Robot Control 1 Sami Haddadin, Lars Johannsmeier
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
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.
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
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.
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
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!
Assembly Planning
• Framework for multi-agent assembly
• Optimal assignment of agents to tasks is planned
• Local motion and manipulation 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