Robot Control

1

Sami Haddadin, Lars Johannsmeier

Physical Interaction

Overview

performing a specific task

Control Design

Motion planning

SensingActuation

Task planning

Controller choice Stability analysis

e.g. Model-based control e.g. Passivity

Model Identification

Modeling and essential theories

Modeling and Essential Theories

Kinematics

Rotation matrixOrthonormal matrix

9 elements -3 orthogonality relationships -3 unitary relationships= 3 independent elements

Euler angles

Unit quaternions

Non unique and singularities

Transformation matrixAlways invertible Composition:

Direct Kinematics

Inverse Kinematics

JointSpace

TaskSpace

AnalyticJacobian

GeometricJacobian

(Twists)

(Wrenches)

du

al s

pac

es

du

al spaces

Manipulability vs. Singularity

Sic

iliano, B

., Scia

vic

co

, L., V

illani, L

., Orio

lo, G

., Robotic

s: M

odellin

g, P

lannin

g a

nd C

ontro

l, 3rd

Editio

n, S

prin

ger, 2

009

Space of linear operators on vector space V.

When Jacobian loses rank.

How far from singularity?

Redundancy

FRANKA EMIKA Non-invertible Jacobian

Inverse kinematics problems

Moore-Penrose Pseudo-inverseUnique and always existsSuch that (almost ident. for weighted):

Weighted pseudo-inverseDifferential inverse kinematics:Minimization of:

Null-space control

No motion

No Wrench

Task prioritization

Primary task Secondary task

Slo

tine, S

. B. (1

991, J

une). A

genera

l fram

ew

ork

for m

anagin

g m

ultip

le ta

sks in

hig

hly

redundant ro

botic

syste

ms. In

pro

ceedin

g o

f 5th

Inte

rnatio

nal C

onfe

rence o

n A

dvanced R

obotic

s (V

ol. 2

, pp. 1

211

-1216).

On velocity level

On torque level

RedundancyM

ansfre

d, N

., Dje

llab, B

., Rald

ua V

euth

ey, J

., Beck, F

., Ott, C

., Haddadin

, S., Im

pro

vin

g th

e P

erfo

rmance o

f

Bio

mechanic

ally

Safe

Velo

city

Contro

l for R

edundant R

obots

thro

ugh R

efle

cte

d M

ass M

inim

izatio

n

RedundancyM

ansfe

ld, N

., Beck, F

., Die

trich, A

., Haddadin

, S., In

tera

ctiv

e N

ull s

pace C

ontro

l for In

tuitiv

ely

Inte

rpre

table

Reconfig

ura

tion o

f Redundant M

anip

ula

tors

,

Dynamics Direct Dynamics

Inverse Dynamics

Newton-Euler method(Wrench balance approach)

(numeric)

Euler-Lagrange method(energy-based approach)

(symbolic)

vs.

Sic

iliano, B

., Scia

vic

co, L

., Villa

ni, L

., Orio

lo, G

., Robotic

s: M

odellin

g, P

lannin

g a

nd C

ontro

l, 3rd

Editio

n, S

prin

ger, 2

009

Skew-symmetry of:

& skew-symmetric

Operational Space Dynamics

Flexible-joint robots

Fully coupled model

Reduced model (Large transmission ratio)

Inertia shaping

Damping shaping

with: Joint torque sensing

Alb

u-S

chäffe

r, A., O

tt, C., &

Hirz

inger, G

. (2007). A

unifie

d p

assiv

ity-b

ased c

ontro

l fram

ew

ork

for p

ositio

n, to

rque

and im

pedance c

ontro

l of fle

xib

le jo

int ro

bots

. The in

tern

atio

nal jo

urn

al o

f robotic

s re

searc

h, 2

6(1

), 23

-39.

De L

uca, A

., & B

ook, W

. J. (2

016). R

obots

with

flexib

le e

lem

ents

. In S

prin

ger H

andbook o

f Robotic

s (p

p. 2

43

-282).

Sprin

ger In

tern

atio

nal P

ublis

hin

g.

