Control of Parallel Robots:
Towards Very High Accelerations
PhD. Defense of:
Guilherme SARTORI NATAL
Advisor: François PIERROT
Co-advisor: Ahmed CHEMORI
Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier
LIRMM, Université Montpellier 2 - CNRS
Montpellier, France
Monday, 26th of November, 2012
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 2
Context and motivation
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 3
Medical robotics Haptic robotics
Tyre testing Flight
simulation
Context and motivation
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 4
Pick-and-place
applications
Context and motivation
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012
! Coupled/redundant actuation
! High accelerations/stop points Highly nonlinear dynamics
! High accelerations/stop points Mechanical vibrations
! Uncertainties in model/environment
5
Main objective:
Main difficulties:
• Control of parallel robots for extremely high accelerations
Main contributions:
Proposition of advanced control schemes, in order to guarantee good
tracking performances and robustness towards uncertainties
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 6
Outline of the presentation
1. Overview of the state of the art
2. Description and dynamics of our parallel robots
3. Proposed control solutions
4. Simulation and real-time experimental results
5. Conclusion and perspectives
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 7
State of the art Robots Proposed solutions Results Conclusion
State of the art
Overview of the existing control schemes Kinematic control schemes for parallel manipulators Dynamic control schemes for parallel manipulators
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 8
State of the art Robots Proposed solutions Results Conclusion
Overview of the existing control schemes:
Kinematic control:
PID/PD [Ziegler and Nichols, 1942], Nonlinear PD (NPD) [Han, 1994].
Dynamic control:
Augmented PD (APD) [Koditscheck, 1984], PD with computed feedforward [An et al., 1988], Nonlinear augmented PD (NAPD) [Shang et al., 2009], Computed torque (CT) [Luh et al., 1980], [Khalil and Dombre, 2002], Nonlinear CT (NCT) [Shang et al., 2009], Adaptive [Honegger et al., 2000], [Shang and Cong, 2010].
Further control schemes:
Fuzzy logic control [Begon et al., 1995], [Qi et al., 2006], Passivity based control [Beji et al., 1998], Impedance control [Fasse and Gosselin, 1999], Neural network control [Pernechele et al., 2000], Decoupled motion/null-space torque feedback [Kock and Schumacher, 2000], Sliding mode [Park et al., 2001], [Oh et al., 2004], Predictive control [Vivas et al., 2003], [Belda et al., 2006], Hybrid force/position adaptive control [Hui et al., 2003], Cross-coupled control approach [Sun et al., 2006], Vision-based CT [Paccot et al., 2008].
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 9
MAIN PROPOSED CONTROL SCHEMES FOR PARALLEL ROBOTS IN THE LITERATURE
Kinematic control Dynamic control
• Proportional-Derivative (PD) • Nonlinear PD (NPD)
• Augmented PD (APD) • Nonlinear APD (NAPD) • PD + Feedforward (FF) • Computed Torque (CT) • Nonlinear CT • Adaptive
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 10
Main existing control schemes for parallel robots:
Controller Advantages Disadvantages
PD/PID Simplicity • Lack of performance
• Lack of robustness
Nonlinear PD Can provide better tracking performance than a simple
PD
• Less simple than a PD
• Not based on the dynamics of the system
Kin
em
atic
co
ntr
ol
Augmented PD (APD) / PD+FF / CT
Better tracking performances when taking dynamics of the
system into consideration
• Lack of robustness with respect to uncertainties
• Computing time may be prohibitive
NAPD / NCT Further improvement of
tracking performance
• Lack of robustness with respect to uncertainties
• Computing time may be prohibitive
Adaptive Can provide very good
tracking performance, robust towards uncertainties
• Computing time may be even more prohibitive
Dyn
amic
co
ntr
ol
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 11
Description and modeling of our
parallel robots
Structural characteristics Dynamic models
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 12
Pass
ive a
rms
Active arms
Par2: Non-redundant
• 2 actuators/2 dof (X-Z) • 50G of max. acceleration
R4: Redundantly actuated • 4 actuators/3 dof (X-Y-Z) • 100G of max. acceleration
Structural characteristics
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 13
Dynamic models
Non-redundant case (Par2): Joint space
.q
.q
f)g
0.q
.J(MJ
)qcos(l
)qcos(l)MM(
2
g..q
..q
I
2
1vmtot
Tm
22
11
forearmarm
2
1eq
where:
JMJIII mtotTmarmmoteq , being ,
2
MnMM
forearmtptot •
State of the art Robots Proposed solutions Results Conclusion
• q
.q
..q, , represent the joint positions, velocities and accelerations,
• armM forearmM, correspond to the masses of the arms and forearms,
•
denote the length of the arms,
ll 21
• , symbolize the Jacobian of the robot and its derivative,
mJ m
.J
Imot, , tag the inertia of the motors and arms, and the mass of the trav. plate,
• Iarm
is equivalent to the torques,
• fv expresses the viscous friction,
g represents the gravity acceleration. •
Mtp
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 14
Dynamic models
Redundantly actuated case (R4): Dual-space
..XMH
..qI tot
Ttot
III armmottot • ,
)J(pinvH m• is the pseudo-inverse of the Jacobian of the robot.
