Contributions à la commande adaptative non linéaire des ...chemori/Temp/Maxence/CST_2_Bennehar.pdf · Outline of the Presentation ?? Context and Problematic of the Thesis State

Commité de Suivi de Thèse (CST)

Ecole Doctorale : Information, Structures et Systèmes

Contributions à la commande adaptative non linéaire des robots parallèles

?? Friday Oct. 3rd, 2014

Bennehar Moussab Doctorant en 2ème année de thèse

Cadre: Projet ANR ARROW

Directeur de thèse : François Pierrot Encadrant : Ahmed Chemori

Outline of the Presentation

?? Context and Problematic of the Thesis

State of the Art on Dynamics and Control of Mechanical Manipulators

Adaptive Compensation of Parametric Uncertainties

Solution 1: Extended DCAL Control

Solution 2: Adaptive RISE Control

Adaptive Compensation of Nonparametric Uncertainties

Solution 1: L1 Adaptive Control

Solution 2: L1 Adaptive Control with Feedforward

Conclusion and Future Work ?? Plan ne correpond pas à la barre

Context and Problematic of the Thesis

Context State of the Art Parametric Nonparametric Thesis Progress

Parallel Manipulators Parallel VS Serial Issues and Challenges

Parallel Manipulators Parallel VS Serial Applications Issues and Challenges

1


End-effector

Base

Base

End-effector

Parallel Kinematic Manipulator (PKM)

“A mechanism in closed kinematic loop, whose end-effector is

connected to the base through at least two independent kinematic

chains” [Merlet, 2006]

Main Characteristics

Closed Kinematic Chains

Extremely fast motion

Accurate positioning

High stiffness

…


2


Large workspace

High dexterity

Relatively simple dynamic modeling

Simple forward kinematics

Low stiffness

Low load/mass ratio

Complex inverse kinematics

Low positioning accuracy

Relatively slow motion capabilities

High stiffness

Large load/mass ratio

Simple inverse kinematics

Very accurate positioning

Extremely fast motion

Limited workspace

Complex dynamic modeling

Complex forward kinematics


3


Space

applications

Haptic interfaces Medical

applications Food packaging

Other applications

Machine tools


4


! Coupled/redundant actuation

! High accelerations Highly nonlinear dynamics

! High accelerations/stop points Mechanical vibrations

! Uncertainties in model / environment

! Payload Unknown / variable

Main Control Difficulties:

Proposed Solution

Cancel all existing nonlinearities in the system to improve its tracking performance and cancel disturbances

Application

Numerical simulations and real-time experiments:

Redundant case: Dual-V

Non-redundant case : VELOCE

Du

al-V

Kinematic Control Fixed Model-based Control Adaptive Control Other Control

State of the Art on Control of Mechanical Manipulators


Kinematic Control Fixed Model-based Control Adaptive Control Others

5


Main Control Schemes for Mechanical Manipulators

Kinematic Control Fixed Model-based

Control Adaptive Control (AC) Others

• PID Control [Ziegler and Nichols, 1942]

• Nonlinear PD Control [Han et al., 1994]

• Motion Coordination [Shang et al., 2010]

• Augmented PD (APD)

[Reyes et al., 1984]

• Nonlinear APD (NAPD)

[Shang et al., 2009c]

• PD+ [Reyes et al. , 2001]

• Computed Torques (CT)

[Luh et al. 1980]

• Nonlinear CT (NCT) [Shang

et al., 2009]

• Model Reference AC

(MRAC) [Dubowsky &

DesForges, 1979]

• Inverse Dynamics Based

AC [Craig et al., 1986]

• Passivity Based AC

[Sadegh & Horowitz 1987]

• Backstepping AC [Wang et

al., 2009]

• Vision Control [Paccot et

al., 2008]

• Fuzzy Logic Control [Begon

et al., 1995]

• Predictive Control [Vivas

et al., 2003]


6



Kinematic Control

• PID Control [Ziegler and Nichols, 1942]

• Nonlinear PD Control [Han et al., 1994]

• Motion Coordination [Shang et al., 2010] Very Simple Structure

Computationally efficient

No dynamic model is required

Widely known by industrials

Dynamics not considered

High energy consumption

Poor performance on high accelerations

Hard tuning of parameters


7



• Augmented PD (APD)

[Reyes et al., 1984]

• Nonlinear APD (NAPD)

[Shang et al., 2009c]

• PD+ [Reyes et al. , 2001]

