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
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))
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
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