•
..qJ
.q
.J
..X mm
State of the art Robots Proposed solutions Results Conclusion
represents the Cartesian acceleration.
Redundantly actuated case (R4): Cartesian space
).X
.JI(J)JIJM(
..X mtot
Tm
1mtot
Tmtot
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 15
Non-redundant case (Par2): Joint space Controllers: PD, Dual Mode State observers: Lead-lag based (LL), Alpha-beta-gamma (ABG), High- gain observer (HGO)
Proposed control solutions
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Cartesian PID, Dual-space FF, Dual-space adaptive
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 16
Non-redundant case (Par2): Joint space Controllers: PD, Dual Mode [Sartori-Natal et al., 2009, 2010a, 2010b]
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 17
Non-redundant case (Par2): Joint space State observers: Lead-lag based (LL), Alpha-beta-gamma (ABG), High- gain observer (HGO)
Lead
-lag
bas
ed (
LL)
ob
serv
er
Alp
ha-
Bet
a-G
amm
a
(AB
G)
ob
serv
er
Hig
h-G
ain
Ob
serv
er (
HG
O)
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 18
Non-redundant case (Par2): Joint space Controllers: PD, Dual Mode [Sartori-Natal et al., 2009, 2010a, 2010b]
State of the art Robots Proposed solutions Results Conclusion
eq
^ 0.
, if ^
or Adaptation mechanism:
jj sK)s(SatdYa Control law [Pazos and Hsu, 2003]:
)qcos(l.q
..q0
)qcos(l.q0
..q
Y
22r2r2
11r1r1
fa
v
am
am
MM2
gf
II
II
a,
being the upper bound of the estimated parameters’ errors; , with , where and are positive gains. jjj e
.es
2
M 0eq ^
|| || or M 0eq , if
with:
^
^ nom
^
aa^
a^
^ . .
;
M j
Teq sY
^ /
|| ||
|| ||
^
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012
• corresponds to the slope of the SVS term, is equivalent to the maximum disturbance, is a function of the parameter in the SVS term and is equivalent to the PD term,
• represents the adaptation gain,
19
Non-redundant case (Par2): Joint space Controllers: PD, Dual Mode [Sartori-Natal et al., 2009, 2010a, 2010b]
State of the art Robots Proposed solutions Results Conclusion
Stability analysis:
The Par2 robot, subject to bounded disturbances and with initial conditions near the origin (position and velocity errors), in closed loop with the Dual Mode controller (complied with the HGO for vel. estimation), will be uniformly bounded, having its tracking error converging exponentially to the residual domain given by:
maxd
where:
'Ok
)d(cdO
1Oe max
j
)d(c d
k
• denotes the HGO gain. '
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 20
Non-redundant case (Par2): Joint space Controllers: PD, Dual-Mode State observers: Lead-lag based (LL), Alpha-beta-gamma (ABG), High- gain observer (HGO)
Proposed control solutions
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Cartesian PID, Dual-space FF, Dual-space adaptive
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 21
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Cartesian PID, Dual-space FF, Dual-space adaptive
H PID Δq Δx τdqdx
I.K. -
R4 manipulator
F
+
mq
mq
TH
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 22
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Cartesian PID, Dual-space FF [Sartori-Natal et al., 2012a], Dual-space adaptive
PID THΔq Δx τ
dq
mq
I.K. +
R4 manipulator
mq+
Kffc
Kffa Kffa
dx F
- +
H
State of the art Robots Proposed solutions Results Conclusion
..XMH
..qI tot
Ttot
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 23
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Cartesian PID, Dual-space FF, Dual-space adaptive [Sartori-Natal et al., 2012b] ICRA’12 Best Automation Paper Award, Finalist
H PD Δq Δx τ
dq
mq
I.K. +
R4 manipulator
mq+
Kffc
Kffa Kffa
dx F
- +
Itot
^
Mtot ^
TH
State of the art Robots Proposed solutions Results Conclusion
..XMH
..qI tot
Ttot
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 24
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Cartesian PID, Dual-space FF, Dual-space adaptive [Sartori-Natal et al., 2012b] ICRA’12 Best Automation Paper Award, Finalist
H PD Δq Δx τ
dq
mq
I.K. +
R4 manipulator
mq+
Kffc
Kffa Kffa
dx F
- +
Itot ^
Mtot ^
TH
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 25
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Cartesian PID, Dual-space FF, Dual-space adaptive [Sartori-Natal et al., 2012b] ICRA’12 Best Automation Paper Award, Finalist
State of the art Robots Proposed solutions Results Conclusion
iii
ii
iii
ii
iii
^
a1
b1
.
