Contributions à la commande adaptative non linéaire des robots parallèles

Transcription

1 Commité de Suivi de Thèse (CST) Ecole Doctorale : Information, Structures et Systèmes Contributions à la commande adaptative non linéaire des robots parallèles Bennehar Moussab Doctorant en 2 ème année de thèse Cadre: Projet ANR ARROW Directeur de thèse : François Pierrot Encadrant : Ahmed Chemori?? Friday Oct. 3 rd, 2014

2 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

3 Parallel Manipulators Parallel VS Serial Issues and Challenges Context and Problematic of the Thesis

4 Parallel Manipulators Parallel VS Serial Applications Issues and Challenges Parallel Kinematic Manipulator (PKM) End-effector 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 Base Closed Kinematic Chains Extremely fast motion Accurate positioning High stiffness Base End-effector 1

5 Parallel Manipulators Parallel VS Serial Applications Issues and Challenges 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 2

6 Parallel Manipulators Parallel VS Serial Applications Issues and Challenges Space applications Haptic interfaces Medical applications Food packaging Machine tools Other applications 3

7 Dual-V Parallel Manipulators Parallel VS Serial Applications Issues and Challenges Main Control Difficulties:! Coupled/redundant actuation! High accelerations Highly nonlinear dynamics! High accelerations/stop points Mechanical vibrations! Uncertainties in model / environment! Payload Unknown / variable 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 4

8 Kinematic Control Fixed Model-based Control Adaptive Control Other Control State of the Art on Control of Mechanical Manipulators

9 Kinematic Control Fixed Model-based Control Adaptive Control Others Main Control Schemes for Mechanical Manipulators Kinematic Control PID Control [Ziegler and Nichols, 1942] Nonlinear PD Control [Han et al., 1994] Motion Coordination [Shang et al., 2010] Fixed Model-based Control 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] Adaptive Control (AC) 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] Others Vision Control [Paccot et al., 2008] Fuzzy Logic Control [Begon et al., 1995] Predictive Control [Vivas et al., 2003] 5

10 Kinematic Control Fixed Model-based Control Adaptive Control Others Main Control Schemes for Mechanical Manipulators 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 6

11 Kinematic Control Fixed Model-based Control Adaptive Control Others Main Control Schemes for Mechanical Manipulators Fixed Model-based Control 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 7

12 Kinematic Control Fixed Model-based Control Adaptive Control Others Main Control Schemes for Mechanical Manipulators Adaptive Control (AC) 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 8

13 Dynamics Parameterization Extended DCAL Adaptive RISE Shortcomings and Issues Adaptive Compensation of Parametric Uncertainties

14 Dynamics Extended DCAL Adaptive RISE Limitations Joint Space Inverse Dynamic Model Inertia Centrifugal + Coriolis + gravity Parametric Nonlinearities Very often addressed in research Easy to model CAD values are accurate Easily compensated by control Can be parameterized Parameterization friction General disturbances Nonparametric Nonlinearities Rarely reported in the literature Very complex to model Cannot be parameterized Usually not considered in modern control Regressor Vector of constant parameters 9

15 Dynamics Extended DCAL Adaptive RISE Limitations Background on Desired Compensation Adaptation Rule (DCAL) [Sadegh & Horowitz, 1990] Advantages of DCAL 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 10

16 Dynamics Extended DCAL Adaptive RISE Limitations Block Diagram of DCAL Adaptive Feedforward Trajectory Generator Linear PD Controller Stabilizing term Robot 11

17 Dynamics Extended DCAL Adaptive RISE Limitations DCAL Control Law PD Controller Adaptive Feedforward + + Stabilizing Term Poor performance with nonlinear (NL) systems Sensitive to disturbances Poor performance on high accelerations Limited tuning capabilities Proposed Solution Replace the linear gains in the feedback loop by NL ones Extended DCAL Controller NL PD Controller Adaptive Feedforward + + Stabilizing Term 12

18 Dynamics Extended DCAL Adaptive RISE Limitations Proposed Extended Desired Compensation Adaptation Rule (EDCAL) [Bennehar et al., 2014] Nonlinear gains functions [Shang et al., 2009] Nonlinear Linear Expected Improvements Better tracking performance Reduced control inputs More robustness toward uncertainties small errors = small gains large errors = large gains 13

