control of parallel robots: towards very high accelerationsmontpellier, 26 th of november, 2012 phd....

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


Medical robotics Haptic robotics

Tyre testing Flight

simulation



Pick-and-place

applications


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


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


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



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].


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



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



Description and modeling of our

parallel robots

Structural characteristics Dynamic models



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



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 •


• 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


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


represents the Cartesian acceleration.

Redundantly actuated case (R4): Cartesian space

).X

.JI(J)JIJM(

..X mtot

Tm

1mtot

Tmtot


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



Non-redundant case (Par2): Joint space Controllers: PD, Dual Mode [Sartori-Natal et al., 2009, 2010a, 2010b]



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)





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

^ /

|| ||

|| ||

^


• 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



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. '


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







H PID Δq Δx τdqdx

I.K. -

R4 manipulator

F

+

mq

mq

TH




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


..XMH

..qI tot

Ttot



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


..XMH

..qI tot

Ttot




H PD Δq Δx τ

dq

mq

I.K. +

R4 manipulator

mq+

Kffc

Kffa Kffa

dx F

- +

Itot ^

Mtot ^

TH






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 ,





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:


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



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



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



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




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


Scenario 1: Cartesian PID x Dual-space FF Scenario 2: Dual-space FF x Dual-space adaptive Extra scenario: The 100G experiment



2D Pick and place desired trajectory for the non-redundant case (Par2):

Values

Max. Accelerations

20G/15G

Cycle times 0.32s/0.42s



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



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



Summary of the experimental results for the non-redundant case (Par2)



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]



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




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


Scenario 1: Cartesian PID x Dual-space FF Scenario 2: Dual-space FF x Dual-space adaptive Extra scenario: The 100G experiment



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




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

)





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



Summary of the experimental results for the redundantly actuated case (R4)




Cart. PID Dual-Space FF

Error peaks [-5.6°, 6.25°]mm [-1.23°, 1.58°]mm

[Sartori-Natal, 2012a]


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]



Operation of the R4 parallel manipulator (red. actuated): 20/30G


Cart. PID Dual-Space FF

Error peaks [-5.6°, 6.25°]mm [-1.23°, 1.58°]mm

[Sartori-Natal, 2012a]


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]



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 Description Control Results Conclusion

Conclusion and perspectives


! 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.


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:


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.


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:



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.



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.



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


Non-redundant case (Par2): Joint space Controller: Dual Mode [Sartori-Natal et al., 2009, 2010a, 2010b]


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


Redundantly actuated case (R4): Dual-space

Controller: Dual-space adaptive [Sartori-Natal et al., 2012b] ICRA’12 Best Automation Paper Award, Finalist


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

‘



Controllers: Dual-space adaptive [Sartori-Natal et al., 2012b] ICRA’12 Best Automation Paper Award, Finalist


Stability analysis:

Configuration 1:

Configuration 2:

100)Qsup(

300)Qsup(


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:


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:


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:

control of parallel robots: towards very high accelerationsmontpellier, 26 th of november, 2012 phd....

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