, if ii
^
i ba , or ii
^
b and 0i
or ii
^
a and 0i
,
, if ii
^
b and 0i
, if and 0i ii
^
a
Adapt. mech. [Lee and Khalil, 1997]:
cdcp
^ .eKeKYF
Control law:
d
..
4x4d3x3 qI..XHIY
tot
^tot
^^
I
M, being , the upper and lower bounds of the estimated parameters; , with , where , being and positive gains.
ia ibsYT
i
cc e.es )e1/( c0
0
with: xec ,
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 26
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Cartesian PID, Dual-space FF, Dual-space adaptive [Sartori-Natal et al., 2012b] ICRA’12 Best Automation Paper Award, Finalist
State of the art Robots Proposed solutions Results Conclusion
Stability analysis:
Q
dOe max2
ss
0
d1d
1dp
2
KM
2
3K
2
1
M2
3K
2
1K
Q
where:
c
c
ss .e
ee and
The R4 robot, subject to bounded disturbances, in closed loop with the Dual-space adaptive controller, will be uniformly bounded, having its tracking error converging exponentially to the residual domain given by:
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 27
Non-redundant case (Par2):
Scenario 1: PD x Dual Mode controllers (HGO for velocity estimation)
Simulation results
Redundantly actuated case (R4):
Scenario 1: Cartesian PID x Dual-space FF Scenario 2: Dual-space FF x Dual-space adaptive
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 28
Simulation results: Non-redundant case (Par2):
Scenario 1: PD x Dual Mode controllers (HGO for velocity estimation), 2D Pick-and-place trajectory, payload of 500g, 35G of max. acceleration
Traj
ecto
ry t
rack
ing
Traj
ecto
ry t
rack
ing
(zo
om
)
Trac
kin
g er
rors
Co
ntr
ol i
np
uts
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 29
Simulation results: Redundantly actuated case (R4):
Scenario 1: Cartesian PID x Dual-space FF, 2D straight line (X-Y), no payload, 65G of max. acceleration
Traj
ecto
ry t
rack
ing
Traj
ecto
ry t
rack
ing
(zo
om
)
Trac
kin
g er
rors
Co
ntr
ol i
np
uts
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 30
Simulation results: Redundantly actuated case (R4):
Scenario 2: Dual-space FF x Dual-space adaptive, 2D straight line (X-Y), pick-and-place (payload of 200g), 65G of max. acceleration
Trac
kin
g er
rors
Esti
mat
ed p
aram
eter
s
Co
ntr
ol i
np
uts
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 31
Non-redundant case (Par2):
Scenario 1: PD x Dual Mode controllers (HGO for vel. estimation) Scenario 2: LL x ABG x HGO observers (complied with the DM controller)
Real-time experimental results
Redundantly actuated case (R4):
Scenario 1: Cartesian PID x Dual-space FF Scenario 2: Dual-space FF x Dual-space adaptive Extra scenario: The 100G experiment
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 32
2D Pick and place desired trajectory for the non-redundant case (Par2):
Values
Max. Accelerations
20G/15G
Cycle times 0.32s/0.42s
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 33
Real-time experimental results: Non-redundant case (Par2):
Scenario 1: PD x Dual Mode controllers (HGO for vel. estimation), 2D pick-and-place trajectory, no payload, 20G of max. acceleration
Co
ntr
ol i
np
uts
Traj
ecto
ry t
rack
ing
Trac
kin
g er
rors
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 34
Real-time experimental results: Non-redundant case (Par2):
Scenario 2: LL x ABG x HGO observers (complied with the same DM controller), 2D pick-and-place trajectory, no payload, 15G of max. acceleration
Co
ntr
ol i
np
uts
Traj
ecto
ry t
rack
ing