• Computed Torques (CT)

[Luh et al. 1980]

• Nonlinear CT (NCT) [Shang

et al., 2009]

Good tracking performance

Low energy consumption

Low feedback gains

Compensation of nonlinearities

Require accurate dynamic model

Complex computations require recent

hardware

Measurement noise affects the performance

Fixed Model-based Control


8



• Model Reference AC

(MRAC) [Dubowsky &

DesForges, 1979]

• Inverse Dynamics Based

AC [Craig et al., 1986]

• Passivity Based AC

[Sadegh & Horowitz 1987]

• Backstepping AC [Wang et

al., 2009]

Nonlinearities adaptively

compensated

Lead to linear model in ideal case

It can deal with external disturbances

Very complex architecture

Parameters convergence sometimes not

achieved

Low performance when parameters do not

converge

Adaptive Control (AC)

Dynamics Parameterization Extended DCAL Adaptive RISE Shortcomings and Issues

Adaptive Compensation of Parametric Uncertainties


Dynamics Extended DCAL Adaptive RISE Limitations

9

Joint Space Inverse Dynamic Model

Inertia Centrifugal + Coriolis + gravity

friction General disturbances

Very often addressed in research

Easy to model

CAD values are accurate

Easily compensated by control

Can be parameterized

Rarely reported in the literature

Very complex to model

Cannot be parameterized

Usually not considered in

modern control

Parametric Nonlinearities Nonparametric Nonlinearities

Parameterization Regressor

Vector of constant parameters



10

Background on Desired Compensation Adaptation Rule (DCAL) [Sadegh & Horowitz, 1990]

Rely heavily on desired quantities

Desired quantities can be stored offline

Reduced computation time

More robust to measurement noise

Adaptive parameters are less noisy

Parameters converge faster

Advantages of DCAL



11

Block Diagram of DCAL

Robot

Adaptive Feedforward

Stabilizing term Trajectory Generator

Linear PD Controller



12

PD Controller Adaptive

Feedforward Stabilizing Term + +

DCAL Control Law

Replace the linear gains in the feedback

loop by NL ones

Proposed Solution Poor performance with nonlinear (NL) systems

Sensitive to disturbances

Poor performance on high accelerations

Limited tuning capabilities

NL PD Controller Adaptive

Feedforward Stabilizing Term + +

Extended DCAL Controller



13

Proposed Extended Desired Compensation Adaptation Rule (EDCAL) [Bennehar et al., 2014]

Better tracking performance

Reduced control inputs

More robustness toward uncertainties

Expected Improvements

Nonlinear gains functions [Shang et al., 2009]

Linear

Nonlinear

small errors = small gains

large errors = large gains



14

Solving the Internal Forces Issue in RA-PKM

RA-PKM inputs contain antagonistic forces

These forces create pre-stress

They deteriorate performance, create vibrations and harm the robot

These forces can be reduced using the projector [Muller and Hufnagel, 2011]:

The proposed control input becomes


2 dof versus 3 actuators

Redundantly actuated


15

Application to the Dual-V

Experienced Scenarios

Scenario 2 ?? : Nominal Case Scenario 2 ?? : Payload

Handling



16

Real-time Experimental Results

Nominal Case Payload Handling

Estim

ated

Par

amet

ers

DCAL EDCAL DCAL EDCAL


?? ?? ?? ??


17

Conclusions

DCAL implemented in simulation/experiments on Dual-V

Overall performance could be improved by careful

choice/tuning of feedback gains

Constant gains replaced by NL ones EDCAL

EDCAL implemented on Dual-V

Results demonstrated the relevance of EDCAL

The feedback loop is essential in improving the

performance of the system

More sophisticated modern feedback strategies can be

investigated

Remarks for upcoming work

IROS’14, Chicago, Sep. 2014 ?? Ref



18

What is RISE ?

Robust Integral of the Sign of the Error

Non-model based feedback control strategy

Features a unique signum function

Why RISE ?

