t for Two: Linear Synergy Advances the Evolution of

Directional Pointing Behaviour

Marieke Rohde & Ezequiel Di Paolo

Centre for Computational Neuroscience and Robotics

University of Sussex

Presentation Structure

• Background

– The Degrees of Freedom Problem

– Motor Synergies

• Experiments in Directional Pointing

– Inspiration

– Model

– Results

• Conclusion

1.) Bernstein, the Degrees of Freedom Problem and Motor Synergies

Picture from Bernstein (1967)

The Degrees of Freedom Problem

• Nicolas Bernstein (English:1967)

– Physiology of Activity

– Biomechanics

• The DoF Problem:

– “Cartesian Puppeteer”-view

– Countless number of motor units

– Simultaneous Control

7

26

2600

DoF

Picture from Turvey et. Al. (1982)

Motor Equivalence and Context-Conditioned Variability

• Motor Equivalence

– Redundancy through many degrees

of freedom

• Context-Conditioned Variability

– Anatomical (role of a muscle is

context dependent)

– Mechanical (commands are ignorant

against motion/non-muscular forces)

– Physiological (the spinal cord is not

just a relay station)

Picture from Turvey et. Al. (1982)

Picture from Kandel et. Al. (2000)

A = right hand; B = wrist immobilised; C = left hand; D = teeth; E = foot;

Bernstein’s Solution

Motor Synergies:

Systematic relationships between actuators (constraints)

– Can form functional motor units (e.g. wheel position in a car)

– Thereby reduce the degrees of freedom

• Skill Acquisition

– First freezing degrees of freedom

– Then freeing them and exploiting passive dynamics

Biological Evidence for Synergies

• Systematicities in

kinetics/kinematics:

– Different types of gaits, shooting,

breathing (Overview: Tuller et. Al.

1982)

– Linear relation between shoulder and

elbow torque (Gottlieb et. Al. 1999)

• Complex behaviour as

composition of synergies?

Synergy between elbow

and shoulder joint in a

skilled marksperson

Picture from Tuller et. Al. 1982

Problems with Motor Synergies

• Explaining the homunculus?

• Acquisition and maintenance of synergies

• Non-linearities when combining synergies

• “Motor coordination is not the goal but a means to achieve

the goal of an action” (Weiss and Jeannerod (1998))

2.) Experiments in Directional Pointing

Picture from Bernstein (1967)

Linear Synergies in Directional Pointing

• Gottlieb et. Al. 1997:

– Pointing in the sagittal plane

– Linear relation:

– Systematic variation of scaling

constant with pointing direction

– Linear synergies learned?

• Zaal et. Al. 1999:

– Linear Synergies are not learned, they

constrain learning

Hand trajectories Scaling constant

Pre-reaching period

Picture from Gottlieb et Al. 1997

Picture from Zaal et Al. 1999

Simulated Robot Arm• Controllers/Motors:

– “Garden CTRNNs” with two motor neurons

per degree of freedom (UC)

– “Split Brain CTRNNs” with separate

controllers for joints (SB)

– Linear Synergy networks with one motor

output and evolved scaling function (FS)

– 2 vs. 4 degrees of freedom

• Sensors:

– Proprioception (joint angle)

– Direction

Screenshot of the simulated arm

Different Controller Architectures

Evolutionary Robotics Experiments

• Scaling Function: Linear (FSa) or RBFN (FSb)

• Most severe simplifications:

– Hand of 4 degrees model does not deviate from plane

– No gravity

• Fitness: Position at endpoint

– Start with 2 points, go up to 6 (additional goal once mean fitness >0.4)

– The worse a trial, the more it weighs (exponential)

– For comparison: all at once.

Results: Performance Differences

• Forcing Linear Synergy:

– Quicker evolution

– Better performance

– Even with linear scaling function

– Unclear why (local fitness analysis)

• Redundant DoFs

– Better performance

• “Split brain” CTRNN:

– Negligible disadvantage

Results: Number of Degrees of Freedom

• Perturbations

– Not applying torques

– Blocking DoFs

• Redundant DoFs

– Much more sensitive to

blocking

– More passive dynamics (i.e.

forces mediated through

environment)

Results: Evolved Synergies

• Evolved Behaviour

– 3D uses different starting

position

• Evolution of Linear Synergy

– Not in normal CTRNNs

– Not in split brain CTRNNs

• Evolved RBFN

– Behavioural diversity through

displacement of peaks

3.) Conclusions

Picture from Bernstein (1967)

Conclusions: Evolutionary Robotics

• Constraining of the search space (i.e. Motor Synergies)

facilitates evolution

• Extension of the search space (i.e. more degrees of freedom)

facilitates evolution

• Reshaping the fitness landscape

• The presented results may be task dependent (no

generalisation)

• Inspiration from empirical research a good idea

Conclusions: Motor Synergies

• No definite conclusions about the role of motor synergies can

be drawn

• No synergies without neural basis, but passive dynamics

(prerequisite) played a role in evolved solution

• However, the findings comply with the findings by Zaal et Al.

(1999):

– Synergies are not learned

– Synergies aid a developmental process

Problems/Future Research

• Experiments with Gravity

• Experiments with deviation of hand from plane

• Analysis of evolved synergies

• Energetic constraints

• Experiments to evolve constraints for ontogenetic

development

Any questions?