Trac
kin
g er
rors
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 35
Summary of the experimental results for the non-redundant case (Par2)
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 36
PD Dual Mode
Error peaks during trajectories [-4.15°, 3.3°] [-2.8°, 1.9°]
Stop points [-2.3°, 2.3°] [-0.7°, 0.7°]
[Sartori-Natal et al., 2009]
- Mechanical vibrations that arise with the increase of the involved accelerations and possible solutions to avoid/compensate them [Sartori-Natal et al., 2010a]
ABG LL HGO
Error peaks [-0.2°, 0.55°] [-0.5°, 0.7°] [-0.6°, 1.2°]
Scenario 2: ABG x LL x HGO observers (same DM controller), 15G
Scenario 1: PD x Dual Mode controllers (HGO for vel. estimation), 20G
[Sartori-Natal et al., 2010b]
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 37
PD Dual Mode
Error peaks during trajectories [-4.15°, 3.3°] [-2.8°, 1.9°]
Stop points [-2.3°, 2.3°] [-0.7°, 0.7°]
[Sartori-Natal et al., 2009]
- Mechanical vibrations that arise with the increase of the involved accelerations and possible solutions to avoid/compensate them [Sartori-Natal et al., 2010a]
ABG LL HGO
Error peaks [-0.2°, 0.55°] [-0.5°, 0.7°] [-0.6°, 1.2°]
Scenario 2: ABG x LL x HGO observers (same DM controller), 15G
[Sartori-Natal et al., 2010b]
Scenario 1: PD x Dual Mode controllers (HGO for vel. estimation), 20G
Operation of the Par2 parallel manipulator (non-redundant): 20G
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 38
Non-redundant case (Par2):
Scenario 1: PD x Dual Mode controllers (HGO for vel. estimation) Scenario 2: LL x ABG x HGO observers (complied with the DM controller)
Real-time experimental results
Redundantly actuated case (R4):
Scenario 1: Cartesian PID x Dual-space FF Scenario 2: Dual-space FF x Dual-space adaptive Extra scenario: The 100G experiment
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 39
Real-time experimental results: Redundantly actuated case (R4):
Scenario 1: Cartesian PID x Dual-space FF, 2D spiral trajectory (X-Y), no payload, 20G max. acceleration
Des
ired
tra
ject
ory
Des
ired
tra
ject
ory
(X
)
Trac
kin
g er
rors
Co
ntr
ol i
np
uts
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 40
Real-time experimental results: Redundantly actuated case (R4):
Scenario 2: Dual-space FF x Dual-space adaptive, 3D pick-and-place trajectory, with/without payload , 20/30G of max. accelerations
Des
ired
tra
ject
ory
Des
ired
tra
ject
ory
(X
-Y-Z
) Tr
acki
ng
erro
rs (
30
G/N
o lo
ad)
Trac
kin
g er
rors
(2
0G
/20
0g
load
)
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 41
Real-time experimental results: Redundantly actuated case (R4):
Scenario 2: Dual-space FF x Dual-space adaptive, 3D pick-and-place trajectory, with/without payload , 20/30G of max. accelerations
Evo
l. o
f es
t. m
ass
(no
load
)
Evo
l. o
f es
t. m
ass
(20
0g
load
)
Co
ntr
ol i
np
uts
Co
ntr
ol i
np
uts
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 42
Summary of the experimental results for the redundantly actuated case (R4)
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 43
Scenario 1: Cartesian PID x Dual-space FF, 2D spiral trajectory (X-Y), no payload, 20G max. acceleration
Cart. PID Dual-Space FF
Error peaks [-5.6°, 6.25°]mm [-1.23°, 1.58°]mm
[Sartori-Natal, 2012a]
Scenario 2: Dual-space FF x Dual-space adaptive, 3D pick-and-place trajectory, with/without payload , 20/30G of max. accelerations
Adaptive FF (Kffc = 0.625/0.825)