Stability of the system guaranteed

High order nonlinearities taken into account

MIMO systems supported

Large class of general disturbances assimilated

Very reasonable Hypotheses Xian et al., 2003 ?? Ref



19

Overview of Some Successful Applications

[Patre et al. 2008]

Direct-drive motor

[MacKunis et al. 2013]

Synthetic Jet Actuators

[Dupree e al. 2010]

Two-link robot

[Taktak-Meziou et al . 2014]

Hard Disk Drive

[Haibo et al. 2010]

Spacecraft Coordination

[Fischer et al. 2011]

Autonomous Underwater Vehicule


Combined Tracking Errors

Control Law


20

Background on RISE for MIMO Systems



21

RISE law solely is enough for tracking

The performance can be enhanced if some

knowledge about the system is available

The dynamics can be included in the control loop

Some Remarks on RISE

Proposed Solution Augment RISE with Adaptive Feedforward

RISE

Adaptive FF

Robot



22

Dynamics of the robot Regressor

Vector of constant parameters

Proposed Adaptive RISE Controller [Bennehar et al., 2014]

Better tracking performance (parametric uncertainties partially compensated)

Reduced control inputs (thanks to the dynamics-based feedforward)

More robustness toward uncertainties (inherent to RISE)

Expected Enhancements

Control Law After Projection



23



24

Experimental Results

Adaptive RISE RISE Adaptive RISE RISE

Trac

king

err

ors

Nominal Case ?? Payload Handling



25

Experimental Results

Estim

ated

Par

amet

ers

Nominal Case ?? Payload Handling



26

Conclusions

RISE Implemented on the first time on PKMs

The performance of RISE is evaluated

RISE is augmented with adaptive FF

The adaptive FF compensates for some nonlinearities

Experiments on Dual-V demonstrated the relevance

of the proposed extension ?? IROS’14, Chicago, Sep. 2014



27

General Conclusions on Model-based Adaptive Compensation of Parametric Uncertainties

• Mechanical manipulators are complex NL systems • Classical linear controllers are not suitable to control them • Most of the nonlinearities are inherent to the dynamics of the system • To achieve the best tracking performance, these nonlinearities have to be compensated • The best solution for that is, if available, to include the dynamics of the model in the control loop

Advantages of Model-based Adaptive Compensation of Parametric Uncertainties

Intuitive solution to compensate for the nonlinearities Achieves better results than fixed model-based control Assimilates a large class of uncertainties Reduces the energy consumption

Limitations of Model-based Adaptive Compensation of Parametric Uncertainties

Only a specific class of uncertainties is considered A dynamic model is required in the control loop The computation cost is often expensive Convergence of the parameters is not gurenteed


?? oui

Adaptive Compensation of Nonparametric Uncertainties

MRAC Limitations of MRAC L1 Adaptive Extended L1 Adaptive


MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks

28

Main limitations of Conventional Model-based Control

Dynamic model should be available ?? Proper initialization of the parameters Persistence excitation of the parameters

Solution Model Reference Adaptive

Control (MRAC)

Principle of MRAC ??

Robot

Adjustable Gains

Adaptation Mechanism

Reference Model

Inputs Outputs

Issues

Specifications are specified only asymptotically Uncertainties may lie outside the actuators’ bandwidth High adaptation gain High gain feedback

Solution

L1 Adaptive Control [Hovakimyan & Cao, 2006]


A améliorer !!!!!

29



Main Characteristics L1 Adaptive Control

Inspired from MRAC

Features a State Predictor

A Filter is introduced in the control loop

A projection-based adaption law is used

Principle of L1 Adaptive Control

Define error dynamics

Lump all nonlinearities

Stabilizing Term

Adaptive Term

• Projection-based • Filtered ??

Control Law


30



Tracking Error

Control Law

Stabilizing Term

Adaptive Term

Error Dynamics

Filter Estimated Parameters

Adaptation Laws


31


Trajectory Generator

Combined Error

Robot

Adaptive Laws with Projection

State Predictor

Stabilizing Term

Adaptive Term


??

32


Experimental Results: Application on Veloce

L1 adaptive control (solid), PD (dashed)

Trac

king

err

ors


33



Estim

ated

Par

amet

ers


34


L1 Adaptive Control

No model needed

Decoupled Estimation

& Robustness

Parameters Boundedness

Better performance

than PD

Compensates all NLs

Q: Can we improve the performance by including the available dynamic model ?

A: Definitely!!!! Q: How ????


35



L1 Adaptive Control Law

Stabilizing Term

Adaptive Term

Adaptation Laws

Proposed Control Law Model-based Feedforward

Same as the L1 Adaptive Control


36


Trajectory Generator

Combined Error

Robot

Adaptive Laws with Projection

State Predictor

Stabilizing Term

Adaptive Term

Model-based Feedforward

Proposed Extended L1 Adaptive Controller


??

37



Trac

king

Err

ors

L1-AC (dashed), Extended L1-AC(dashed)


38



Estim

ated

Par

amet

ers

Extended L1-AC (left), L1-AC (right)



39


Tackled Problems

• Trajectory tracking of PKMs

• Adaptive compensation of all uncertainties in the system

• Guarantee fast adaptation without hurting robustness

• Include dynamics in the control loop to improve performance

Difficulties

• Inherent high nonlinearities

• Parameters uncertainties/variations

• Guarantee fast adaptation without hurting robustness

Proposed Solution

• Extended L1 Adaptive Controller with Feedforward

?? Conclusions as previously presented

?? Pourquoi la photo

Progress of the Thesis ?? and Future Work

Schedule Publications Teaching Doctoral Courses


40



IROS’13 ICRA’14 IROS’14 ICRA’15

15/10 22/03 16/09 06/02 02/10

Today

15/10

SSD’14

19/04

TSSD

30/06 14/11

Journées ARROW

Journées ARROW

21/05

Journées ARROW

Thesis Kickoff

2014 2013 2012

State of the art on control and trajectory generation of mechanical manipulators

Real-times experiments on Dual-V (trajectory generator, classical control, adaptive control, EDCAL, ARISE, …)

Contribution 1

Development of EDCAL

Experiments on VELOCE (L1 and

Extended L1)

State of the art on the L1 AC theory

State of the art on adaptive control

Development of ARISE

Development of L1 and

Extended L1

Simulations on the Dual-V (trajectory generator, classical control, adaptive control, EDCAL, ARISE, …)

Simulations on VELOCE

41



01/11

End 2015

2015 2014

Writing thesis manuscript

01/03

IROS’15

01/04

15 days intern at EPFL Lausanne

Contribution: Control of ARROW ?

Simulations & experiments on

ARROW

20/10

Today ECC’15

Journal paper 1 : on adaptive control of parallel manipulators

Journal paper 2 : a survey on control of PKMs

04/12

Journées ARROW

42



Journals

International Conferences ?? Ordre / Numéro [ ]

• ?? Bennehar M., Chemori A., Krut S. and Pierrot F., "Control of Redundantly Actuated PKMs for Closed-Shape Trajectories Tracking with Real-Time Experiments," in the International Journal “Transactions on Systems, Signals and Devices" (Issues on Systems, Analysis & Automatic Control). [Submitted]

• Bennehar M., Chemori A., Krut S. and Pierrot F., "Continuous Closed Form Trajectories Generation and Control of Redundantly Actuated Parallel Kinematic Manipulators," in Proc. IEEE International Multi-Conference on Systems, Signals & Devices (SSD'14), Barcelona, Spain, Feb. 2014.

• Bennehar M.; Chemori A.; Pierrot F., “A Novel RISE-Based Adaptive Feedforward Controller for Redundantly Actuated Parallel Manipulators,” IEEE/RSJ International Conference on Intelligent Robots and Systems ??(IROS’14), Sep. 2014.

• Bennehar M.; Chemori A.; Pierrot F., “A New Extension of Desired Compensation Adaptive Control and its Real-Time Application to Redundantly Actuated PKMs,” IEEE/RSJ International Conference on Intelligent Robots and Systems ??, Sep. 2014.

• Bennehar M.; Chemori A.; Pierrot F., “A Novel Application of L 1 Adaptive Control for PKMs: Design and Real-Time Experiments,” ?? S IEEE/RSJ International Conference on Robotics and Automation, May 2015. [Submitted]

• Bennehar M.; Chemori A.; Pierrot F., “Augmented Feedforward L 1 Adaptive Controller for PKMs with • Improved Tracking Performance,” ?? European Control Conference, Jul. 2015. [Submitted]

43



Academic Year 2013/2014

University of Montpellier 2

Science Faculty (FDS)

• 3rd year bachelor level:

Tutorials on Control of Linear

Systems.


Practicals on System Control.




64 h


Practicals on Control of Discrete

Systems.


Practicals on System Control.




• Extended Teaching Contract

44



English Courses [LIRMM, Montpellier]

20 hours

Predictive Control [EECI, Supelec, Paris]

21 hours

Nonlinear Systems [EECI, Supelec, Paris]

21 hours

Total: 62 hours

Refs biblio ??

Documents

Contributions à la commande adaptative non linéaire des ...chemori/Temp/Maxence/CST_2_Bennehar.pdf · Outline of the Presentation ?? Context and Problematic of the Thesis State