19 Dynamics Extended DCAL Adaptive RISE Limitations 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 14

20 Dynamics Extended DCAL Adaptive RISE Limitations Application to the Dual-V Experienced Scenarios Scenario 2?? : Nominal Case Scenario 2?? : Payload Handling 15

21 Estimated Parameters Context State of the Art Parametric Nonparametric Thesis Progress Dynamics Extended DCAL Adaptive RISE Limitations Real-time Experimental Results Nominal Case Payload Handling???????? DCAL EDCAL DCAL EDCAL 16

22 Dynamics Extended DCAL Adaptive RISE Limitations 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 Remarks for upcoming work The feedback loop is essential in improving the performance of the system More sophisticated modern feedback strategies can be investigated IROS 14, Chicago, Sep. 2014?? Ref 17

23 Dynamics Extended DCAL Adaptive RISE Limitations 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 18

24 Dynamics Extended DCAL Adaptive RISE Limitations Overview of Some Successful Applications Two-link robot Direct-drive motor Synthetic Jet Actuators [Dupree e al. 2010] Hard Disk Drive [Patre et al. 2008] Spacecraft Coordination [MacKunis et al. 2013] Autonomous Underwater Vehicule [Taktak-Meziou et al. 2014] [Haibo et al. 2010] [Fischer et al. 2011] 19

25 Dynamics Extended DCAL Adaptive RISE Limitations Background on RISE for MIMO Systems Combined Tracking Errors Control Law 20

26 Dynamics Extended DCAL Adaptive RISE Limitations Some Remarks on RISE 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 Proposed Solution Augment RISE with Adaptive Feedforward Adaptive FF RISE Robot 21

27 Dynamics Extended DCAL Adaptive RISE Limitations Dynamics of the robot Regressor Vector of constant parameters Proposed Adaptive RISE Controller [Bennehar et al., 2014] Control Law After Projection Expected Enhancements Better tracking performance (parametric uncertainties partially compensated) Reduced control inputs (thanks to the dynamics-based feedforward) More robustness toward uncertainties (inherent to RISE) 22

28 Dynamics Extended DCAL Adaptive RISE Limitations 23

29 Tracking errors Context State of the Art Parametric Nonparametric Thesis Progress Dynamics Extended DCAL Adaptive RISE Limitations Experimental Results Nominal Case?? Payload Handling RISE Adaptive RISE RISE Adaptive RISE 24

30 Estimated Parameters Context State of the Art Parametric Nonparametric Thesis Progress Dynamics Extended DCAL Adaptive RISE Limitations Experimental Results Nominal Case?? Payload Handling 25

31 Dynamics Extended DCAL Adaptive RISE Limitations 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

32 Dynamics Extended DCAL Adaptive RISE Limitations 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 27

33 MRAC Limitations of MRAC L1 Adaptive Extended L1 Adaptive Adaptive Compensation of Nonparametric Uncertainties

34 MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Main limitations of Conventional Model-based Control A améliorer!!!!! Dynamic model should be available?? Proper initialization of the parameters Persistence excitation of the parameters Solution Model Reference Adaptive Control (MRAC) Principle of MRAC?? Inputs Reference Model Robot Adjustable Gains Adaptation Mechanism 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] 28

35 MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Joint Space Inverse Dynamic Model 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 Control Law Define error dynamics Lump all nonlinearities Stabilizing Term Adaptive Term Projection-based Filtered?? 29

36 MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Joint Space Inverse Dynamic Model Tracking Error Control Law Error Dynamics Stabilizing Term Adaptive Term Adaptation Laws Filter Estimated Parameters 30

37 MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks?? Trajectory Generator Combined Error Stabilizing Term Robot Adaptive Term State Predictor Adaptive Laws with Projection 31

38 Tracking errors Context State of the Art Parametric Nonparametric Thesis Progress MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Experimental Results: Application on Veloce L1 adaptive control (solid), PD (dashed) 32

39 Estimated Parameters Context State of the Art Parametric Nonparametric Thesis Progress MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Experimental Results: Application on Veloce 33

40 MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks L1 Adaptive Control No model needed Better performance than PD Decoupled Estimation & Robustness Parameters Boundedness Compensates all NLs Q: Can we improve the performance by including the available dynamic model? A: Definitely!!!! Q: How???? 34

41 MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Joint Space Inverse Dynamic Model L1 Adaptive Control Law Proposed Control Law Model-based Feedforward Stabilizing Term Adaptive Term Adaptation Laws Same as the L1 Adaptive Control 35

42 MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks?? Proposed Extended L1 Adaptive Controller Model-based Feedforward Trajectory Generator Combined Error Stabilizing Term Robot Adaptive Term State Predictor Adaptive Laws with Projection 36

43 Tracking Errors Context State of the Art Parametric Nonparametric Thesis Progress MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Experimental Results: Application on Veloce L1-AC (dashed), Extended L1-AC(dashed) 37

44 Estimated Parameters Context State of the Art Parametric Nonparametric Thesis Progress MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Experimental Results: Application on Veloce Extended L1-AC (left), L1-AC (right) 38

45 MRAC L1 Adaptive Extended L1 Adaptive Concluding Remarks Tackled Problems Trajectory tracking of PKMs Adaptive compensation of all uncertainties in the system Guarantee fast adaptation without hurting robustness?? Conclusions as previously presented Include dynamics in the control loop to improve performance Difficulties Inherent high nonlinearities Parameters uncertainties/variations Guarantee fast adaptation without hurting robustness?? Pourquoi la photo Proposed Solution Extended L1 Adaptive Controller with Feedforward 39

46 Schedule Publications Teaching Doctoral Courses Progress of the Thesis?? and Future Work

47 Schedule Publications Teaching Doctoral Courses /10 22/03 30/06 16/09 15/10 14/11 06/02 19/04 21/05 02/10 Thesis Kickoff IROS 13 Journées ICRA 14 SSD 14 Journées IROS 14 TSSD Journées ICRA 15 ARROW ARROW ARROW Today State of the art on control and trajectory generation of mechanical manipulators State of the art on adaptive control State of the art on the L1 AC theory Contribution 1 Development of EDCAL Development of ARISE Real-times experiments on Dual-V (trajectory generator, classical control, adaptive control, EDCAL, ARISE, ) Development of L1 and Extended L1 Experiments on VELOCE (L1 and Extended L1) Simulations on the Dual-V (trajectory generator, classical control, adaptive control, EDCAL, ARISE, ) Simulations on VELOCE 40

48 Schedule Publications Teaching Doctoral Courses Today 20/10 ECC /11 04/12 Journées ARROW /03 IROS 15 01/04 End days intern at EPFL Lausanne Simulations & experiments on ARROW Journal paper 1 : on adaptive control of parallel manipulators Contribution: Control of ARROW? Writing thesis manuscript Journal paper 2 : a survey on control of PKMs 41

49 Journals Schedule Publications Teaching Doctoral Courses?? 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] International Conferences?? Ordre / Numéro [ ] 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 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 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 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 [Submitted] Bennehar M.; Chemori A.; Pierrot F., Augmented Feedforward L 1 Adaptive Controller for PKMs with Improved Tracking Performance,?? European Control Conference, Jul [Submitted] 42

50 Schedule Publications Teaching Doctoral Courses Academic Year 2012/2013 Academic Year 2013/2014 Academic Year 2014/2015 University of Montpellier 2 Science Faculty (FDS) University of Montpellier 2 Science Faculty (FDS) University of Montpellier 2 Science Faculty (FDS) 64 h 3rd year bachelor level: 3rd year bachelor level: Extended Teaching Contract Practicals on Control of Discrete Systems. Tutorials on Control of Linear Systems. 3rd year bachelor level: 3rd year bachelor level: Practicals on System Control. Practicals on System Control. 43

51 Schedule Publications Teaching Doctoral Courses English Courses [LIRMM, Montpellier] 20 hours Predictive Control [EECI, Supelec, Paris] 21 hours Nonlinear Systems [EECI, Supelec, Paris] 21 hours Refs biblio?? Total: 62 hours 44