RMSE (No payload, 30G) 1.44mm 2.1mm/2.36mm
RMSE (200g payload, 20G) 1.3mm 2.14mm/1.76mm
[Sartori-Natal, 2012b]
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 44
Operation of the R4 parallel manipulator (red. actuated): 20/30G
Scenario 1: Cartesian PID x Dual-space FF, 2D spiral trajectory (X-Y), no payload, 20G max. acceleration
Cart. PID Dual-Space FF
Error peaks [-5.6°, 6.25°]mm [-1.23°, 1.58°]mm
[Sartori-Natal, 2012a]
Scenario 2: Dual-space FF x Dual-space adaptive, 3D pick-and-place trajectory, with/without payload , 20/30G of max. accelerations
Adaptive FF (Kffc = 0.625/0.825)
RMSE (No payload, 30G) 1.44mm 2.1mm/2.36mm
RMSE (200g payload, 20G) 1.3mm 2.14mm/1.76mm
[Sartori-Natal, 2012b]
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 45
Proposed comparisons for the redundantly actuated case (R4):
Extra scenario: The 100G experiment
Des
ired
tra
ject
ory
Traj
ecto
ry t
rack
ing
(zo
om
) To
rqu
es x
an
g. s
pee
ds
Co
ntr
ol i
np
uts
Operation of the R4 redundantly actuated parallel manipulator: 100G
State of the art Robots Proposed solutions Results Conclusion
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 46
State of the art Description Control Results Conclusion
Conclusion and perspectives
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012
! Control of parallel manipulators for very high acceleration applications,
! Important operational changes must be considered (such as movements with
and without load),
! Only the joint positions are measured.
47
Problems:
Validation:
20G of maximum acceleration (Solution 1/Par2),
30G/100G of maximum acceleration (Solution 2/R4).
Proposed solutions:
1. Control in the joint space (non-redundant case): PD and DM controllers,
complied with the LL based, ABG and HGO observers,
2. Control in the Cartesian/Dual-space (redundantly actuated case): Cart. PID,
Dual-space FF and Adaptive controllers.
Obtained experimental results:
Simulations,
Real-time experiments.
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012
Implementation of the proposed control solutions for one robot on the other
robot, as well as on other Delta robots,
Increase of the accelerations of the pick-and-place movements with the
acquisition of stiffer springs for the R4 redundantly actuated parallel manipulator,
Development of fast enough end-effectors for the actual manipulation of
objects at such high speed.
48
Perspectives:
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012
G. Sartori Natal, A. Chemori, F. Pierrot and O. Company, ‘‘Nonlinear Dual Mode
Adaptive Control of PAR2: a 2-dof Planar Parallel Manipulator, with Real-Time
Experiments’’, IEEE/RSJ IROS’09, St. Louis, USA, 2009.
G. Sartori Natal, A. Chemori, F. Pierrot and O. Company, ‘‘Nonlinear Control of
Parallel Manipulators without Velocity Measurement: A Comparison Between State
Observers, with Real-Time Experiments’’, IEEE/RSJ IROS’10, Taipei, Taiwan, 2010.
49
Publications:
G. Sartori Natal, A. Chemori, F. Pierrot and O. Company: ‘‘Control of Parallel
Manipulators for Very High Accelerations: The Mechanical Vibrations Issue’’,
PACAM XI, Foz do Iguaçu, Brazil, 2010.
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012
G. Sartori Natal, A. Chemori, M. Michelin and F. Pierrot, ‘‘Dual-Space
Feedforward Control of a Redundantly Actuated Parallel Manipulator for Very High
Speed Applications’’, IFAC Conf. on Adv. in PID Control, Brescia, Italy, 2012.
