ = − −=

0hzx x x

g= − &&

ZMP equation

Balance of moment

0 1 2 3 4 5 6 7

-0.1-0.05

00.050.1

time [s]

zmp ref

0 1 2 3 4 5 6 7

-0.1-0.05

time [s]

0hzx x x

g= − &&

Input and OutputInput and Output

0xCart trajectory

Walking pattern generation↓

Find the cart trajectory to realize the given ZMP pattern

Servo tracking control of the ZMPServo tracking control of the ZMP

Target ZMP Controller

0 1 0 00 0 1 00 0 0 1

x xd x x udt

xzx xg

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥= +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

⎡ ⎤⎡ ⎤ ⎢ ⎥= −⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ ⎦

Proper dynamics ofCart-Table model

From ZMP reference to Cart motion

ZMP referenceController

0refx + − x

The cart must move beforebefore ZMP changes !→Servo controller must use FUTURE information

0 0.5 1 1.5 2 2.5

time [s]

referencex

Ordinal servo control

time [s]

zmp refx

Walking pattern

The Preview ControlThe Preview Control

Concept and naming Concept and naming [Sheridan 1966][Sheridan 1966]LQ optimal controllerLQ optimal controller[Tomizuka and Rosenthal 1979][Tomizuka and Rosenthal 1979][Katayama et.al 1985][Katayama et.al 1985]

[ , , ]( )

k I k k x ki

f fx fx

⎡ ⎤⎢ ⎥− ⎢= ⎥⎢⎣ ⎦

−⎥

− −∑ L Mx

State feedback Preview gainTarget ZMP ofN-step future

AccumulateServo error

Control law

On a winding road, we steer a car by watching ahead, by previewing the future reference.

Preview gainPreview gain1 ( 1)

( ) ( )

T T T i Ti

f R B PB B A BK C Q

K R B PB B PA

− ∗ −

= + −

+0 +0.5 +1 +1.5 +2 0

future time [s]

・The preview gain is approximately zero after 1.6s future.・Controller does not need the future ZMP farther than 1.6s.

LQ optimal feedback gain

ZMP Tracking ExampleZMP Tracking Example

0 1 2 3 4 5 6 7

]xzmpzmp_ref

0 1 2 3 4 5 6 7

time [s]

yzmpzmp_ref

Walking Pattern GeneratorWalking Pattern Generator

HRP-2L HRP-2P[Kajita et al.]

Experiment of HRPExperiment of HRP--22

Configuration of the Feedback ControllerConfiguration of the Feedback Controller

Accelerometer

Force/torquesensor

Joint servo

Kalmanfilter

Bodyinclination

Stabilizer

References of Joint angles, body inclination and ZMP

Balancer Module

encoder

ZMPZMPcalculator

Feedback Controller is essentialFeedback Controller is essential

Without stabilizer With stabilizer

Feedback Control of the Table OrientationFeedback Control of the Table Orientation

Cart on a table

2 2( ) ( sin cos ) 2 0c c cx z xz g z x xx+ θ+ − θ+ θ + θ =&& &&& &

Equation of motion:

2 2( )c c cx z gx gz z x+ θ = − θ−&& &&

Linearize at 0θ ≈

Table inclination Cart acceleration

Feedback Control of the Cart PositionFeedback Control of the Cart Position

O0ZMP =

01 ( )

1hzx x x

sT g= −

ZMP equation with sensor delay T

0 01/ 1/ 0 /( )0 0 1 00 0 0 1

cx T T x z gTd x x xdt

− −⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥= +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

System representation

1 0 2 3x k x k x k x= − − −&& &Stabilization by state feedback

ZMP errorCart position modification

[Nagasaka, Inaba and Inoue, 1999]

Used in the walking controller of H7.Good for robots with hard feet.

Experiment on a SlopeExperiment on a Slope

不整地歩行予備実験

－不整地移動技術(1/2)－

HRPHRP--2 walks on a Rough Terrain2 walks on a Rough Terrain

Gap < ±20 mm Slope < 5%

Japanese Traditional DanceJapanese Traditional Dance

[Nakaoka et al. 2005]

The First Running HumanoidThe First Running HumanoidSony Sony QrioQrio [Dec.,2003][Dec.,2003]

Qrio runs at 0.84 km/h.

Running Biped [AIST Apr.,2004]Running Biped [AIST Apr.,2004]

Slow motionsSpeed 0.58km/hour

Walking on a floor with low frictionWalking on a floor with low friction

μ: 0.5 → 0.1 μ: 0.5 → 0.05

μ＝０.１５ between a tire of a car and a wet snow surface

Reduction of the Slip by a Tuning of Walking PatternReduction of the Slip by a Tuning of Walking Pattern

•Rotation about Yaw-axis may occur at μ＝０.３ due to the change of the acceleration when the supporting leg is exchanged.

•The pattern generator is tuned to reduce the peak of the jerk.

μ=0.3 Conventional pattern μ=0.3 Improved pattern0 0.5 1 1.5

showzmp0.m (sliptest3b_mu03\sim-astate.log) /ZMP trajectory

Walk direction

0 0.5 1 1.5

0.8showzmp0.m (sliptest3_mu03\sim-astate.log) /ZMP trajectory

Walk direction

Walk on a Floor with a Low FrictionWalk on a Floor with a Low Friction

Contact States GraphContact States Graph

Balance Control for the TransitionBalance Control for the Transition

The position of the The position of the torso link is under a torso link is under a compliance control.compliance control.

Landing

m] toe

Dynamic SimulationDynamic Simulation

Lying down and Getting upLying down and Getting up

Preliminary Experiment for FallingPreliminary Experiment for Falling

With the knee extended With the knee bended

Falling Motion of a Leg RobotFalling Motion of a Leg Robot

Impact TestImpact Test

Falling Motion of Humanoid RobotFalling Motion of Humanoid Robot

Implies thatImplies thatWalking on a flat floor and rough terrainWalking on a flat floor and rough terrainGoing up and down stairs and laddersGoing up and down stairs and laddersLying down, crawling and getting upLying down, crawling and getting upFalling down safely and getting upFalling down safely and getting upOpening and closing doorsOpening and closing doorsArms and legs coordinationArms and legs coordination

Walking and TouchingWalking and Touching Leaning on Leaning on BalancingBalancing

PullingPulling PushingPushing

Several Configurations of Arm/Leg CoordinationSeveral Configurations of Arm/Leg Coordination

A Generalized ZMP A Generalized ZMP [Harada et al. 2004][Harada et al. 2004]

2D Convex Hull 3D Convex Hull

Small Acceleration

Large Acceleration

Moment around the edge

pG ( )=~ pG~

Projection of the ZMPProjection of the ZMP

Numerical ExampleNumerical Example

Area of the Generalized ZMPArea of the Generalized ZMPFront Front

Push a heavy objectPush a heavy object

25.9 kg

[Harada et al. 2004]

Pushing a button withPushing a button withthe support of a handthe support of a hand

[Harada et al. 2004]

An Open QuestionAn Open Question

Can we plan motions of humanoid robots Can we plan motions of humanoid robots based on the unified criterion?based on the unified criterion?

What the ZMP criterion can judge?What the ZMP criterion can judge?The ZMP can judge if the contact should be The ZMP can judge if the contact should be kept without solving the equations of motions kept without solving the equations of motions when the robot moves when the robot moves on a flat planeon a flat plane under under the sufficient friction assumption.the sufficient friction assumption.

Our Goal areOur Goal are

to create a new criterion that can judge the to create a new criterion that can judge the contact stability of humanoids which may contact stability of humanoids which may touch an arbitrary terrain with two, three or touch an arbitrary terrain with two, three or four feet, andfour feet, and

to prove that the criterion is equivalent to to prove that the criterion is equivalent to ZMP in a specific case and more universal, ZMP in a specific case and more universal, and to claim to say and to claim to say ““Adios ZMPAdios ZMP””..

Related WorksRelated Works

Legged RobotsLegged RobotsZMP [ZMP [VukobratovicVukobratovic 1972]1972]Locomotion with hand contact [Locomotion with hand contact [YonedaYoneda 1996]1996]FRI [FRI [GoswaniGoswani 1999]1999]FSW [FSW [SaidaSaida 2003]2003]Generalized ZMP [Harada 2004]Generalized ZMP [Harada 2004]

Mechanical AssemblyMechanical AssemblyStrong and Weak Stability [Strong and Weak Stability [TrinkleTrinkle 1997]1997]

FormulationFormulation

( )K L

l lC k k k k

ε µ= =

= +∑∑f n t

( )K L

l lC k k k k k

ε µ= =

= × +∑∑τ p n t

( )G GM= −f g p&&( )G G GM= × − −τ p g p L

Gravity and Inertia Wrench

⇒ Polyhedral Convex Cone

Gp : Center of the mass

: Angular momentum around COG

Contact Wrench

Strong Stability CriterionStrong Stability Criterion

The contact state The contact state mustmust be stable if (be stable if (--ffGG,,--ττGG)) is is an internal element of the contact wrench cone an internal element of the contact wrench cone under the sufficient friction assumption.under the sufficient friction assumption.

(proof)(proof)

( )K L

l l lC k k k k

f n tε ε= =

= +∑∑1 1

( )K L

l l lC k k k k k k

τ p n p tε ε= =

= × + ×∑∑

, ,( , ) 0, ( ) int( ); ( , ) ( ) 0,G G G G G G G Gx f CWC x fδ τ δ τ∀ Ω ≠ − − ∈ Ω <

where the CWC is given by

The work done by ((ffGG,,ττGG)) is negative for any motion;is negative for any motion;

G k kk

Mx ε ε=

= −∑3 4

G k kk

My ε ε=

= −∑

3 4 1 2

( ) ( ) )K

G G G G z k k k k k kk

Mx y My x x yε ε ε ε=

− + = − − −∑L

G G G G x k kk

M z g y My z yε=

+ − + =∑L

G G G G y k kk

M z g x Mx z xε=

− + + + =−∑L

M z g ε=

+ =∑Strong stability holdsif the moment alongthe horizontal axesis inside the CWC.

Horizontal forceshould balance the friction from the assumption

Example 1. Walking on a horizontal plane Example 1. Walking on a horizontal plane with sufficient frictionwith sufficient friction

Strong Stability Determination by ZMPStrong Stability Determination by ZMP

λ λ=

= ≥∑

( )( )

KG G G G x

M z g y My z yM z g

+ − + =+ ∑L

( )( )

KG G G G y

M z g x Mx zx

M z gλ

+ − −=

+ ∑L

λ λ=

= ≥∑

G G G G x k kk

M z g y My z yε=

+ − + =∑L

G G G G y k kk

M z g x Mx z xε=

− + + + =−∑L

( )( )

KG G G G x

M z g y My z yM z g

+ − + =+ ∑L

( )( )

KG G G G y

M z g x Mx zx

M z gλ

+ − −=

+ ∑L

M z g ε=

+ =∑

Equivalence between the ZMP and the CWCEquivalence between the ZMP and the CWC

Dividing the equations by

Equivalence between the ZMP and the CWCEquivalence between the ZMP and the CWC

λ λ=

= ≥∑

( )( )

KG G G G x k

M z g y My z yM z g

+ − + =+ ∑L

( )( )

KG G G G y k

M z g x Mx zx

M z gεε=

− + + +=−

+ ∑L

( )( )

KG G G G x

M z g y My z yM z g

+ − + =+ ∑L

( )( )

KG G G G y

M z g x Mx zx

M z gλ

+ − −=

+ ∑LZMP

ε εε ε=

= ≥∑

The CWC for a 2DThe CWC for a 2D--Robot on a LineRobot on a Line

A Desired Trajectory in the CWCA Desired Trajectory in the CWC

The CWC is the direct product of a 2D polyhedral cone and 1D linear subspace,which is identical for the single and double support phases.

( )G G G

M z g y M

ε λ λ=

+ − +

−= −∑

Example 2. Robot on a Stair (1/2)Example 2. Robot on a Stair (1/2)

1yλ 2Fz

11 1 2 2

( )G G G G y

M z g x Mx z

λ λε=

− + + +

=− + +∑

Example 2. Robot on a Stair (2/2)Example 2. Robot on a Stair (2/2)

01 1 2 2

0 1 21 2

1 1 2 1 2

( )G G G G xK

y yk k F F

k k G F Fy y y yk

M z g y My z

y My z z

whereMy

ε λ λ

λ λελ λ λ λ

+ − +

= − −

⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎟⎜ ⎟ ⎟⎜ ⎜ ⎟⎟ ⎟= − +⎜⎜ ⎜ ⎟⎟ ⎟⎜⎜ ⎜ ⎟⎟ ⎟⎜ ⎜ ⎟⎜ + +⎝ ⎠ ⎝ ⎠⎝ ⎠

1 21 2

1 2 1 2

( ) ( )K

G G G G x k kk

F F Fy y y y

FM z g y My z y

λ λλ λ λ λ

+ − − + =

⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜⎟ ⎟= +⎜ ⎜⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜+ +⎝ ⎠ ⎝ ⎠

∑1yλ

2Fz1Fz

Pattern Generation of the COGPattern Generation of the COG

0 1 0 00 0 1 00 0 0 1

tx G G

ref refy

y yd y y udt

yMg M z y

⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟= +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠

⎛ ⎞⎜ ⎟= − − ⎜ ⎟⎜ ⎟⎝ ⎠

The CWC for a 2DThe CWC for a 2D--Robot on a StairRobot on a Stair

A Desired Trajectory in the CWCA Desired Trajectory in the CWC

The CWC is the direct product of a 2D polyhedral cone and 1D linear subspace,which is not identical for the single support phases of the lower and the higher feet,and is the product of the 2D cone and 2D linear subspace for a double support phase.

Vertical Trajectory of the ZMPVertical Trajectory of the ZMP

Pseudo Plane on which the ZMPtrajectory is defined [Honda]

Equivalent trajectory of the ZMPbased on the proposed criterion

Not admissiblein the singlesupport phase

Horizontal Contact Force while Climbing StairsHorizontal Contact Force while Climbing Stairs

0 0.1 0.2 0.3

Black curve is generated from a continuous trajectory in the CWCRed curve is generated from a discontinuous one in the CWC

single double single single double single

ZMPZMP ｖｓ．ｖｓ．CWCCWC

ZMPZMP CWCCWC

Flat planeFlat planeFoot contactFoot contactSufficient frictionSufficient friction

Strong StabilityStrong Stability Strong StabilityStrong Stability

Strong StabilityStrong StabilityArbitrary terrainArbitrary terrainHand/Foot contactHand/Foot contactSufficient frictionSufficient friction

N/AN/A

Summary of the CWCSummary of the CWC

The proposed criterion is equivalent to ZMP The proposed criterion is equivalent to ZMP in the specific case and can judge the strong in the specific case and can judge the strong stability in generic cases.stability in generic cases.

Therefore we claim to say Therefore we claim to say ““Adios ZMPAdios ZMP””, and , and the voice can be louder when we can plan the voice can be louder when we can plan motions in a variety of cases based on the motions in a variety of cases based on the proposed criterion.proposed criterion.

Open Problems in the ControlOpen Problems in the Control

Robust walkingRobust walkingBiped walking is still not robust enough for a Biped walking is still not robust enough for a large disturbance.large disturbance.

Walking on a natural rough terrainWalking on a natural rough terrainWalking must be more generalized with the Walking must be more generalized with the recognition of the working environment.recognition of the working environment.

Falling motion controlFalling motion controlThe humanThe human--size humanoid just crashes when size humanoid just crashes when it falls down without a proper control.it falls down without a proper control.

Humanoids in Real EnvironmentHumanoids in Real Environment

Research PlatformsResearch Platforms

HRP-2 (Kawada)154cm, 0.5M EuroAvailable at LAAS, France

HOAP (Fujitsu)60cm, 50K Euro

HRP-2m Choromet(General Robotix)35cm, 5K Euro

Free Research PlatformFree Research Platform

OpenHRP: Open Architecture Humanoid Robotics Platformhttp://www.aist.go.jp/is/humanoid/openhrp/

Implementation Features of Implementation Features of OpenHRPOpenHRP

Concurrent development using an arbitrary Concurrent development using an arbitrary operating system and language operating system and language

OpenHRPOpenHRP is written in Java, C++ and runs on Linux is written in Java, C++ and runs on Linux and Windowsand Windows

Distributed Object System based on CORBA

CORBA Objects of CORBA Objects of OpenHRPOpenHRP

ISEISE : I: Integrated ntegrated SSimulation imulation EEnvironmentnvironment

VRMLfile

Modelfile

Projectfile

Our Current ChallengeOur Current Challenge

A Famous Project of Takeo KanadeA Famous Project of Takeo KanadeEyeVisionEyeVision at the at the SuperballSuperballLetLet’’s watch NBA in the court.s watch NBA in the court.

Our ChallengeOur ChallengeLetLet’’s go to the cafeteria with a humanoid.s go to the cafeteria with a humanoid.

Robust biped walkingRobust biped walkingGoing up and down stairsGoing up and down stairsOpening and closing doorsOpening and closing doors3D SLAM3D SLAM

Powered SuitsPowered Suits

HAL [U of Tsukuba] Bleex [UC Berkeley]

Autonomous WalkingAutonomous Walking--AidAid

Range Sensor

Stairs

ObstaclesRough Terrain

A Measure of the Ability of a RobotA Measure of the Ability of a Robot

Artificial IntelligenceArtificial IntelligenceThis robot has the intelligence that is This robot has the intelligence that is compatible to three years old child.compatible to three years old child.

Mobility of a HumanoidMobility of a HumanoidThis robot has the mobility that is compatible This robot has the mobility that is compatible to eighty years old person.to eighty years old person.

ΕνχαριστωΕνχαριστω

May, my dog on a summer vacation

on humanoid control - hellas · 2010-11-05 · on humanoid control hiro hirukawa humanoid robotics...

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