ORF -MOSAIC M. Mahdi Ghazaei Ardakani*, Henrik Jrntell**, and Rolf - - PowerPoint PPT Presentation

▶
orf mosaic
SMART_READER_LITE
LIVE PREVIEW

ORF -MOSAIC M. Mahdi Ghazaei Ardakani*, Henrik Jrntell**, and Rolf - - PowerPoint PPT Presentation

Feb 27, 2024 231 likes •674 views

ORF -MOSAIC M. Mahdi Ghazaei Ardakani*, Henrik Jrntell**, and Rolf Johansson* * Dep. of Automatic Control and ** Exp. Medical Science Group Lund University, Sweden How it began! 2 LCCC Symposium, 2012-04-19 Mahdi Ghazaei 3 LCCC Symposium,

slide-1
SLIDE 1
  • M. Mahdi Ghazaei Ardakani*, Henrik Jörntell**, and Rolf Johansson*

* Dep. of Automatic Control and ** Exp. Medical Science Group Lund University, Sweden

ORF-MOSAIC

slide-2
SLIDE 2

How it began!

2 LCCC Symposium, 2012-04-19 Mahdi Ghazaei

slide-3
SLIDE 3

3 LCCC Symposium, 2012-04-19 Mahdi Ghazaei

slide-4
SLIDE 4

Outline

 Introduction

 Cerebellum  Different cerebellar models  MOSAIC

 Problem formulation  Modeling  Methods  Experimental Design  Simulations  Results  Discussion  Conclusions

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 4

slide-5
SLIDE 5

Cerebellum and its Role

[1 ] Modified from Neuroscie, 3rd Ed. [2] Courtesy of H.Jörntell

[1 ] [2] LCCC Symposium, 2012-04-19 Mahdi Ghazaei 5

slide-6
SLIDE 6

Microznoe circuitry

[1 ] Figure form Handbook of Robotics, Springer 2008,

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 6

slide-7
SLIDE 7

Principles in Cerebellum

 Feedforward processing  Divergence and convergence  Modularity  Plasticity

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 7

slide-8
SLIDE 8

Computational Models

 Cerebellar Model Articulation Controller (CMAC)  Adjustable Pattern Generator (APG)  Schweighofer-Arbib  Cerebellar feedback-error-learning model (CBFELM)  Multiple paired forward-inverse model (MPFIM)

[1] Figure adapted form Handbook of Robotics, Springer 2008

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 8

slide-9
SLIDE 9

MOSAIC Structure

 Internal Model

 Forward Models  Inverse Models

 Modularity  Adaptation  Reduction of motor error  Efference copy  Spin-offs

 HMM-MOSAIC  HMOSAIC  e-MOSAIC  MMRL  AMA-MOSAICI

[1] Figure from D.M. Wolpert and M. Kawato, Neural Net.,11:1325, 1998

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 9

slide-10
SLIDE 10

MOSAIC based Models

 Original MOSAIC

 Tested for switching between 3 objects, and generalizing to a new

  • ne

 No of modules are manually tuned  Requires careful tuning of parameters  The quality of forward models are critical

 HMM MOSAIC

 Same experiments as above  Probabilistic model using HMM  heavy computation  Fixed to linear forward models  Originally in batch mode  Improved parameter tuning and resp. estimation by EM

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 10

slide-11
SLIDE 11

MOSAIC based Model

HMOSAIC

Same experiments

Two layers of MOSAIC

Higher layer provides estimate of prior probabilities 

eMOSAIC

Humanoid robot control

LQG for controllers

Forward models replaced by Kalman filters

No adaptation

AMA-MOSAICI

Sit-to-stand control

Clustering algorithm for determining no of modules

Clustering and training Off-line 

MMRL

Controllers are replaced by RL agents

Discrete and continuous case

Self-organization of modules

Haunting task in a grid world and controlling an inverted pendulum

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 11

slide-12
SLIDE 12

MOSAIC based Model

 Toy problems  More serious problems

 Resorting to classic controllers or RL  Simplification

 No dealy  No adaptation

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 12

slide-13
SLIDE 13

Objectives

 Investigation of the

applicability of a biologically inspired model

  • f cerebellum to deal with:

 More complex

embodiments

 Less accurate models

(delays, noise, …)

[1] Figure from F.M.M.O. Camposa, J.M.F. Calado, Ann. Rev. In Control 33 (2009), 70

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 13

slide-14
SLIDE 14

Problem Statement

ORF-MOSAIC as a biologically inspired cerebellar model to adaptively control a human-like robotic arm with potential delays

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 14

slide-15
SLIDE 15

Methodology

 Models as faithful as possible to biology  Fixes according well-established theories in control

engineering

Choose models Simulation Fix assumptions Validation

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 15

slide-16
SLIDE 16

Modeling

 Motor Cortex (Trajectory Generation, …)  Cerebellum (MOSAIC )  Sensory System and Lower Motor Control  Arm  Muscle Systems

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 16

slide-17
SLIDE 17

Lower Motor Control

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 17

slide-18
SLIDE 18

Musculoskletal Model

 Preserves essential features of an arm  Mono-articular and bi-articular  Hill-type muscle model

[1] Figure from Handbook of brain theory, MIT press, 1995

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 18

slide-19
SLIDE 19

Assumptions

 Minimum jerk trajectory by CTX  Planning in task space, control in joint space and

transformation to muscle space

 Minimum tension principle for muscle control  Internal model

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 19

slide-20
SLIDE 20

Methods

 Linear models representing cellular structure  Low level control represented by a feedback controller

and a transformation

 Approximation to known adaptive controllers

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 20

slide-21
SLIDE 21

Customization of MOSAIC

 Introduction of receptive fields for modules  Dissociation of adaptation from control in a module  Why different modules?

 Taking care of different subtasks which are domains in state space

 Plasticity role?

 Adapt existing internal models to cope with small changes in plant  To acquire new skills but no retention

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 21

slide-22
SLIDE 22

Soft max 2

n

Cerebellar Controller

τff τcopy × Linear Forward Prediction

RF1

Σ

×

Likelihood Model

Linear Inverse Model λ 1 θd,θd,θd .. . θ,θ,θ .. . (θ,θ) .

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 22

slide-23
SLIDE 23

Model of Arm

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 23

slide-24
SLIDE 24

Minimum Tension Controller

 Convex optimization  With some mathematical tricks reformulated to a

quadratic programming problem

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 24

slide-25
SLIDE 25

Simulation of Arm

Constant muscle activation

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 25

slide-26
SLIDE 26

Simulation of Arm

Constant muscle activation

1 2 3 4 5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (s) Normalized Muscle Activation u1 u2 u3 u4 u5 u6 1 2 3 4 5

  • 1200
  • 1000
  • 800
  • 600
  • 400
  • 200

200 400 States vs. time Time (s) q1 q2 w1 w2

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 26

slide-27
SLIDE 27

Simulation of Arm

Minimum Tension

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 27

slide-28
SLIDE 28

Simulation of Arm

Minimum Tension

0.2 0.4 0.6 0.8 1

  • 0.2

0.2 0.4 0.6 0.8 1 Time (s) Normalized Muscle Activation u1 u2 u3 u4 u5 u6 0.2 0.4 0.6 0.8 1

  • 200
  • 150
  • 100
  • 50

50 100 150 States vs. time Time (s) q1 q2 w1 w2

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 28

slide-29
SLIDE 29

End-2-end Simulation

Inverse Kinematics

Muscles A(q)

Cerebellar Controller

Arm dynamics

Trajectory generator

C3/C4 Synergy Spinal Cord

X

θd,θd,θd

τsp u T τ +

Feedback Controller

feedback motor cmd

30 30 θ,θ,θ .. . θ,θ . θ,θ . .. . θd,θd .

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 29

slide-30
SLIDE 30

Final Experimental Design

 30 [ms] delay in the path to the cerebellar controller  PD controller with stiffness parameter of human arm and

no delay

 Movement 0.65 [s] , wait for 0.65 [s]  16 modules in a15x15 [cm] workspace  External translation invariant force field in task space  Object : 60 [cm] rod with 2 [Kg], perpendicular to the arm

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 30

slide-31
SLIDE 31

Mapping of modules to workspace

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 31

Numbering and color coding of modules Samples of receptive fields in static configuration

slide-32
SLIDE 32

Hand Trajectory

Before Training After Training

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 32

slide-33
SLIDE 33

Feedback & Feedforward contributions

Before Training After Training

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 33

slide-34
SLIDE 34

Contributions from modules

Before Training After Training

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 34

slide-35
SLIDE 35

Controlling Modules

Before Training After Training

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 35

slide-36
SLIDE 36

External Field Test

Before Training After Training

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 36

slide-37
SLIDE 37

Handling an Object

Before Training Adaptation After Training

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 37

slide-38
SLIDE 38

Parameters Across Modules

No object With an object

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 38

slide-39
SLIDE 39

Parameters Across Modules

w/ External Field

LCCC Symposium, 2012-04-19 Mahdi Ghazaei 39

slide-40
SLIDE 40

Different trajectory

40

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.36 0.38 0.4 0.42 0.44 0.46 0.48 x(m) y(m) 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.36 0.38 0.4 0.42 0.44 0.46 0.48 x(m) y(m)

LCCC Symposium, 2012-04-19 Mahdi Ghazaei

slide-41
SLIDE 41

Discussion

 Learning of non-linearities by the cerbellar controller  Specialization of modules with 7-parameters to different

areas of the force field

 Trade-offs

 Unit complexity vs. the number of modules  Unit adaptation vs. effective switching or combination

 How to localize the model in cerebellum and brain?

 Microzones and modules  Biologically plausible signals

41 LCCC Symposium, 2012-04-19 Mahdi Ghazaei

slide-42
SLIDE 42

Conclusion

 Cerebellar Model for Control Inspired by the Microzonal

Structure

 Arm Model with Musculo-skeletal structure  Adaptation to the changes in the load and external

disturbances despite delay

 Highly sparse representation with not full knowledge of

the model as a priority

 Model for distributed control and adaptation

42 LCCC Symposium, 2012-04-19 Mahdi Ghazaei

slide-43
SLIDE 43

Thank you!

Questions…?

43 LCCC Symposium, 2012-04-19 Mahdi Ghazaei