50
G. Sartori Natal, A. Chemori and F. Pierrot, ‘‘Dual-Space Adaptive Control of
Redundantly Actuated for Extremely Fast Operations with Load Changes’’,
IEEE/RSJ ICRA’12, Minnesota, USA, 2012. Best Automation Paper Award of
IEEE-RAS, Finalist
Publications:
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 51
State of the art Robots Proposed solutions Results Conclusion
Bibliographic references
[An et al., 1988] An, C. H., Atkeson, C. G. and Hollerbach, J.M., “Model-based control of a robot manipulator”, MIT Press. [Begon et al., 1995] Begon, P., Pierrot, F. and Dauchez, P., “Fuzzy sliding mode control of a fast parallel manipulator”, Proc. ICRA. [Beji et al., 1998] Beji, L., Abichou, A. and Pascal, M., “Tracking control of a parallel robot in the task space”, Proc. ICRA. [Belda and Böhm, 2006] Belda, K. and Böhm, J., “Predictive control of parallel manipulators and trajectory planning”, Proc. of the PKM in Research and Practice. [Fasse and Gosselin, 1999] Fasse, E. D. and Gosselin, C. M., “Spatio-geometric impedance control of Gough-Stewart platforms”, IEEE TRA. [Han, 1994] Han, J., “Nonlinear PID controller”, Acta Automat Sinica. [Honegger et al., 2000] Honegger, M., Brega, R. and Schweitzer, G., “Application of a nonlinear adaptive controller to a 6 dof parallel manipulator”, Proc. ICRA. [Hui et al., 2003] Hui, S., Xu-Zhang, W., Guan-Feng, L. and Ze-Xiang, L., “Hybrid force/position adaptive control of redundantly actuated parallel manipulators”, Acta Automatica Sinica. [W. Khalil and Dombre, 2002] Khalil, W. and Dombre, E., “Modeling, identification and control of robots”, Hermes Penton, London. [Kock and Schumacher, 2000] Kock, S. and Schumacher, W., “Control of a fast parallel robot with a redundant chain and gearboxes: experimental results”, Proc. ICRA. [Koditscheck, 1984] Koditscheck, D. E., “Natural motion for robot arms”, Proc. CDC.
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 52
State of the art Robots Proposed solutions Results Conclusion
Bibliographic references [Luh et al., 1980] Lu, J., Walker, M. and Paul, R., “Resolved-acceleration control of mechanical manipulators”, IEEE TRA. [Oh et al., 1995] Oh, S.-R., Mankala, K., Agrawal, S. K. and Albus, J. S., “Dynamic modelling and robust controller design of a two-stage parallel cable robot”, Proc. ICRA. [Paccot et al., 2008] Paccot, F., Lemoine, P., Andreff, N., Chablat, D. and Martinet, P.,“A vision-based computed torque control for parallel kinematic machines”, Proc. ICRA. [Park et al., 2001] Park, M. K., Lee, M. C. and Go, S. J., “The design of sliding mode controller with perturbation observer for a 6-dof parallel manipulator”, Int. Symp. on Ind. Electronics. [Pernechele, 2000] Pernechele, C., Bortoletto, F. and Giro, E., “Neural network algorithm controlling a hexapod platform”, Proc. Int. Joint Conf. on Neural Networks. [Qi, 2006] Qi, Z., Mcinroy, J. E. and Jafari, F., “Trajectory tracking with parallel robots using low chattering, fuzzy sliding mode controller”, Journal of Intel. and Rob. Systems. [Shang et al., 2009] Shang, W. W., Cong, S. and Zhang, Y., “Nonlinear friction compensation of a 2-dof planar parallel manipulator”, Advanced robotics. [Shang and Cong, 2010] Shang, W. W. and Cong, S., “Nonlinear adaptive task space control for a 2-dof redundantly actuated parallel manipulator”, Nonlinear Dynamics. [Sun et al., 2006] Sun, D., Lu, R., Mills, J. K. and Wang, C., “Synchronous tracking control of parallel manipulators using cross-coupling approach”, Int. J. Robotics Research. [Vivas and Poignet, 2003] Vivas, A. and Poignet, P., “Model based predictive control of a fully parallel robot”, IFAC Symp. on Rob. Control. [Ziegler and Nichols, 1942] Ziegler, J. G. and Nichols, N. B., “Optimum settings for automatic controllers”, Trans. of the Am. Soc. of Mech. Eng.
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 53
State of the art Robots Proposed solutions Results Conclusion
Bibliographic references
[Pazos and Hsu, 2003] Pazos, F. and Hsu, L., “Controle de robôs manipuladores em modo dual adaptativo/robusto”, Revista Controle & Automação.