Take Me by the Hand!A

lbu-S

chäffe

r et. a

l. ICR

A 2

002, A

lbu

-Schäffe

r et. a

l. IJR

R2007

Collision HandlingH

addadin

, S., D

e L

uca, A

., Alb

u-S

chäffe

r, A. (2

017). R

obot C

ollis

ions: A

Surv

ey o

n D

ete

ctio

n, Is

ola

tion, a

nd Id

entific

atio

n,

Accepte

d fo

r IEE

E T

ransactio

ns o

n R

obotic

s

External Joint Torque Observer

Generalized momentum:

Component-wise:

Collision on the i-th link: DLR Lightweight Robot

Haddadin

, S., D

e L

uca, A

., Alb

u-S

chäffe

r, A. (2

017). R

obot C

ollis

ions: A

Surv

ey o

n D

ete

ctio

n, Is

ola

tion, a

nd Id

entific

atio

n,

Accepte

d fo

r IEE

E T

ransactio

ns o

n R

obotic

s

Collision HandlingH

addadin

et. a

l. RS

S 2

007

Haddadin

et. a

l. IJR

R 2

009

2012 G

eorg

e G

iralt P

hD

Aw

ard

ICR

A B

est S

erv

ice R

obotic

s A

ward

Model Identification

Identification ProcedureK

halil, W

., & D

om

bre

, E. (2

004). M

odelin

g, id

entific

atio

n a

nd c

ontro

l of ro

bots

. Butte

rworth

-Hein

em

ann.

Control Design

Early pHRI

Joint Impedance Control

Robot dynamics:

Required control input:

Avoidance of inertia shaping:

Desired impedance behavior:

Closed-loop dynamics:

PD+ controller

No need for external joint torque sensing

Compliance control

DLR Lightweight Robot

Ott, C

. (2008). C

arte

sia

n im

pedance c

ontro

l of re

dundant a

nd fle

xib

le-jo

int ro

bots

. Sprin

ger.

Cartesian Impedance Control & Damping Design

Desired impedance behavior (without inertia shaping):

Required control input:

Design of stiffness:

Design of damping:Constant & defined by the application (Normally symmetric & positive).

Constant & diagonal not good.

Non-constant & non-diagonal inertia e.g. based on general eigenvalue decomposition of symmetric matrices

For any positive-definite matrix and symmetric matrix ,there is a non-singular matrix and a diagonal matrix such that:

In quasi-static case, at each position :

Damping factor:

Compliance control

DLR Lightweight Robot

Ott, C

. (2008). C

arte

sia

n im

pedance c

ontro

l of re

dundant a

nd fle

xib

le-jo

int ro

bots

. Sprin

ger.

i-th diagonalelement of

Stiffen up!

Adaptive Impedance Control

Cartesian impedance control with the feedforward wrench

Similar to the principles of motor adaptation:

& Learning rate (positive definite)

Forgetting factor (positive definite)&DLR Lightweight Robot with Adaptive Impedance control in peg-in-hole experiment

e.g.

Yang, C

., Ganesh, G

., Haddadin

, S., P

aru

sel, S

., Alb

u-S

chaeffe

r, A., &

Burd

et, E

. (2011). H

um

an

-like a

dapta

tion o

f forc

e

and im

pedance in

sta

ble

and u

nsta

ble

inte

ractio

ns. IE

EE

transactio

ns o

n ro

botic

s, 2

7(5

), 918

-930.

Hybrid Force Position ControlV

illani, D

e S

chutte

r Handbook o

f Robotic

s 2

008

Khatib

IJR

R, 1

987

Classical approach: partition motion and force space via selection matrix Ω

Disadvantage: Exact environment model has to be known!

Unified Force/Impedance Controller

Without shaping function

With shaping function

Unified Force/Impedance Controller

Assembly and Soft Manipulation

Assembly and Soft Manipulation

Assembly and Soft Manipulation

Assembly Planning

• Framework for multi-agent assembly

• Optimal assignment of agents to tasks is planned

• Local motion and manipulation planning

Assembly Planning

• Robot knows a general strategy• Controller and skill parameters

are learned• Parameter space limits are

derived from known system limits and task context

Assembly Planning

The Endfund

konec

ende

край

enda

Endepää

fineinde

end

ände

τέλος son

ბოლოს

fine

समाप्त

конец

结束

fim

끝پایان

đầu cuối

終わり

ทา้ย

Соңы

അവസാനിക്കുന്നു

finisآخر

النهاية

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aħħar

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