[Lee and Khalil, 1997] Lee, K. W. and Khalil, H. K., “Adaptive output feedback control of robot manipulators using high-gain observer”, Int. Journal of Control.
Non-redundant case (Par2): Dual Mode controller
Redundantly actuated case (R4): Dual-space adaptive controller
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 54
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 55
Non-redundant case (Par2): Joint space Controller: Dual Mode [Sartori-Natal et al., 2009, 2010a, 2010b]
State of the art Robots Proposed solutions Results Conclusion
Stability analysis, disturb. compensation:
with:
s
sdds)s(f
2
max
• corresponds to the slope of the SVS term, is equivalent to the maximum disturbance, is a function of the parameter in the SVS term and is equivalent to the PD term.
maxd
)d(c d
k
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 56
Redundantly actuated case (R4): Dual-space
Controller: Dual-space adaptive [Sartori-Natal et al., 2012b] ICRA’12 Best Automation Paper Award, Finalist
State of the art Robots Proposed solutions Results Conclusion
Stability analysis:
Q
dOe max2
ss
0
d1d
1dp
2
KM
2
3K
2
1
M2
3K
2
1K
Q
where:
c
c
ss .e
ee and
‘
‘
• , for any vector v, consists in the vectorial representation of the partial derivative of , being , and is equivalent to the upper bound of the maximum desired velocity.
)q(MD)Iv()v(M sqq
).q,q(C)
.q,q(
.M)q(M eqeq
s
)q(JI)q(JM)q(M mTOTTmTOTeq )
.q,q(
.JI)q(J)q(C mTOT
Tmeq 1
‘
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 57
Redundantly actuated case (R4): Cartesian/Dual-space
Controllers: Dual-space adaptive [Sartori-Natal et al., 2012b] ICRA’12 Best Automation Paper Award, Finalist
State of the art Robots Proposed solutions Results Conclusion
Stability analysis:
Configuration 1:
Configuration 2:
100)Qsup(
300)Qsup(
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012
G. Sartori Natal, A. Chemori, F. Pierrot and O. Company, ‘‘Nonlinear Dual Mode
Adaptive Control of PAR2: a 2-dof Planar Parallel Manipulator, with Real-Time
Experiments’’, IEEE/RSJ IROS’09, St. Louis, USA, 2009.
Real-time experimental comparison between a PD and a nonlinear Dual Mode controller, both
complied with a High-gain observer to estimate the joint velocities, on the Par2 parallel
manipulator.
G. Sartori Natal, A. Chemori, F. Pierrot and O. Company, ‘‘Nonlinear Control of
Parallel Manipulators without Velocity Measurement: A Comparison Between State
Observers, with Real-Time Experiments’’, IEEE/RSJ IROS’10, Taipei, Taiwan, 2010.
Analysis of the tracking performance improvements obtained on the Par2 parallel manipulator
by changing only the velocity estimator.
58
Publications:
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012
G. Sartori Natal, A. Chemori, F. Pierrot and O. Company: ‘‘Control of Parallel
Manipulators for Very High Accelerations: The Mechanical Vibrations Issue’’,
PACAM XI, Foz do Iguaçu, Brazil, 2010.
Discussion about the mechanical vibrations generated when reaching high accelerations and
possible solutions to avoid/damp these vibrations.
G. Sartori Natal, A. Chemori, M. Michelin and F. Pierrot, ‘‘Dual-Space
Feedforward Control of a Redundantly Actuated Parallel Manipulator for Very High
Speed Applications’’, IFAC Conf. on Adv. in PID Control, Brescia, Italy, 2012.
Real-time experimental comparison between a Cartesian PID and a Dual-Space Feedforward
controller on the R4 redundantly actuated parallel manipulator.
59
Publications:
PhD. Defense: Guilherme SARTORI NATAL Montpellier, 26 th of November, 2012 60
G. Sartori Natal, A. Chemori and F. Pierrot, ‘‘Dual-Space Adaptive Control of
Redundantly Actuated for Extremely Fast Operations with Load Changes’’,
IEEE/RSJ ICRA’12, Minnesota, USA, 2012. Best Automation Paper Award of
IEEE-RAS, Finalist
Real-time experimental comparison between a Dual-Space Feedforward controller and a Dual-
Space Adaptive controller (with and without load) on the R4 redundantly actuated parallel
manipulator.
Publications: